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Some Operator Inequalities Associated With Kantorovich And Hölder-Mccarthyinequalities And Their Applications, Hamdullah Başaran, Mehmet Gürdal, Ayşe Nur Güncan
Some Operator Inequalities Associated With Kantorovich And Hölder-Mccarthyinequalities And Their Applications, Hamdullah Başaran, Mehmet Gürdal, Ayşe Nur Güncan
Turkish Journal of Mathematics
We prove analogs of certain operator inequalities, including Hölder-McCarthy inequality, Kantorovich inequality, and Heinz-Kato inequality, for positive operators on the Hilbert space in terms of the Berezin symbols and the Berezin number of operators on the reproducing kernel Hilbert space.
Curves Over Finite Fields And Permutations Of The Form $X^K-\Gamma \Mathrm{Tr}(X)$, Nurdagül Anbar Meidl
Curves Over Finite Fields And Permutations Of The Form $X^K-\Gamma \Mathrm{Tr}(X)$, Nurdagül Anbar Meidl
Turkish Journal of Mathematics
We consider the polynomials of the form $P(x)=x^k-\gamma \mathrm{Tr}(x)$ over $\mathbb{F}_{q^n}$ for $n\geq 2$. We show that $P(x)$ is not a permutation of $\mathbb{F}_{q^n}$ in the case $\gcd(k, q^n-1)>1$. Our proof uses an absolutely irreducible curve over $\mathbb{F}_{q^n}$ and the number of rational points on it.
On The Composition And Exterior Products Of Double Forms And $P$-Pure Manifolds, Abdelhadi Belkhirat, Mohammed Labbi
On The Composition And Exterior Products Of Double Forms And $P$-Pure Manifolds, Abdelhadi Belkhirat, Mohammed Labbi
Turkish Journal of Mathematics
We translate into double forms formalism the basic Greub and Greub-Vanstone identities that were previously obtained in mixed exterior algebras. In particular, we introduce a second product in the space of double forms, namely the composition product, which provides this space with a second associative algebra structure. The composition product interacts with the exterior product of double forms; we show that the resulting relations provide simple alternative proofs to some classical linear algebra identities as well as to recent results in the exterior algebra of double forms. We define and study a refinement of the notion of pure curvature of …
Rt Distance And Weight Distributions Of Type 1 Constacyclic Codes Of Length\\ $4p^S$ Over $\Frac{\Mathbb F_{P^M}[U]}{\Left\Langle U^A \Right\Rangle}$, Hai Dinh, Bac Nguyen, Songsak Sriboonchitta
Rt Distance And Weight Distributions Of Type 1 Constacyclic Codes Of Length\\ $4p^S$ Over $\Frac{\Mathbb F_{P^M}[U]}{\Left\Langle U^A \Right\Rangle}$, Hai Dinh, Bac Nguyen, Songsak Sriboonchitta
Turkish Journal of Mathematics
For any odd prime $p$ such that $p^m \equiv 1 \pmod{4}$, the class of $\Lambda$-constacyclic codes of length $4p^s$ over the finite commutative chain ring ${\cal R}_a=\frac{\mathbb F_{p^m}[u]}{\left\langle u^a \right\rangle}=\mathbb F_{p^m} + u \mathbb F_{p^m}+ \dots + u^{a-1}\mathbb F_{p^m}$, for all units $\Lambda$ of $\mathcal R_a$ that have the form $\Lambda=\Lambda_0+u\Lambda_1+\dots+u^{a-1}\Lambda_{a-1}$, where $\Lambda_0, \Lambda_1, \dots, \Lambda_{a-1} \in \mathbb F_{p^m}$, $\Lambda_0 \,{\not=}\, 0, \, \Lambda_1 \,{\not=}\, 0$, is investigated. If the unit $\Lambda$ is a square, each $\Lambda$-constacyclic code of length $4p^s$ is expressed as a direct sum of a $-\lambda$-constacyclic code and a $\lambda$-constacyclic code of length $2p^s$. In the …
Exponential Stabilization Of A Neutrally Delayed Viscoelastic Timoshenko Beam, Sebti Kerbal, Nasser Eddine Tatar
Exponential Stabilization Of A Neutrally Delayed Viscoelastic Timoshenko Beam, Sebti Kerbal, Nasser Eddine Tatar
Turkish Journal of Mathematics
A Timoshenko type beam subject to a viscoelastic damping in the rotational displacement component is considered. Taking into account a neutral type delay, we prove a fast stability result despite the previously observed destabilizing effect due to delays in such systems. The proof relies on the introduction of nine different functionals with which we modify the energy of the system. These functionals are carefully selected and adapted to cope with both the viscoelasticity and the neutral delay.
