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Articles 1201 - 1230 of 2494
Full-Text Articles in Physical Sciences and Mathematics
Approximation By Chlodowsky Type Of Szasz Operators Based On Boas--Buck-Type Polynomials, Mohammad Mursaleen, A.A.H. Al-Abied, Ana Maria Acu
Approximation By Chlodowsky Type Of Szasz Operators Based On Boas--Buck-Type Polynomials, Mohammad Mursaleen, A.A.H. Al-Abied, Ana Maria Acu
Turkish Journal of Mathematics
A Chlodowsky variant of generalized Szasz-type operators involving Boas-Buck-type polynomials is considered and some convergence properties of these operators by using a weighted Korovkin-type theorem are given. A Voronoskaja-type theorem is proved. The convergence properties of these operators in a weighted space of functions defined on $[0,\infty)$ are studied. The theoretical results are exemplified choosing the special cases of Boas-Buck polynomials, namely Appell-type polynomials, Laguerre polynomials, and Charlier polynomials.
Three Binomial Sums Weighted By Falling And Rising Factorials, Emrah Kiliç
Three Binomial Sums Weighted By Falling And Rising Factorials, Emrah Kiliç
Turkish Journal of Mathematics
In this paper, we will investigate and evaluate, in closed forms, three binomial sums weighted by falling and rising factorials. We first use the relationships between the rising, falling factorials and the binomial coefficients. Then we rewrite the claimed identities in terms of generalized hypergeometric functions to prove the claimed results.
Dynamic Optimal Contract Under Parameter Uncertainty With Risk-Averse Agent And Principal, Kerem Uğurlu
Dynamic Optimal Contract Under Parameter Uncertainty With Risk-Averse Agent And Principal, Kerem Uğurlu
Turkish Journal of Mathematics
We consider a continuous-time principal--agent model on a finite time horizon, where we look for the existence of an optimal contract that both parties agreed on. Contrary to the mainstream, where the principal is modeled as risk-neutral, we assume that both the principal and the agent have exponential utility and are risk-averse with same risk awareness level. Moreover, the agent's quality is unknown and is modeled as a filtering term in the problem, which is revealed as time passes. The principal cannot observe the agent's real action, but can only recommend action levels to the agent. Hence, we have a …
An Expansion Theorem For $Q$-Sturm-Liouville Operators On The Wholeline, Bi̇lender Paşaoğlu Allahverdi̇ev, Hüseyi̇n Tuna
An Expansion Theorem For $Q$-Sturm-Liouville Operators On The Wholeline, Bi̇lender Paşaoğlu Allahverdi̇ev, Hüseyi̇n Tuna
Turkish Journal of Mathematics
In this work, we establish a Parseval equality and an expansion formula in eigenfunctions for a singular $q-$Sturm-Liouville operator on the whole line.
More On Sequential Order Of Compact Scattered Spaces, Alan Dow, Seçi̇l Tokgöz
More On Sequential Order Of Compact Scattered Spaces, Alan Dow, Seçi̇l Tokgöz
Turkish Journal of Mathematics
The proper forcing axiom is shown to imply that a compact scattered sequential space with scattering height at most $\omega_1$ must have sequential order at most $\omega$.
Conformable Fractional Sturm-Liouville Equation And Some Existenceresults On Time Scales, Tüba Gülşen, Emrah Yilmaz, Hi̇kmet Kemaloğlu
Conformable Fractional Sturm-Liouville Equation And Some Existenceresults On Time Scales, Tüba Gülşen, Emrah Yilmaz, Hi̇kmet Kemaloğlu
Turkish Journal of Mathematics
In this study, we analyze a conformable fractional (CF) Sturm-Liouville (SL) equation with boundary conditions on an arbitrary time scale $\mathbb{T}$. Then we extend the basic spectral properties of the classical SL equation to the CF case. Finally, some sufficient conditions are established to guarantee the existence of a solution for this CF-SL problem on $\mathbb{T}$ by using certain fixed point theorems. For explaining these existence theorems, we give an example with appropriate choices.
