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- Oscillation (23)
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- Fixed point theorem (18)
- Bi-univalent functions (16)
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- Fractional derivative (10)
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- Spectrum (10)
- Green's function (9)
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Articles 1261 - 1290 of 2494
Full-Text Articles in Physical Sciences and Mathematics
On Focal Curves Of Null Cartan Curves, Hakan Şi̇mşek
On Focal Curves Of Null Cartan Curves, Hakan Şi̇mşek
Turkish Journal of Mathematics
The focal curve, which is determined as the locus of centers of osculatingpseudo-spheres of a null Cartan curve, is investigated in Minkowski(n+2)-space $\mathcal{M}^{n+2}.$ Moreover, a curve called \textit{accelerationfocal curve }of a null Cartan curve is introduced by using a new family of functions.
Extension Of The Darboux Frame Into Euclidean 4-Space And Its Invariants, Mustafa Düldül, Bahar Uyar Düldül, Nuri̇ Kuruoğlu, Ertuğrul Özdamar
Extension Of The Darboux Frame Into Euclidean 4-Space And Its Invariants, Mustafa Düldül, Bahar Uyar Düldül, Nuri̇ Kuruoğlu, Ertuğrul Özdamar
Turkish Journal of Mathematics
In this paper, by considering a Frenet curve lying on an oriented hypersurface, we extend the Darboux frame field into Euclidean 4-space $\mathbb{E}^4$. Depending on the linear independency of the curvature vector with the hypersurface's normal, we obtain two cases for this extension. For each case, we obtain some geometrical meanings of new invariants along the curve on the hypersurface. We also give the relationships between the Frenet frame curvatures and Darboux frame curvatures in $\mathbb{E}^4$. Finally, we compute the expressions of the new invariants of a Frenet curve lying on an implicit hypersurface.
A Note On Dynamics In Functional Spaces, Liangxue Peng, Chong Yang
A Note On Dynamics In Functional Spaces, Liangxue Peng, Chong Yang
Turkish Journal of Mathematics
In this note, we study topologically transitive and hypercyclic composition operators on $C_p(X)$ or $C_k(X)$. We prove that if $G$ is a semigroup of continuous self maps of a countable metric space $X$ with the following properties: (1) every element of $G$ is one-to-one on $X$, (2) the action of $G$ is strongly run-away on $X$, then the action of $\hat{G}$ on $C_p(X)$ is topologically transitive and hypercyclic. If $G$ is the set of all one-to-one and continuous self maps of $\mathbb{R}\setminus \mathbb{Z}$, then the action of $\hat{G}$ on $C_k(\mathbb{R}\setminus \mathbb{Z})$ is hypercyclic. We also show that the action of …
On The Volume Of The Indicatrix Of A Complex Finsler Space, Elena Popovici
On The Volume Of The Indicatrix Of A Complex Finsler Space, Elena Popovici
Turkish Journal of Mathematics
Following the study on volume of indicatrices in a real Finsler space, in this paper we are investigating some volume properties of the indicatrix considered in an arbitrary fixed point of a complex Finsler manifold. Since for each point of a complex Finsler space the indicatrix is an embedded CR-hypersurface of the punctured holomorphic tangent bundle, by means of its normal vector, the volume element of the indicatrix is determined. Thus, the volume function is pointed out and its variation is studied. Conditions under which the volume is constant are also determined and some classes of complex Finsler spaces with …
Graph-Directed Fractal Interpolation Functions, Ali̇ Deni̇z, Yunus Özdemi̇r
Graph-Directed Fractal Interpolation Functions, Ali̇ Deni̇z, Yunus Özdemi̇r
Turkish Journal of Mathematics
It is known that there exists a function interpolating a given data set such that the graph of the function is the attractor of an iterated function system, which is called a fractal interpolation function. We generalize the notion of the fractal interpolation function to the graph-directed case and prove that for a finite number of data sets there exist interpolation functions each of which interpolates a corresponding data set in $\mathbb{R}^2$ such that the graphs of the interpolation functions are attractors of a graph-directed iterated function system.