Spectral Properties Of Boundary-Value-Transmission Problems With A Constant Retarded Argument, Erdoğan Şen
Spectral Properties Of Boundary-Value-Transmission Problems With A Constant Retarded Argument, Erdoğan Şen
Turkish Journal of Mathematics
In this work, spectra and asymptotics of eigenfunctions of a generalized class of boundary value problems with constant retarded argument are obtained. Contrary to previous works in the literature, the problem has nonclassical transmission conditions.
Positivity Of Sums And Integrals For $N$-Convex Functions Via The Fink Identity, Asif R. Khan, Josip Pecaric, Marjan Praljak, Sanja Varosanec
Positivity Of Sums And Integrals For $N$-Convex Functions Via The Fink Identity, Asif R. Khan, Josip Pecaric, Marjan Praljak, Sanja Varosanec
Turkish Journal of Mathematics
We consider the positivity of the sum $\sum_{i=1}^n\rho_i\digamma(\xi_i)$, where $\digamma$ is a convex function of higher order, as well as analogous results involving the integral $\int_{a_0}^{b_0}\rho(\xi)\digamma(g(\xi))d\xi$. We use a representation of the function $\digamma$ via the Fink identity and the Green function that leads us to identities from which we obtain conditions for positivity of the above-mentioned sum and integral. We also obtain bounds for the integral remainders which occur in these identities, as well as corresponding mean value results.
Stability Analysis For A Class Of Nabla $(Q,H)$-Fractional Difference Equations, Xiang Liu, Baoguo Jia, Lynn Erbe, Allan Peterson
Stability Analysis For A Class Of Nabla $(Q,H)$-Fractional Difference Equations, Xiang Liu, Baoguo Jia, Lynn Erbe, Allan Peterson
Turkish Journal of Mathematics
This paper investigates stability of the nabla $(q,h)$-fractional difference equations. Asymptotic stability of the special nabla $(q,h)$-fractional difference equations are discussed. Stability theorems for discrete fractional Lyapunov direct method are proved. Furthermore, we give some new lemmas (including important comparison theorems) related to the nabla $(q,h)$-fractional difference operators that allow proving the stability of the nabla $(q,h)$-fractional difference equations, by means of the discrete fractional Lyapunov direct method, using Lyapunov functions. Some examples are given to illustrate these results.
$N$-$T$-Torsionfree Modules, Peiyu Zhang, Jie Geng
$N$-$T$-Torsionfree Modules, Peiyu Zhang, Jie Geng
Turkish Journal of Mathematics
As a generalization of the Auslander-Reiten transpose, Xi introduced and studied a more general transpose, called the relative transpose (or, $T$-transpose). Based on this notion, the notion of relative $n$-torsionfree modules (or, $n$-$T$-torsionfree modules) is introduced in this paper, which is a generalization of the $n$-torsionfree modules introduced by Auslander and Bridger. We show that relative $n$-torsionfree modules have many similar properties of $n$-torsionfree modules.
Inclusion Properties Of Lucas Polynomials For Bi-Univalent Functionsintroduced Through The $\Mathfrak{Q}$-Analogue Of The Noor Integral Operator, Şahsene Altinkaya
Inclusion Properties Of Lucas Polynomials For Bi-Univalent Functionsintroduced Through The $\Mathfrak{Q}$-Analogue Of The Noor Integral Operator, Şahsene Altinkaya
Turkish Journal of Mathematics
In this paper, by using the $(\mathbf{P},\mathbf{Q})$-Lucas polynomials and the $\mathfrak{q}$-analogue of the Noor integral operator, we aim to build a bridge between the theory of geometric functions and that of special functions.
A Generalization Of $\Pi$-Regular Rings, Peter Danchev
A Generalization Of $\Pi$-Regular Rings, Peter Danchev
Turkish Journal of Mathematics
We introduce the class of so-called { regularly nil clean rings} and systematically study their fundamental characteristic properties accomplished with relationships among certain classical sorts of rings such as exchange rings, Utumi rings etc. These rings of ours naturally generalize the long-known classes of $\pi$-regular and strongly $\pi$-regular rings. We show that the regular nil cleanness possesses a symmetrization which extends the corresponding one for strong $\pi$-regularity that was visualized by Dischinger \cite{Dis}. Likewise, our achieved results substantially improve on establishments presented in two recent papers by Danchev and \v{S}ter \cite{DS} and Danchev \cite{Da}.