A Study Of The Tubular Surfaces Constructed By Thespherical Indicatrices In Euclidean $3-$Space, Fatma Ateş, Erdem Kocakuşakli, İsmai̇l Gök, Yusuf Yayli
A Study Of The Tubular Surfaces Constructed By Thespherical Indicatrices In Euclidean $3-$Space, Fatma Ateş, Erdem Kocakuşakli, İsmai̇l Gök, Yusuf Yayli
Turkish Journal of Mathematics
A basic goal of this paper is to investigate the tubular surface constructed by the spherical indicatrices of any spatial curve in the Euclidean $3-$ space. This kind of tubular surface is designed for the alternative moving frame $\{N,C,W\}$ in conjunction with finding a relationship between the tubular surfaces and their special curves, such as geodesic curves, asymptotic curves, and minimal curves. The minimal curve $\gamma $ on a surface is defined by the property that its fundamental coefficients satisfy Eq. (3.7) along the curve $\gamma $. At the end of this article, we exemplify these curves on the tubular …
On The Coefficient Problem For Close-To-Convex Functions, Katarzyna Trabka Wieclaw, Pawel Zaprawa
On The Coefficient Problem For Close-To-Convex Functions, Katarzyna Trabka Wieclaw, Pawel Zaprawa
Turkish Journal of Mathematics
This paper is concerned with the problem of estimating $ a_4-a_2a_3 $, where $a_k$ are the coefficients of a given close-to-convex function. The bounds of this expression for various classes of analytic functions have been applied to estimate the third Hankel determinant $H_3(1)$. The results for two subclasses of the class $\mathcal{C}$ of all close-to-convex functions are sharp. This bound is equal to 2. It is conjectured that this number is also the exact bound of $ a_4-a_2a_3 $ for the whole class $\mathcal{C}$.
Integral Laminations On Nonorientable Surfaces, S. Öykü Yurttaş, Mehmetci̇k Pamuk
Integral Laminations On Nonorientable Surfaces, S. Öykü Yurttaş, Mehmetci̇k Pamuk
Turkish Journal of Mathematics
We describe triangle coordinates for integral laminations on a nonorientable surface $N_{k,n}$ of genus $k$ with $n$ punctures and one boundary component, and we give an explicit bijection from the set of integral laminations on $N_{k,n}$ to $(\mathbb{Z}^{2(n+k-2)}\times \mathbb{Z}^k)\setminus \left\{0\right\}$.
On $H$-Antimagicness Of Cartesian Product Of Graphs, Martin Baca, Andrea Semanicova-Fenovcikova, Muhammad Awais Umar, Des Welyyanti
On $H$-Antimagicness Of Cartesian Product Of Graphs, Martin Baca, Andrea Semanicova-Fenovcikova, Muhammad Awais Umar, Des Welyyanti
Turkish Journal of Mathematics
A graph $G=(V(G),E(G))$ admits an $H$-covering if every edge in $E$ belongs to a~subgraph of $G$ isomorphic to $H$. A graph $G$ admitting an $H$-covering is called {\it $(a,d)$-$H$-antimagic} if there is a bijection $f:V(G)\cup E(G) \to \{1,2,\dots, V(G) + E(G) \}$ such that, for all subgraphs $H'$ of $G$ isomorphic to $H$, the $H$-weights, $wt_f(H')= \sum_{v\in V(H')} f(v) + \sum_{e\in E(H')} f(e),$ constitute an arithmetic progression with the initial term $a$ and the common difference $d$. In this paper we provide some sufficient conditions for the Cartesian product of graphs to be $H$-antimagic. We use partitions subsets of integers …
Applications Of Extended Watson's Summation Theorem, Young Sup Kim, Sebastien Gaboury, Arjun Kumar Rathie
Applications Of Extended Watson's Summation Theorem, Young Sup Kim, Sebastien Gaboury, Arjun Kumar Rathie
Turkish Journal of Mathematics
In this research paper, several interesting applications of the extended classical summation theorem are given. As special cases, we recover several known results available in the literature.