Optimality Conditions Via Weak Subdifferentials In Reflexive Banach Spaces, Sara Hassani, Musa Mammadov, Mina Jamshidi
Optimality Conditions Via Weak Subdifferentials In Reflexive Banach Spaces, Sara Hassani, Musa Mammadov, Mina Jamshidi
Turkish Journal of Mathematics
In this paper the relation between the weak subdifferentials and the directional derivatives, as well as optimality conditions for nonconvex optimization problems in reflexive Banach spaces, are investigated. It partly generalizes several related results obtained for finite dimensional spaces.
Some Fixed Point Theorems For Single Valued Strongly Contractive Mappings In Partially Ordered Ultrametric And Non-Archimedean Normed Spaces, Hamid Mamghaderi, Hashem Parvaneh Masiha, Meraj Hosseini
Some Fixed Point Theorems For Single Valued Strongly Contractive Mappings In Partially Ordered Ultrametric And Non-Archimedean Normed Spaces, Hamid Mamghaderi, Hashem Parvaneh Masiha, Meraj Hosseini
Turkish Journal of Mathematics
Let $ (X,d,\preceq) $ be a partially ordered ultrametric space and $ f:X\to X $ a single valued mapping. We obtain sufficient conditions for the existence of a fixed point for the strongly contractive mapping $ f $. We also investigate the existence of a fixed point for strongly contractive mappings defined on partially ordered non-Archimedean normed spaces under the same conditions. Finally, we give some examples to discuss the assumptions of the theorems.
Extensions Of Quasipolar Rings, Orhan Gürgün
Extensions Of Quasipolar Rings, Orhan Gürgün
Turkish Journal of Mathematics
An associative ring with identity is called quasipolar provided that for each $a\in R$ there exists an idempotent $p\in R$ such that $p\in comm^2(a)$, $a+p\in U(R)$ and $ap\in R^{qnil}$. In this article, we introduce the notion of quasipolar general rings (with or without identity). Some properties of quasipolar general rings are investigated. We prove that a general ring $I$ is quasipolar if and only if every element $a\in I$ can be written in the form $a=s+q$ where $s$ is strongly regular, $s\in comm^2(a)$, $q$ is quasinilpotent, and $sq=qs=0$. It is shown that every ideal of a quasipolar general ring is …
Correcting A Paper On The Randic And Geometric-Arithmetic Indices, Toufik Mansour, Mohammad Ali Rostami, Suresh Elumalai, Britto Antony Xavier
Correcting A Paper On The Randic And Geometric-Arithmetic Indices, Toufik Mansour, Mohammad Ali Rostami, Suresh Elumalai, Britto Antony Xavier
Turkish Journal of Mathematics
The Randic index $(R)$ and the geometric--arithmetic index $(GA)$ are found to be useful tools in QSPR and QSAR studies. In the Journal of Inequalities and Applications 180, 1-7, Lokesha, Shwetha Shetty, Ranjini, Cangul, and Cevik gave "New bounds for Randic and GA indices." In the paper, we first point out that Theorems 1, 2, and 4 are incorrect and in this short note we present the correct inequalities for Randic and GA indices. In the same paper, we provide the equality cases for Theorems 3, 5, and 6.
More Characterizations Of Dedekind Domains And V-Rings, Thuat Van Do, Hai Dinh Hoang, Samruam Baupradist
More Characterizations Of Dedekind Domains And V-Rings, Thuat Van Do, Hai Dinh Hoang, Samruam Baupradist
Turkish Journal of Mathematics
In this paper, cyclic $c-$injective modules are introduced and investigated. It is shown that a commutative Noetherian domain is Dedekind if and only if every simple module is cyclic $c-$injective. Finally, it is shown that injectivity, principal injectivity, mininjectivity, and simple injectivity are all equal to characterize right V-rings, right GV-rings, right pV-rings, and WV-rings.
