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2019

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Articles 1201 - 1230 of 1386

Full-Text Articles in Mathematics

On Hypercyclic Fully Zero-Simple Semihypergroups, Mario De Salvo, Domenico Freni, Giovanni Lo Faro Jan 2019

On Hypercyclic Fully Zero-Simple Semihypergroups, Mario De Salvo, Domenico Freni, Giovanni Lo Faro

Turkish Journal of Mathematics

Let $\mfI$ be the class of fully zero-simple semihypergroups generated by a hyperproduct. In this paper we study some properties of residual semihypergroup $(H_+, \star)$ of a semihypergroup $(H,\circ)\in \mfI$. Moreover, we find sufficient conditions for $(H,\circ)$ and $(H_+, \star)$ to be cyclic.

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Fixed Point Properties For A Degenerate Lorentz-Marcinkiewicz Space, Veysel Nezi̇r Jan 2019

Fixed Point Properties For A Degenerate Lorentz-Marcinkiewicz Space, Veysel Nezi̇r

Turkish Journal of Mathematics

We construct an equivalent renorming of $\ell^1$, which turns out to produce a degenerate $\ell^1$-analog Lorentz-Marcinkiewicz space $\ell_{\delta,1}$, where the weight sequence $\delta={(\delta_n)}_{n\in\N}=(2,1,1,1,\cdots)$ is a decreasing positive sequence in $\ell^\infty\backslash c_0$, rather than in $c_0\backslash\ell^1$ (the usual Lorentz situation). Then we obtain its isometrically isomorphic predual $\ell^0_{\delta,\infty}$ and dual $\ell_{\delta,\infty}$, corresponding degenerate $c_0$-analog and $\ell^\infty$-analog Lorentz-Marcinkiewicz spaces, respectively. We prove that both spaces $\ell_{\delta,1}$ and $\ell^0_{\delta,\infty}$ enjoy the weak fixed point property (w-fpp) for nonexpansive mappings yet they fail to have the fixed point property (fpp) for nonexpansive mappings since they contain an asymptotically isometric copy of $\ell^1$ and $c_0$, …

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Some Results Related To The Berezin Number Inequalities, Ulaş Yamanci, Mübari̇z Tapdigoğlu Jan 2019

Some Results Related To The Berezin Number Inequalities, Ulaş Yamanci, Mübari̇z Tapdigoğlu

Turkish Journal of Mathematics

In this paper, we prove reverse inequalities for the so-called Berezin number of some operators. Also, by using the classical Jensen and Young inequalities, we obtain upper bounds for Berezin number of $A^{\alpha}XB^{\alpha}$ and $A^{\alpha}XB^{1-\alpha}$ for the case when $0\leq\alpha\leq1$.

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An Integral-Boundary Value Problem For A Partial Differential Equation Of Second Order, Anar Assanova Jan 2019

An Integral-Boundary Value Problem For A Partial Differential Equation Of Second Order, Anar Assanova

Turkish Journal of Mathematics

An integral-boundary value problem for a hyperbolic partial differential equation in two independent variables is considered. By introducing additional functional parameters, we investigate the solvability of the problem and develop an algorithm for finding its approximate solutions. The problem is reduced to an equivalent one, consisting of the Goursat problem for a hyperbolic equation with parameters and boundary value problems with an integral condition for ODEs with respect to the parameters entered. We propose an algorithm to find an approximate solution to the original problem, which is based on the algorithm for finding a solution to the equivalent problem. The …

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Some Applications Of Differential Subordination For Certain Starlike Functions, Rahim Kargar, Lucyna Trojnar Spelina Jan 2019

Some Applications Of Differential Subordination For Certain Starlike Functions, Rahim Kargar, Lucyna Trojnar Spelina

Turkish Journal of Mathematics

Let $\mathcal{S}^*(q_c)$ denote the class of functions $f$ analytic in the open unit disc $\Delta$, normalized by the condition $f(0)=0=f'(0)-1$ and satisfying the following inequality $\left \left(\frac{zf'(z)}{f(z)}\right)^2-1\right < c \quad (z\in\Delta, 0