Somos's Theta-Function Identities Of Level 10, Belakavadi Radhakrishna Srivatsa Kumar, Devadas Anu Radha
Somos's Theta-Function Identities Of Level 10, Belakavadi Radhakrishna Srivatsa Kumar, Devadas Anu Radha
Turkish Journal of Mathematics
Somos discovered about 6277 theta-function identities of different levels using a computer and offered no proof for them, and these identities closely resemble Ramanujan's recordings. The purpose of this paper is to prove some of his theta-function identities of level 10 and to establish certain partition identities for them.
Stability Of Abstract Dynamic Equations On Time Scales By Lyapunov's Second Method, Alaa Hamza, Karima Oraby
Stability Of Abstract Dynamic Equations On Time Scales By Lyapunov's Second Method, Alaa Hamza, Karima Oraby
Turkish Journal of Mathematics
In this paper, we use the Lyapunov's second method to obtain new sufficient conditions for many types of stability like exponential stability, uniform exponential stability, $h$-stability, and uniform $h$-stability of the nonlinear dynamic equation \begin{equation*} x^{\Delta}(t)=A(t)x(t)+f(t,x),\;t\in \mathbb{T}^+_\tau:=[\tau,\infty)_{\mathbb T}, \end{equation*} on a time scale $\mathbb T$, where $A\in C_{rd}(\mathbb T,L(X))$ and $f:\mathbb T\times X\to X$ is rd-continuous in the first argument with $f(t,0)=0.$ Here $X$ is a Banach space. We also establish sufficient conditions for the nonhomogeneous particular dynamic equation \begin{equation*} x^{\Delta}(t)=A(t)x(t)+f(t),\,t\in\mathbb{T}^+_{\tau}, \end{equation*} to be uniformly exponentially stable or uniformly $h$-stable, where $f\in C_{rd}(\mathbb T,X)$, the space of rd-continuous functions from …
Fedja's Proof Of Deepti's Inequality, Sofiya Ostrovska, Mehmet Turan
Fedja's Proof Of Deepti's Inequality, Sofiya Ostrovska, Mehmet Turan
Turkish Journal of Mathematics
The paper aims to present, in a systematic way, an elegant proof of Deepti's inequality. Both the inequality and various ideas concerning the issue were discussed on the Mathoverflow website by a number of users, but none have appeared in the literature thus far. In this work, suggestions pertaining to users 'Deepti' and 'fedja' are traced, whence the title. The results or the paper are new, and the proof is divided into a series of statements, many of which are of interest in themselves.
The United Stable Solution Set Of Interval Continuous-Time Algebraic Riccati Equation And Verified Numerical Computation Of Its Outer Estimation, Tayyebe Haqiri, Mahmoud Mohseni Moghadam, Azim Rivaz
The United Stable Solution Set Of Interval Continuous-Time Algebraic Riccati Equation And Verified Numerical Computation Of Its Outer Estimation, Tayyebe Haqiri, Mahmoud Mohseni Moghadam, Azim Rivaz
Turkish Journal of Mathematics
This paper introduces the interval continuous-time algebraic Riccati equation $\mathbf{A}^* X + X\mathbf{A} + \mathbf{Q} -X \mathbf{G} X=0$, where $\mathbf{A}, \mathbf{G}$, and $\mathbf{Q}$ are known $n \times n$ complex interval matrices, $\mathbf{G}$ and $\mathbf{Q}$ are Hermitian, and $X$ is an unknown matrix of the same size, and develops two approaches for enclosing the united stable solution set of this interval equation. We first discuss the united stable solution set and then derive a nonlinear programming method in order to find an enclosure for the united stable solution set. We also advance an efficient technique for enclosing the united stable solution …
Some Series Involving The Euler Zeta Function, Min-Soo Kim
Some Series Involving The Euler Zeta Function, Min-Soo Kim
Turkish Journal of Mathematics
In this paper, using the Boole summation formula, we obtain a new integral representation of $n$-th quasi-periodic Euler functions $\overline{E}_n(x)$ for $n=1,2,\ldots.$ We also prove several series involving Euler zeta functions $\zeta_{E}(s),$ which are analogues of the corresponding results by Apostol on some series involving the Riemann zeta function $\zeta(s).$
Jakimovski-Leviatan Operators Of Durrmeyer Type Involving Appell Polynomials, Pooja Gupta, Purshottam Narain Agrawal
Jakimovski-Leviatan Operators Of Durrmeyer Type Involving Appell Polynomials, Pooja Gupta, Purshottam Narain Agrawal
Turkish Journal of Mathematics
The purpose of the present paper is to establish the rate of convergence for a Lipschitz-type space and obtain the degree of approximation in terms of Lipschitz-type maximal function for the Durrmeyer type modification of Jakimovski-Leviatan operators based on Appell polynomials. We also study the rate of approximation of these operators in a weighted space of polynomial growth and for functions having a derivative of bounded variation.