Maximal Subsemigroups And Finiteness Conditions On Transformation Semigroups With Fixed Sets, Yanisa Chaiya, Preeyanuch Honyam, Jintana Sanwong
Maximal Subsemigroups And Finiteness Conditions On Transformation Semigroups With Fixed Sets, Yanisa Chaiya, Preeyanuch Honyam, Jintana Sanwong
Turkish Journal of Mathematics
Let $Y$ be a fixed subset of a nonempty set $X$ and let $Fix(X,Y)$ be the set of all self maps on $X$ which fix all elements in $Y$. Then under the composition of maps, $Fix(X,Y)$ is a regular monoid. In this paper, we prove that there are only three types of maximal subsemigroups of $Fix\left(X,Y\right)$ and these maximal subsemigroups coincide with the maximal regular subsemigroups when $X\setminus Y$ is a finite set with $ X\setminus Y \geq 2$. We also give necessary and sufficient conditions for $Fix(X,Y)$ to be factorizable, unit-regular, and directly finite.
Dynamic Shum Inequalities, Ravi Agarwal, Martin Bohner, Donal O'Regan, Samir Saker
Dynamic Shum Inequalities, Ravi Agarwal, Martin Bohner, Donal O'Regan, Samir Saker
Turkish Journal of Mathematics
Recently, various forms and improvements of Opial dynamic inequalities have been given in the literature. In this paper, we give refinements of Opial inequalities on time scales that reduce in the continuous case to classical inequalities named after Beesack and Shum. These refinements are new in the important discrete case.
Sampling Theorem By Green's Function In A Space Ofvector-Functions, Hassan Atef Hassan
Sampling Theorem By Green's Function In A Space Ofvector-Functions, Hassan Atef Hassan
Turkish Journal of Mathematics
In this paper we give a sampling expansion for integral transforms whose kernels arise from Green's function of differential operators in a space of vector-functions. The differential operators are in a space of dimension $m$ and consist of systems of $m$ equations in $m$ unknowns. We assume the simplicity of the eigenvalues.
Quasi-Metric Trees And $Q$-Hyperconvex Hulls, Zechariah Mushaandja, Olivier Olela Otafudu
Quasi-Metric Trees And $Q$-Hyperconvex Hulls, Zechariah Mushaandja, Olivier Olela Otafudu
Turkish Journal of Mathematics
The investigation of metric trees began with J. Tits in 1977. Recently we studied a more general notion of quasi-metric tree. In the current article we prove, among other facts, that the $q$-hyperconvex hull of a $q$-hyperconvex $T_0$-quasi-metric tree is itself a $T_0$-quasi-metric tree. This is achieved without using the four-point property, a geometric concept used by Aksoy and Maurizi to show that every complete metric tree is hyperconvex.
On A Family Of Saturated Numerical Semigroups With Multiplicity Four, Meral Süer, Sedat İlhan
On A Family Of Saturated Numerical Semigroups With Multiplicity Four, Meral Süer, Sedat İlhan
Turkish Journal of Mathematics
In this study, we will give some results on Arf numerical semigroups of multiplicity four generated by $\left\{ 4,k,k+1,k+2\right\} $ where $k$ is an integer not less than $5$ and $k\equiv 1(\mbox{mod } 4)$.
$\Mathcal{W}$-Gorenstein Objects In Triangulated Categories, Chaoling Huang, Kaituo Liu
$\Mathcal{W}$-Gorenstein Objects In Triangulated Categories, Chaoling Huang, Kaituo Liu
Turkish Journal of Mathematics
We fix a proper class of triangles $\xi$ in a triangulated category $\mathcal{C}$. Let $\mathcal{W}$ be a class of objects in $\mathcal{C}$ such that $\xi xt^i_\xi(W,\ W')=0$ for all $W, W'\in\mathcal{W}$ and all $i\geq 1$. In this paper, we introduce the notion of $\mathcal{W}$-Gorenstein objects and $\mathcal{G}(\mathcal{W})$-(co)resolution dimensions of any object in $\mathcal{C}$ and study the properties of $\mathcal{W}$-Gorenstein objects and characterize the finite $\mathcal{G}(\mathcal{W})$-(co)resolution dimensions of any object. Some applications are given.