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The Large Contraction Principle And Existence Of Periodic Solutions For Infinite Delay Volterra Difference Equations, Paul Eloe, Jaganmohan Jonnalagadda, Youssef Raffoul Jan 2019

The Large Contraction Principle And Existence Of Periodic Solutions For Infinite Delay Volterra Difference Equations, Paul Eloe, Jaganmohan Jonnalagadda, Youssef Raffoul

Turkish Journal of Mathematics

In this article, we establish sufficient conditions for the existence of periodic solutions of a nonlinear infinite delay Volterra difference equation: $$\Delta x(n) = p(n) + b(n)h(x(n)) + \sum^{n}_{k = -\infty}B(n, k)g(x(k)).$$ We employ a Krasnosel'ski\u{i} type fixed point theorem, originally proved by Burton. The primary sufficient condition is not verifiable in terms of the parameters of the difference equation, and so we provide three applications in which the primary sufficient condition is verified.

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Multiplication Modules With Prime Spectrum, Ortaç Öneş, Mustafa Alkan Jan 2019

Multiplication Modules With Prime Spectrum, Ortaç Öneş, Mustafa Alkan

Turkish Journal of Mathematics

The subject of this paper is the Zariski topology on a multiplication module $M$ over a commutative ring $R$. We find a characterization for the radical submodule $rad_{M}(0)$ and also show that there are proper ideals $I_{1},...,I_{n}$ of $R$ such that $rad_{M}(0)=rad_{M}(\left( I_{1}...I_{n}\right) M)$. Finally, we prove that the spectrum $Spec(M)$ is irreducible if and only if $M$ is the finite sum of its submodules, whose $ \mathcal{T}$-radicals are prime in $M$.

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Studying New Generalizations Of Max-Min Matrices With A Novel Approach, Emrah Kiliç, Talha Arikan Jan 2019

Studying New Generalizations Of Max-Min Matrices With A Novel Approach, Emrah Kiliç, Talha Arikan

Turkish Journal of Mathematics

We consider new kinds of max and min matrices, $\left[ a_{\max(i,j)}\right] _{i,j\geq1}$ and $\left[ a_{\min(i,j)}\right] _{i,j\geq1},$ as generalizations of the classical max and min matrices. Moreover, their reciprocal analogues for a given sequence $\left\{ a_{n}\right\} $ have been studied. We derive their $LU$ and Cholesky decompositions and their inverse matrices as well as the $LU$-decompositions of their inverses. Some interesting corollaries will be presented.

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A Description For The Compactification Of The Orbit Space, Dünya Karapinar, Ali̇ Arslan Özkurt Jan 2019

A Description For The Compactification Of The Orbit Space, Dünya Karapinar, Ali̇ Arslan Özkurt

Turkish Journal of Mathematics

Let$\ X$ be a locally compact and noncompact$\ G-$space with a compact group $G$. In this paper, we give some useful description of a compactification of the orbit space $X/G$ when it is an orbit space of a $G-$compactification of $X$. As an application, we show that the closed bounded interval $[a,b]$ is homeomorphic to the space of maximal ideals with Stone topology of uniformly continuous even functions subring of $\ C^{\ast }(\mathbb{R})$.

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Approximation By Generalized Bernstein-Stancu Operators, Nursel Çeti̇n, Voichita Adriana Radu Jan 2019

Approximation By Generalized Bernstein-Stancu Operators, Nursel Çeti̇n, Voichita Adriana Radu

Turkish Journal of Mathematics

In this paper, we investigate approximation properties of the Stancu type generalization of the $\alpha$-Bernstein operator. We obtain a recurrence relation for moments and the rate of convergence by means of moduli of continuity. Also, we present Voronovskaya and Grüss-Voronovskaya type asymptotic results for these operators. Finally, the study contains numerical considerations regarding the constructed operators based on Maple algorithms.