On Radial Solutions For Monge-Ampére Equations, Ronghua Liu, Fanglei Wang, Yukun An
On Radial Solutions For Monge-Ampére Equations, Ronghua Liu, Fanglei Wang, Yukun An
Turkish Journal of Mathematics
In this paper,we obtain some new existence, uniqueness, and multiplicity results of radial solutions of an elliptic system coupled by Monge-Ampére equations using the fixed point theorem.
Extended Laguerre-Appell Polynomials Via Fractional Operators And Their Determinant Forms, Subuhi Khan, Shahid Ahmad Wani
Extended Laguerre-Appell Polynomials Via Fractional Operators And Their Determinant Forms, Subuhi Khan, Shahid Ahmad Wani
Turkish Journal of Mathematics
In this article, the extended form of Laguerre-Appell polynomials is introduced by means of generating function and operational definition. The corresponding results for the extended Laguerre-Bernoulli and Laguerre-Euler polynomials are obtained as applications. Further, the determinant forms of these polynomials are established by using operational techniques.
On Dominated Coloring Of Graphs And Some Nordhaus--Gaddum-Type Relations, Fatemeh Choopani, Abbas Jafarzadeh, Ahmad Erfanian, Doost Ali Mojdeh
On Dominated Coloring Of Graphs And Some Nordhaus--Gaddum-Type Relations, Fatemeh Choopani, Abbas Jafarzadeh, Ahmad Erfanian, Doost Ali Mojdeh
Turkish Journal of Mathematics
The dominated coloring of a graph $G$ is a proper coloring of $G$ such that each color class is dominated by at least one vertex. The minimum number of colors needed for a dominated coloring of $G$ is called the dominated chromatic number of $G$, denoted by $\chi_{dom}(G)$. In this paper, dominated coloring of graphs is compared with (open) packing number of $G$ and it is shown that if $G$ is a graph of order $n$ with $diam(G)\geq3$, then $\chi_{dom}(G)\leq n-\rho(G)$ and if $\rho_0 (G)=2n/3$, then $\chi_{dom}(G)= \rho_0 (G)$, and if $\rho(G)=n/2$, then $\chi_{dom}(G)=\rho(G)$. The dominated chromatic numbers of the …
Certain Strongly Clean Matrices Over Local Rings, Tuğçe Pekacar Çalci, Huanyin Chen
Certain Strongly Clean Matrices Over Local Rings, Tuğçe Pekacar Çalci, Huanyin Chen
Turkish Journal of Mathematics
We are concerned about various strongly clean properties of a kind of matrix subrings $L_{(s)}(R)$ over a local ring $R$. Let $R$ be a local ring, and let $s\in C(R)$. We prove that $A\in L_{(s)}(R)$ is strongly clean if and only if $A$ or $I_2-A$ is invertible, or $A$ is similar to a diagonal matrix in $L_{(s)}(R)$. Furthermore, we prove that $A\in L_{(s)}(R)$ is quasipolar if and only if $A\in GL_2(R)$ or $A\in L_{(s)}(R)^{qnil}$, or $A$ is similar to a diagonal matrix $\left( \begin{array}{cc} \lambda&0\\ 0&\mu \end{array} \right)$ in $L_{(s)}(R)$, where $\lambda\in J(R)$, $\mu\in U(R)$ or $\lambda\in U(R)$, $\mu\in J(R)$, …
An Exponential Method To Solve Linear Fredholm-Volterraintegro-Differential Equations And Residual Improvement, Şuayi̇p Yüzbaşi
An Exponential Method To Solve Linear Fredholm-Volterraintegro-Differential Equations And Residual Improvement, Şuayi̇p Yüzbaşi
Turkish Journal of Mathematics
In this paper, a collocation approach based on exponential polynomials is introduced to solve linear Fredholm-Volterra integro-differential equations under the initial boundary conditions. First, by constructing the matrix forms of the exponential polynomials and their derivatives, the desired exponential solution and its derivatives are written in matrix forms. Second, the differential and integral parts of the problem are converted into matrix forms based on exponential polynomials. Later, the main problem is reduced to a system of linear algebraic equations by aid of the collocation points, the matrix operations, and the matrix forms of the conditions. The solutions of this system …