A Mehrotra Predictor-Corrector Interior-Point Algorithm For Semidefinite Optimization, Mohammad Pirhaji, Maryam Zangiabadi, Hossein Mansouri
A Mehrotra Predictor-Corrector Interior-Point Algorithm For Semidefinite Optimization, Mohammad Pirhaji, Maryam Zangiabadi, Hossein Mansouri
Turkish Journal of Mathematics
This paper proposes a second-order Mehrotra-type predictor-corrector feasible interior-point algorithm for semidefinite optimization problems. In each iteration, the algorithm computes the Newton search directions through a new form of combination of the predictor and corrector directions. Using the Ai-Zhang wide neighborhood for linear complementarity problems, it is shown that the complexity bound of the algorithm is $O(\sqrt{n}\log \varepsilon^{-1})$ for the Nesterov-Todd search direction and $O({n}\log \varepsilon^{-1})$ for the Helmberg-Kojima-Monteiro search directions.
Dirac Systems With Regular And Singular Transmission Effects, Eki̇n Uğurlu
Dirac Systems With Regular And Singular Transmission Effects, Eki̇n Uğurlu
Turkish Journal of Mathematics
In this paper, we investigate the spectral properties of singular eigenparameter dependent dissipative problems in Weyl's limit-circle case with finite transmission conditions. In particular, these transmission conditions are assumed to be regular and singular. To analyze these problems we construct suitable Hilbert spaces with special inner products and linear operators associated with these problems. Using the equivalence of the Lax-Phillips scattering function and Sz-Nagy-Foiaş characteristic functions we prove that all root vectors of these dissipative operators are complete in Hilbert spaces.
On The Equivalence Of Alexandrov Curvature And Busemann Curvature, Shijie Gu
On The Equivalence Of Alexandrov Curvature And Busemann Curvature, Shijie Gu
Turkish Journal of Mathematics
It is shown that the curvature bounded above (resp. below) in the sense of Alexandrov is equivalent to the curvature bounded above (resp. below) in the sense of Busemann if and only if the sum of adjacent average angles is at least (resp. at most) $\pi$.
Exponent Of Local Ring Extensions Of Galois Rings And Digraphs Of The $K$Th Power Mapping, Ittiwat Tocharoenirattisai, Yotsanan Meemark
Exponent Of Local Ring Extensions Of Galois Rings And Digraphs Of The $K$Th Power Mapping, Ittiwat Tocharoenirattisai, Yotsanan Meemark
Turkish Journal of Mathematics
In this paper, we consider a local extension $R$ of the Galois ring of the form $GR(p^{n},d)[x]/(f(x)^{a})$, where $n,d$, and $a$ are positive integers; $p$ is a prime; and $f(x)$ is a monic polynomial in $GR(p^{n},d)[x]$ of degree $r$ such that the reduction $\overline{f}(x)$ in $\mathbb{F}_{p^{d}}[x]$ is irreducible. We establish the exponent of $R$ without complete determination of its unit group structure. We obtain better analysis of the iteration graphs $G^{(k)}(R)$ induced from the $k$th power mapping including the conditions on symmetric digraphs. In addition, we work on the digraph over a finite chain ring $R$. The structure of $G^{(k)}_{2}(R)$ …
Existence Of Unpredictable Solutions And Chaos, Marat Akhmet, Mehmet Onur Fen
Existence Of Unpredictable Solutions And Chaos, Marat Akhmet, Mehmet Onur Fen
Turkish Journal of Mathematics
Recently we introduced the concept of Poincaré chaos. In the present paper, by means of the Bebutov dynamical system, an unpredictable solution is considered as a generator of the chaos in a quasilinear system. The results can be easily extended to different types of differential equations. An example of an unpredictable function is provided. A proper irregular behavior in coupled Duffing equations is observed through simulations.