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On Hirano Inverses In Rings, Huanyin Chen, Marjan Sheibani Abdolyousefi Jan 2019

On Hirano Inverses In Rings, Huanyin Chen, Marjan Sheibani Abdolyousefi

Turkish Journal of Mathematics

We completely characterize a subclass of Drazin inverses by means of tripotents and nilpotents. We prove that an element $a$ in a ring $R$ has Hirano inverse if and only if $a^2\in R$ has strongly Drazin inverse, if and only if $a-a^3$ is nilpotent. If $\frac{1}{2}\in R$, we prove that $a\in R$ has Hirano inverse if and only if there exists $p^3=p\in comm^2(a)$ such that $a-p\in N(R)$, if and only if there exist two idempotents $e,f\in comm^2(a)$ such that $a+e-f\in N(R)$. Multiplicative and additive results for this generalized inverse are thereby obtained.

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The Matrix-Valued Numerical Range Over Finite Fields, Edoardo Ballico Jan 2019

The Matrix-Valued Numerical Range Over Finite Fields, Edoardo Ballico

Turkish Journal of Mathematics

In this paper we define and study the matrix-valued $k\times k$ numerical range of $n\times n$ matrices using the Hermitian product and the product with $n\times k$ unitary matrices $U$ (on the right with $U$, on the left with its adjoint $U^\dagger = U^{-1}$). For all $i, j=1,\dots ,k$ we study the possible $(i,j)$-entries of these $k\times k$ matrices. Our results are for the case in which the base field is finite, but the same definition works over $\mathbb {C}$. Instead of the degree $2$ extension $\mathbb {R}\hookrightarrow \mathbb {C}$ we use the degree $2$ extension $\mathbb {F} _q\hookrightarrow \mathbb …

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A New Subclass Of Starlike Functions, Hesam Mahzoon, Rahim Kargar, Janusz Sokol Jan 2019

A New Subclass Of Starlike Functions, Hesam Mahzoon, Rahim Kargar, Janusz Sokol

Turkish Journal of Mathematics

Motivated by the Ronning-starlike class [Proc Amer Math Soc {\bf118}, no. 1, 189-196, 1993], we introduce new class $\mathcal{S}^*_c$ includes of analytic and normalized functions $f$ which satisfy the inequality $$ {\rm Re}\left\{\frac{zf'(z)}{f(z)}\right\}\geq\left \frac{f(z)}{z}-1\right \quad( z 1/2$ in $ z

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On Nonoscillatory Solutions Of Three Dimensional Time-Scale Systems, Elvan Akin, Taher S. Hassan, Özkan Öztürk, İsmai̇l Uğur Ti̇ryaki̇ Jan 2019

On Nonoscillatory Solutions Of Three Dimensional Time-Scale Systems, Elvan Akin, Taher S. Hassan, Özkan Öztürk, İsmai̇l Uğur Ti̇ryaki̇

Turkish Journal of Mathematics

In this article, we classify nonoscillatory solutions of a system of three-dimensional time scale systems. We use the method of considering the sign of components of such solutions. Examples are given to highlight some of our results. Moreover, the existence of such solutions is obtained by Knaster's fixed point theorem.

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Modules In Which Semisimple Fully Invariant Submodules Are Essential In Summands, Ramazan Yaşar Jan 2019

Modules In Which Semisimple Fully Invariant Submodules Are Essential In Summands, Ramazan Yaşar

Turkish Journal of Mathematics

One of the useful generalization of extending notion is $FI$-extending property. A module is called $FI$-extending if every fully invariant submodule is essential in a direct summand. In this paper, we explore Weak $FI$-extending concept by considering only semisimple fully invariant submodules rather than all fully invariant submodules. To this end, we call such a module Weak $FI$-extending. We obtain that $FI$-extending modules are properly contained in this new class of modules. Amongst other structural properties, we also deal with direct sums and direct summands of Weak $FI$-extending modules.