Geometric Properties Of Rotation Minimizing Vector Fields Along Curves In Riemannian Manifolds, Fernando Etayo
Geometric Properties Of Rotation Minimizing Vector Fields Along Curves In Riemannian Manifolds, Fernando Etayo
Turkish Journal of Mathematics
Rotation minimizing (RM) vector fields and frames were introduced by Bishop as an alternative to the Frenet frame. They are used in CAGD because they can be defined even when the curvature vanishes. Nevertheless, many other geometric properties have not been studied. In the present paper, RM vector fields along a curve immersed into a Riemannian manifold are studied when the ambient manifold is the Euclidean 3-space, the hyperbolic 3-space, and a Kähler manifold.
Construction Of Some New Families Of Apostol-Type Numbers And Polynomials Via Dirichlet Character And $P$-Adic $Q$-Integrals, Yilmaz Şi̇mşek
Construction Of Some New Families Of Apostol-Type Numbers And Polynomials Via Dirichlet Character And $P$-Adic $Q$-Integrals, Yilmaz Şi̇mşek
Turkish Journal of Mathematics
In this paper, by applying the $p$-adic $q$-integrals to a family of continuous differentiable functions on the ring of $p$-adic integers, we construct new generating functions for generalized Apostol-type numbers and polynomials attached to the Dirichlet character of a finite abelian group. By using these generating functions with their functional equations, we derive various new identities and relations for these numbers and polynomials. These results are generalizations of known identities and relations including some well-known families of special numbers and polynomials such as the generalized Apostol-type Bernoulli, the Apostol-type Euler, the Frobenius-Euler numbers and polynomials, the Stirling numbers, and other …
Some Results On Hecke And Extended Hecke Groups, Recep Şahi̇n
Some Results On Hecke And Extended Hecke Groups, Recep Şahi̇n
Turkish Journal of Mathematics
Let $q\geq 3$ be a prime number and let $\overline{H}(\lambda _{q})$ be the extended Hecke group associated with $q.$ In this paper, we determine the presentation of the commutator subgroup ($H$($\lambda _{q})\alpha )^{\prime } $ of the normal subgroup $H$($\lambda _{q})\alpha $, where $H$($\lambda _{q})\alpha $ is a subgroup of index $2$ in $\overline{H}$($\lambda _{q}).$ Next we discuss the commutator subgroup ($\overline{H}_{2})^{\prime }$($% \lambda _{q})$ of the principal congruence subgroup $\overline{H}_{2}$($% \lambda _{q})$ of $\overline{H}$($\lambda _{q})$. Then we show that some quotient groups of $\overline{H}$($\lambda _{q})$ are generalized $M^{\ast }- $groups. Finally, we prove some results related to some normal …
Connection Between Bi$^{S}$Nomial Coefficients And Their Analogs And Symmetric Functions, Abdelghafour Bazeniar, Moussa Ahmia, Hacene Belbachir
Connection Between Bi$^{S}$Nomial Coefficients And Their Analogs And Symmetric Functions, Abdelghafour Bazeniar, Moussa Ahmia, Hacene Belbachir
Turkish Journal of Mathematics
In this paper, on one hand, we propose a new type of symmetric function to interpret the bi$^{s}$nomial coefficients and their analogs. On other hand, according to this function, we give an interpretation of these coefficients by lattice paths and tiling. Some identities of these coefficients are also established. This work is an extension of the results of Belbachir and Benmezai's ''A $\mathit{q}$-analogue for bi$^{\mathit{s}}$nomial coefficients and generalized Fibonacci sequences".