Certain Classes Of Multivalent Functions Defined With Higher-Order Derivatives, Muhamed Kamal Aouf, Abdel Moneim Lashin, Teodor Bulboaca
Certain Classes Of Multivalent Functions Defined With Higher-Order Derivatives, Muhamed Kamal Aouf, Abdel Moneim Lashin, Teodor Bulboaca
Turkish Journal of Mathematics
In this paper we derive some properties of multivalent functions belonging to the classes $R_{p,q}(\alpha)$, $B_{p,q}(\alpha)$, and $M_{p,q}(\alpha)$. The results obtained generalize the related works of some authors, and many other new results are obtained.
Mannheim Curves With Modified Orthogonal Frame In Euclidean 3-Space, Mohammad Saleem Lone, Hasan Es, Murat Kemal Karacan, Bahaddi̇n Bükcü
Mannheim Curves With Modified Orthogonal Frame In Euclidean 3-Space, Mohammad Saleem Lone, Hasan Es, Murat Kemal Karacan, Bahaddi̇n Bükcü
Turkish Journal of Mathematics
In this paper, we investigate Mannheim pairs, Frenet--Mannheim curves, and weakened Mannheim curves with respect to the modified orthogonal frame in Euclidean 3-space $(E^3)$. We derive some characterization results of these curves.
Compactness Of The Commutators Of Intrinsic Square Functions On Weighted Lebesgue Spaces, Xiaomei Wu, Xiao Yu
Compactness Of The Commutators Of Intrinsic Square Functions On Weighted Lebesgue Spaces, Xiaomei Wu, Xiao Yu
Turkish Journal of Mathematics
The aim of this paper is to study the compactness for the commutators of intrinsic square functions, including the intrinsic $g_{\lambda}^*$-function and the intrinsic Littlewood-Paley g-function. Using a weighted version of the Frech\'{e}t-Kolmogorov-Riesz theorem, the compactness for their commutators generated with the CMO functions is obtained on the weighted Lebesgue spaces.
Singly Generated Invariant Subspaces In The Hardy Space On The Unit Ball, Beyaz Başak Koca, Nazim Sadik
Singly Generated Invariant Subspaces In The Hardy Space On The Unit Ball, Beyaz Başak Koca, Nazim Sadik
Turkish Journal of Mathematics
In this paper, we give a complete characterization of singly generated invariant subspaces in the Hardy space on the unit ball. Then we construct a singly generated invariant subspace that cannot be generated by a single inner function, contrary to the one-variable case where every invariant subspace is generated by a single inner function. Some important properties of invariant subspaces are also determined for singly generated invariant subspaces.
The Twelvefold Way, The Nonintersecting Circles Problem, And Partitions Of Multisets, Daniel Yaqubi, Toufik Mansour, Madjid Mirzavaziri
The Twelvefold Way, The Nonintersecting Circles Problem, And Partitions Of Multisets, Daniel Yaqubi, Toufik Mansour, Madjid Mirzavaziri
Turkish Journal of Mathematics
Let $n$ be a nonnegative integer and $\mathbb{A}=\{a_1,\ldots,a_k\}$ be a multiset with $k$ positive integers such that $a_1\leqslant\cdots\leqslant a_k$. In this paper, we give a recursive formula for partitions and distinct partitions of positive integer $n$ with respect to a multiset $\mathbb{A}$. We also consider the extension of the twelvefold way. By using this notion, we solve the nonintersecting circles problem, which asks to evaluate the number of ways to draw $n$ nonintersecting circles in the plane regardless of their sizes. The latter also enumerates the number of unlabeled rooted trees with $n+1$ vertices.
On The Number Of $K$-Normal Elements Over Finite Fields, Zülfükar Saygi, Erni̇st Ti̇lenbaev, Çeti̇n Ürti̇ş
On The Number Of $K$-Normal Elements Over Finite Fields, Zülfükar Saygi, Erni̇st Ti̇lenbaev, Çeti̇n Ürti̇ş
Turkish Journal of Mathematics
In this article we give an explicit formula for the number of $k$-normal elements, hence answering Problem 6.1. of Huczynska et al. (Existence and properties of $k$-normal elements over finite fields, Finite Fields Appl 2013; 24: 170-183). Furthermore, for some cases we provide formulas that require the solutions of some linear Diophantine equations. Our results depend on the explicit factorization of cyclotomic polynomials.