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An Approach To Negative Hypergeometric Distribution By Generatingfunction For Special Numbers And Polynomials, İrem Küçükoğlu, Burçi̇n Şi̇mşek, Yilmaz Şi̇mşek Jan 2019

An Approach To Negative Hypergeometric Distribution By Generatingfunction For Special Numbers And Polynomials, İrem Küçükoğlu, Burçi̇n Şi̇mşek, Yilmaz Şi̇mşek

Turkish Journal of Mathematics

The aim of this paper is to not only provide a definition of a new family of special numbers and polynomials of higher-order with their generating functions, but also to investigate their fundamental properties in the spirit of probabilistic distributions. By applying generating functions methods, we derive miscellaneous novel identities and formulas involving the Chu--Vandermonde-type convolution formulas, combinatorial sums, Bernstein basis functions, and the other well-known special numbers and polynomials. Moreover, we provide a computational algorithm which returns special values of these numbers and polynomials. In addition, we show that our new identities and formulas are connected with the interpolation …

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A Certain Subclass Of Bi-Univalent Analytic Functions Introduced Bymeans Of The $Q$-Analogue Of Noor Integral Operator And Horadam Polynomials, Arzu Akgül, Fethi̇ye Müge Sakar Jan 2019

A Certain Subclass Of Bi-Univalent Analytic Functions Introduced Bymeans Of The $Q$-Analogue Of Noor Integral Operator And Horadam Polynomials, Arzu Akgül, Fethi̇ye Müge Sakar

Turkish Journal of Mathematics

In the present study, by using the Horadam Polnomials and $q-$analogue of Noor integral oprerator, we target to construct an interesting connection between the geometric function theory and that of special functions. Also, by defining a new class of bi-univalent analytic functions, we investigate coefficient estimates and famous Fekete-Szegö inequality for functions belonging to this interesting class.

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On The Cover Ideals Of Chordal Graphs, Nursel Erey Jan 2019

On The Cover Ideals Of Chordal Graphs, Nursel Erey

Turkish Journal of Mathematics

The independence complex of a chordal graph is known to be shellable which is equivalent to the fact that cover ideal of a chordal graph has linear quotients. We use this result to obtain recursive formulas for the Betti numbers of cover ideals of chordal graphs. Moreover, we give a new proof of such result which yields different shellings of the independence complex.

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Rational Maps From Euclidean Configuration Spaces To Spheres, Urtzi Buijs, Antonio Garvin, Aniceto Murillo Jan 2019

Rational Maps From Euclidean Configuration Spaces To Spheres, Urtzi Buijs, Antonio Garvin, Aniceto Murillo

Turkish Journal of Mathematics

In this note we give an algorithm to determine the rational homotopy type of the free and pointed mapping spaces $\map(F(\br^m,k),\bs^n)$ and $\map^*(F(\br^m,k),\bs^n)$. An explicit description of these spaces is given for $k=3$. The general case for $n$ odd is also presented as an immediate consequence of the rational version of a classical result of Thom.

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On Operator Systems Generated By Reducible Projective Unitary Representations Of Compact Groups, Grigori Amosov Jan 2019

On Operator Systems Generated By Reducible Projective Unitary Representations Of Compact Groups, Grigori Amosov

Turkish Journal of Mathematics

We study reducible projective unitary representations $(U_g)_{g\in G}$ of a compact group $G$ in separable Hilbert spaces $H$. It is shown that there exist the projections $Q$ and $P$ for which ${\mathcal V}=\overline {span(U_gQU_g^*,\ g\in G)}$ is the operator system and $P{\mathcal V}P=\{{\mathbb C}P\}$. As an example, a bipartite Hilbert space $H={\mathfrak {H}}\otimes {\mathfrak {H}}$ is considered. In this case, the action of $(U_g)_{g\in G}$ has the property of transforming separable vectors to entangled.