Iterative Roots Of Some Functions, Sukrawan Mavecha, Vichian Laohakosol, Boonrod Yuttanan
Iterative Roots Of Some Functions, Sukrawan Mavecha, Vichian Laohakosol, Boonrod Yuttanan
Turkish Journal of Mathematics
The iterative equation $f^{q}(x)=g(x)$, $x\in X$ for a given function $g$ and a positive integer $q$ is solved in the following two main cases: (i) $X=\mathbb{Z}$, $g(x)=ax+b$, ($a,b\in\mathbb{Z}$; $a\neq0,1$); (ii) $X=\mathbb{N}\cup\left\{ 0\right\} $, $g$ is increasing with no fixed point.
Weyl- And Horn-Type Inequalities For Cyclically Compact Operators, Uğur Gönüllü
Weyl- And Horn-Type Inequalities For Cyclically Compact Operators, Uğur Gönüllü
Turkish Journal of Mathematics
A variant of Weyl- and Horn-type inequalities for cyclically compact operators on Kaplansky-Hilbert modules is given.
Reflexivity Of Vector-Valued Köthe-Orlicz Sequence Spaces, Mohamed Ahmed Ould Sidaty
Reflexivity Of Vector-Valued Köthe-Orlicz Sequence Spaces, Mohamed Ahmed Ould Sidaty
Turkish Journal of Mathematics
Let $E$ be a Banach space, $\lambda$ a perfect sequence space, and $M$ an Orlicz function. Denote by $\lambda \left(E, M\right)_{r}$ the space of all weakly $(M, \lambda)$-summable sequences from $E$ that are the limit of their finite sections. In this paper, we describe the continuous linear functionals on $\lambda \left(E, M\right)_{r}$ in terms of strongly $(N, \lambda^{\ast})$-summable sequences in the dual $E^{*}$ of $E$, and then we give a characterization of the reflexivity of $\lambda \left(E, M\right)$ in terms of that of $\lambda$ and of $E$ and the AK-property.
On A New Identity For The H-Function With Applications To The Summation Of Hypergeometric Series, Arjun Kumar Rathie, Luan Carlos De Sena Monteiro Ozelim, Pushpa Narayan Rathie
On A New Identity For The H-Function With Applications To The Summation Of Hypergeometric Series, Arjun Kumar Rathie, Luan Carlos De Sena Monteiro Ozelim, Pushpa Narayan Rathie
Turkish Journal of Mathematics
Using generalized hypergeometric functions to perform symbolic manipulations of equations is of great importance to pure and applied scientists. There are in the literature a great number of identities for the Meijer-G function. On the other hand, when more complex expressions arise, that function is not capable of representing them. The H-function is an alternative to overcome this issue, as it is a generalization of the Meijer-G function. In the present paper, a new identity for the H-function is derived. In short, this result enables one to split a particular H-function into the sum of two other H-functions. The new …