Koebe Sets For The Class Of Functions Convex In Two Directions, Leopold Koczan, Pawel Zaprawa
Koebe Sets For The Class Of Functions Convex In Two Directions, Leopold Koczan, Pawel Zaprawa
Turkish Journal of Mathematics
In this paper, we consider a class $K_\alpha$ of all functions $f$ univalent in the unit disk $\Delta$ that are normalized by $f(0)=f'(0)-1=0$ while the sets $f(\Delta)$ are convex in two symmetric directions: $e^{i\alpha\pi/2}$ and $e^{-i\alpha\pi/2}$, $\alpha\in[0,1]$. It means that the intersection of $f(\Delta)$ with each straight line having the direction $e^{i\alpha\pi/2}$ or $e^{-i\alpha\pi/2}$ is either a compact set or an empty set. We find the Koebe set for $K_\alpha$. Moreover, we perform the same operation for functions in $K_{\beta, \gamma}$, i.e. for functions that are convex in two fixed directions: $e^{i\beta\pi/2}$ and $e^{i\gamma\pi/2}$, $-1\leq \beta\leq\gamma \leq 1$.
On The Zariski Topology Over An $L$-Module $M$, Fethi̇ Çallialp, Gülşen Ulucak, Ünsal Teki̇r
On The Zariski Topology Over An $L$-Module $M$, Fethi̇ Çallialp, Gülşen Ulucak, Ünsal Teki̇r
Turkish Journal of Mathematics
Let $L$ be a multiplicative lattice and $M$ be an $L$-module. In this study, we present a topology said to be the Zariski topology over $\sigma (M),$ the collection of all prime elements of an $L$-module $M.$ We research some results on the Zariski topology over $\sigma (M).$ We show that the topology is a $T_{0}$-space and a $T_{1}$-space under some conditions. Some properties and results are studied for the topology over $\sigma (L)$, the collection of all prime elements of a multiplicative lattice $L.$
Some Results On The $\Mathcal{P}_{V,2n}$, $\Mathcal{K}_{V,N}$, And $\Mathcal{H}_{V,N}$-Integral Transforms, Ayşe Neşe Dernek, Fati̇h Aylikci
Some Results On The $\Mathcal{P}_{V,2n}$, $\Mathcal{K}_{V,N}$, And $\Mathcal{H}_{V,N}$-Integral Transforms, Ayşe Neşe Dernek, Fati̇h Aylikci
Turkish Journal of Mathematics
In this paper, the authors consider the $\mathcal{P}_{v,2n}$-transform, the $\mathcal{G}_n$-transform, and the $\mathcal{K}_{v,n}$-transform as generalizations of the Widder potential transform, the Glasser transform, and the $\mathcal{K}_v$-transform, respectively. Many identities involving these transforms are given. A number of new Parseval-Goldstein type identities are obtained for these and many other well-known integral transforms. Some useful corollaries for evaluating infinite integrals of special functions are presented. Illustrative examples are given for the results.
Positive Solutions Of First Order Boundary Value Problems With Nonlinear Nonlocal Boundary Conditions, Smita Pati, Seshadev Padhi
Positive Solutions Of First Order Boundary Value Problems With Nonlinear Nonlocal Boundary Conditions, Smita Pati, Seshadev Padhi
Turkish Journal of Mathematics
We consider the existence of positive solutions of the nonlinear first order problem with a nonlinear nonlocal boundary condition given by $x^{\prime}(t) = r(t)x(t) + \sum_{i=1}^{m} f_i(t,x(t)), t \in [0,1]$ $\lambda x(0) = x(1) + \sum_{j=1}^{n} \Lambda_j(\tau_j, x(\tau_j)),\tau_j \in [0,1],$ where $r:[0,1] \rightarrow [0,\infty)$ is continuous, the nonlocal points satisfy $0 \leq \tau_1 < \tau_2 < ... < \tau_n \leq 1$, the nonlinear functions $f_i$ and $\Lambda_j$ are continuous mappings from $[0,1] \times [0,\infty) \rightarrow [0,\infty)$ for $i = 1,2,...,m$ and $j = 1,2,...,n$ respectively, and $\lambda >1$ is a positive parameter. The Leray-Schauder theorem and Leggett--Williams fixed point theorem were used to prove our results.
On Certain Gbs-Durrmeyer Operators Based On $Q$-Integers, Dan Barbosu, Ana Maria Acu, Carmen Violeta Muraru
On Certain Gbs-Durrmeyer Operators Based On $Q$-Integers, Dan Barbosu, Ana Maria Acu, Carmen Violeta Muraru
Turkish Journal of Mathematics
In the present paper we introduce the $GBS$ (Generalized Boolean Sum) operators of Durrmeyer type based on $q$-integers and the approximation of B-continuous functions using the above operators is studied. In addition, a uniform convergence theorem is established and the degree of approximation in terms of mixed modulus of continuity is evaluated. The study contains in the last section numerical considerations regarding the constructed operators based on MATLAB algorithms.