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On A Class Of Nonself-Adjoint Multidimensional Periodic Schrödinger Operators, Oktay Veli̇ev Jan 2019

On A Class Of Nonself-Adjoint Multidimensional Periodic Schrödinger Operators, Oktay Veli̇ev

Turkish Journal of Mathematics

We investigate the Schrödinger operator $L(q)$ in $L_{2}\left( \mathbb{R}^{d}\right) \ (d\geq1)$ with the complex-valued potential $q$ that is periodic with respect to a lattice $\Omega.$ Besides, it is assumed that the Fourier coefficients $q_{\gamma}$ of $q$ with respect to the orthogonal system $\{e^{i\left\langle \gamma x\right\rangle }:\gamma\in\Gamma\}$ vanish if $\gamma$ belongs to a half-space, where $\Gamma$ is the lattice dual to $\Omega.$ We prove that the Bloch eigenvalues are $\mid\gamma+t\mid^{2}$ for $\gamma\in\Gamma,$ where $t$ is a quasimomentum and find explicit formulas for \ the Bloch functions. Moreover, we investigate the multiplicity of the Bloch eigenvalue and consider necessary and sufficient conditions …

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Radii Of Starlikeness And Convexity Of $Q$-Mittag-Leffler Functions, Evri̇m Toklu Jan 2019

Radii Of Starlikeness And Convexity Of $Q$-Mittag-Leffler Functions, Evri̇m Toklu

Turkish Journal of Mathematics

In this paper we deal with the radii of starlikeness and convexity of the $q$-Mittag-Leffler function for three different kinds of normalization by making use of their Hadamard factorization in such a way that the resulting functions are analytic in the unit disk of the complex plane. By applying Euler-Rayleigh inequalities for the first positive zeros of these functions tight lower and upper bounds for the radii of starlikeness of these functions are obtained. The Laguerre-P\'olya class of real entire functions plays a pivotal role in this investigation.

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A Convergent Two-Level Linear Scheme For The Generalizedrosenau-Kdv-Rlw Equation, Ayhan Aydin Jan 2019

A Convergent Two-Level Linear Scheme For The Generalizedrosenau-Kdv-Rlw Equation, Ayhan Aydin

Turkish Journal of Mathematics

A new convergent two-level finite difference scheme is proposed for the numerical solution of initial value problem of the generalized Rosenau--KdV--RLW equation. The new scheme is second-order, linear, conservative, and unconditionally stable. It contains one free parameter. The impact of the parameter to error of the numerical solution is studied. The prior estimate of the finite difference solution is obtained. The existence, uniqueness, and convergence of the scheme are proved by the discrete energy method. Accuracy and reliability of the scheme are tested by simulating the solitary wave graph of the equation. Wave generation subject to initial Gaussian condition has …

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Relative Ranks Of Some Partial Transformation Semigroups, Ebru Yi̇ği̇t, Gonca Ayik, Hayrullah Ayik Jan 2019

Relative Ranks Of Some Partial Transformation Semigroups, Ebru Yi̇ği̇t, Gonca Ayik, Hayrullah Ayik

Turkish Journal of Mathematics

Let $P_{n}$, $T_{n}$, $I_{n}$, and $S_{n}$ be the partial transformation semigroup, the (full) transformation semigroup, the symmetric inverse semigroup, and the symmetric group on $X_{n}=\{1,\ldots ,n \}$, respectively. For $1\leq r\leq n-1$, let $PK_{n,r}$ be the subsemigroup consisting $\alpha\in P_{n}$ such that $ \im\alpha \leq r$ and let $SPK_{n,r}=PK_{n,r}\setminus T_{n}$. In this paper, we first examine the subsemigroup $I_{n,r}=I_{n}\cup PK_{n,r}$ and we find the necessary and sufficient conditions for any nonempty subset of $PK_{n,r}$ to be a (minimal) relative generating set of the subsemigroup $I_{n,r}$ modulo $I_{n}$. Then we examine the subsemigroups $PI_{n,r}= SI_{n}\cup PK_{n,r}$ and $SI_{n,r}=SI_{n}\cup SPK_{n,r}$ for $1\leq …

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Fekete-Szegö Problem For A General Subclass Of Analytic Functions, Nesli̇han Uyanik Jan 2019

Fekete-Szegö Problem For A General Subclass Of Analytic Functions, Nesli̇han Uyanik

Turkish Journal of Mathematics

In this present investigation, we introduced a certain subclass of starlike and convex functions of complex order $b$, using a linear multiplier differential operator $D_{\lambda ,\mu }^{m}f(z)$. For this class, the Fekete-Szegö problem is completely solved. Various new special cases are considered.

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Po-Groups And Hypergroups In A Topos, Ali Madanshekaf, Zeinab Kanjanzadeh Jan 2019

Po-Groups And Hypergroups In A Topos, Ali Madanshekaf, Zeinab Kanjanzadeh

Turkish Journal of Mathematics

This paper deals with two constructions in topos theory: po-groups and hypergroups. After a deep analysis of these, we restrict our attention to find a hypergroup associated to a po-group $G$ in a topos $\mathcal{E}$. The method that we use here is based on the Mitchell--B$\acute{{\rm e}}$nabou language. Then, we show that on the negative and positive cones of a po-group $G$ in $\mathcal{E},$ the left and right translations are hyperhomomorphisms in $\mathcal{E}.$ Our aim is to find two faithful and left exact functors from the category of po-groups in $\mathcal{E}$ to the (smallest in some sense) finitely complete category …

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On Walker 4-Manifolds With Pseudo Bi-Hermitian Structures, Si̇bel Turanli Jan 2019

On Walker 4-Manifolds With Pseudo Bi-Hermitian Structures, Si̇bel Turanli

Turkish Journal of Mathematics

$\left(M_{2n},g^w,D\right)$ is a 4-dimensional Walker manifold and this triple is also a pseudo-Riemannian manifold $\left(M_{2n},g^w\right)$ of signature $(++--$) (or neutral), which is admitted a field of null 2-plane. In this paper, we consider bi-Hermitian structures $({\varphi }_1,{\ \varphi }_2)$ on 4-dimensional Walker manifolds. We discuss when these structures are integrable and when the bi-Kahler forms are symplectic.

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On Congruence Equations Arising From Suborbital Graphs, Bahadir Özgür Güler, Murat Beşenk, Serkan Kader Jan 2019

On Congruence Equations Arising From Suborbital Graphs, Bahadir Özgür Güler, Murat Beşenk, Serkan Kader

Turkish Journal of Mathematics

In this paper we deal with congruence equations arising from suborbital graphs of the normalizer of $\Gamma _{0}(m)$ in $PSL(2,\mathbb{R})$. We also propose a conjecture concerning the suborbital graphs of the normalizer and the related congruence equations. In order to prove the existence of solution of an equation over prime finite field, this paper utilizes the Fuchsian group action on the upper half plane and Farey graphs properties.

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Existence Of Solutions Of Bvps For Impulsive Fractional Langevin Equations Involving Caputo Fractional Derivatives, Yuji Liu, Ravi Agarwal Jan 2019

Existence Of Solutions Of Bvps For Impulsive Fractional Langevin Equations Involving Caputo Fractional Derivatives, Yuji Liu, Ravi Agarwal

Turkish Journal of Mathematics

The standard Caputo fractional derivative is generalized for the piecewise continuous functions. A more general boundary value problem for the impulsive Langevin fractional differential equation involving the Caputo fractional derivatives is studied. New existence results for solutions of concerned problems are established.

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Asymptotic Behavior Of Solutions Of Second-Order Difference Equations Of Volterra Type, Malgorzata Migda, Aldona Dutkiewicz Jan 2019

Asymptotic Behavior Of Solutions Of Second-Order Difference Equations Of Volterra Type, Malgorzata Migda, Aldona Dutkiewicz

Turkish Journal of Mathematics

In this paper we investigate the Volterra difference equation of the form $ \D(r_n\D x_n)=b_n+\sum_{k=1}^{n}K(n,k)f(x_k). $ We establish sufficient conditions for the existence of a solution $x$ of the above equation with the property $ x_n=y_n+\o(n^s), $ where $y$ is a given solution of the equation $\D(r_n\D y_n)=b_n$ and $s$ is nonpositive real number. We also obtain sufficient conditions for the existence of asymptotically periodic solutions.

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