Value Distribution And Normality Of Meromorphic Functions Involving Partial Sharing Of Small Functions, Kuldeep Singh Charak, Shittal Sharma
Value Distribution And Normality Of Meromorphic Functions Involving Partial Sharing Of Small Functions, Kuldeep Singh Charak, Shittal Sharma
Turkish Journal of Mathematics
In this paper, we generalize a value distribution result and use it to prove a normality criterion using partial sharing of small functions. Further in the sequel, various known normality criteria are improved and generalized on the domain $D:=\{z: z \lt R, 0\lt R\leq\infty \}$.
Existence And Global Attractivity Of Periodic Solutions In A Max-Type System Of Difference Equations, Imane Dekkar, Nouressadat Touafek
Existence And Global Attractivity Of Periodic Solutions In A Max-Type System Of Difference Equations, Imane Dekkar, Nouressadat Touafek
Turkish Journal of Mathematics
We consider in this paper the following system of difference equations with maximum $$ \left\{ \begin{array}{lll} x(n+1)= & \max\{f_1(n,x(n)),g_1(n,y(n))\}& \\ & &, ~~ n=0,1,2, \ldots, \\ y(n+1)= & \max\{f_2(n,x(n)),g_2(n,y(n))\} & \\ \end{array} \right.$$ where $f_i, g_i$, $i=1,2$, are real-valued functions with periodic coefficients. We use the Banach fixed point theorem to get a sufficient condition under which this system admits a unique periodic solution. Moreover, we show that this periodic solution attracts all the solutions of the current system. Some examples are also given to illustrate our results.
An Age-Structured Model For The Transmission Dynamics Of Hepatitis B: Asymptotic Analysis, Rodrigue Yves M'Pika Makoussou, Aboubakari Traore
An Age-Structured Model For The Transmission Dynamics Of Hepatitis B: Asymptotic Analysis, Rodrigue Yves M'Pika Makoussou, Aboubakari Traore
Turkish Journal of Mathematics
In this paper, we consider the age-structured model for the transmission dynamics of Hepatitis B virus (HBV) proposed earlier in the article by Zou et al.: An age-structured model for transmission dynamics of hepatitis B. SIAM J Appl Math 2010; 70: 3121-3139, where a slight modification is made. We consider that the HBV infection processes act on a time scale different from that of the vital processes. Such a model becomes a multiple time scale model and thus it often can be significantly simplified by various asymptotic methods. We apply, as in the paper of Banasiak and M'pika Massoukou: A …
On Certain Semigroups Of Full Contraction Maps Of A Finite Chain, Goje Uba Garba, Muhammad Jamilu Ibrahim, Abdussamad Tanko Imam
On Certain Semigroups Of Full Contraction Maps Of A Finite Chain, Goje Uba Garba, Muhammad Jamilu Ibrahim, Abdussamad Tanko Imam
Turkish Journal of Mathematics
Let $X_{n}=\{1,2,\ldots,n\}$ with its natural order and let ${\cal T}_{n}$ be the full transformation semigroup on $X_{n}$. A map $\alpha\in{\cal T}_{n}$ is said to be order-preserving if, for all $x,y\in X_{n}$, $x\leq y\Rightarrow x\alpha\leq y\alpha$. The map $\alpha\in{\cal T}_{n}$ is said to be a contraction if, for all $x,y\in X_{n}$, $ x\alpha-y\alpha \leq x-y $. Let ${\cal CT}_{n}$ and ${\cal OCT}_{n}$ denote, respectively, subsemigroups of all contraction maps and all order-preserving contraction maps in ${\cal T}_{n}$. In this paper we present characterisations of Green's relations on ${\cal CT}_{n}$ and starred Green's relations on both ${\cal CT}_{n}$ and ${\cal OCT}_{n}$.