Complete Flat Cone Metrics On Punctured Surfaces, İsmai̇l Sağlam
Complete Flat Cone Metrics On Punctured Surfaces, İsmai̇l Sağlam
Turkish Journal of Mathematics
We prove that each complete flat cone metric on a surface with regular or irregular punctures can be triangulated with finitely many types of triangles. We derive the Gauss-Bonnet formula for this kind of cone metrics. In addition, we prove that each free homotopy class of paths has a geodesic representative.
On $\Lambda$-Pseudo $Q$-Bi-Starlike Functions, Prakash Kamble, Mallikarjun Shrigan, Şahsene Altinkaya
On $\Lambda$-Pseudo $Q$-Bi-Starlike Functions, Prakash Kamble, Mallikarjun Shrigan, Şahsene Altinkaya
Turkish Journal of Mathematics
Making use of the $\lambda$-pseudo-$q$-differential operator, we aim to investigate a new, interesting class of bi-starlike functions in the conic domain. Furthermore, we obtain certain sharp bounds of the Fekete--Szeg\"{o} functional for functions belonging to this class.
Jörgensen's Inequality And Purely Loxodromic Two-Generator Free Kleinian Groups, İlker Savaş Yüce
Jörgensen's Inequality And Purely Loxodromic Two-Generator Free Kleinian Groups, İlker Savaş Yüce
Turkish Journal of Mathematics
Let $\xi$ and $\eta$ be two noncommuting isometries of the hyperbolic $3$-space $\mathbb{H}^3$ so that $\Gamma=\langle\xi,\eta\rangle$ is a purely loxodromic free Kleinian group. For $\gamma\in\Gamma$ and $z\in\hyp$, let $d_{\gamma}z$ denote the hyperbolic distance between $z$ and $\gamma(z)$. Let $z_1$ and $z_2$ be the midpoints of the shortest geodesic segments connecting the axis of $\xi$ to the axes of $\eta\xi\eta^{-1}$ and $\eta^{-1}\xi\eta$, respectively. In this manuscript, it is proved that if $d_{\gamma}z_2
Covariant Differential Calculus On ${\Cal Sp}_H^{2, Sali̇h Çeli̇k, İlknur Temli̇
Covariant Differential Calculus On ${\Cal Sp}_H^{2, Sali̇h Çeli̇k, İlknur Temli̇
Turkish Journal of Mathematics
The $h$-deformed symplectic superspaces via a contraction of the $q$-deformed symplectic superspaces are introduced and a covariant differential calculus on the quantum symplectic superspace ${\cal SP}_h^{2 1}$ is presented.
On Strongly Ozaki Bi-Close-To-Convex Functions, Münevver Tezelci̇, Sevtap Sümer Eker
On Strongly Ozaki Bi-Close-To-Convex Functions, Münevver Tezelci̇, Sevtap Sümer Eker
Turkish Journal of Mathematics
In this paper, we introduce and investigate a new subclass of strongly Ozaki bi-close-to-convex functions in the open unit disk. We have also found estimates for the first two Taylor-Maclaurin coefficients for functions belonging to this class. The results presented in this paper have been shown to generalize and improve the work of Brannan and Taha.
Inverse Problem For Sturm-Liouville Differential Operators With Two Constant Delays, Mohammad Shahriari
Inverse Problem For Sturm-Liouville Differential Operators With Two Constant Delays, Mohammad Shahriari
Turkish Journal of Mathematics
In this manuscript, we study nonself-adjoint second-order differential operators with two constant delays. We investigate the properties of the spectral characteristics and the inverse problem of recovering operators from their spectra. An inverse spectral problem is studied of recovering the potential from spectra of two boundary value problems with one common boundary condition. The uniqueness theorem is proved for this inverse problem.
Fuzzy Soft Topological Spaces And The Related Category Fst, Tuğba Han Şi̇mşekler
Fuzzy Soft Topological Spaces And The Related Category Fst, Tuğba Han Şi̇mşekler
Turkish Journal of Mathematics
In this paper, we consider fuzzy soft sets with a different approach where we generalize the idea initially introduced by \v{S}ostak for fuzzy sets. Subsequently, we define the fuzzy set topology categories of fuzzy soft topological spaces and give certain properties of them. Furthermore, we define the initial and the final fuzzy soft topological spaces.
Global Dynamics Of Perturbation Of Certain Rational Differenceequation, Sabina Hrustic, Mustafa Kulenovic, Samra Moranjkic, Zehra Nurkanovic
Global Dynamics Of Perturbation Of Certain Rational Differenceequation, Sabina Hrustic, Mustafa Kulenovic, Samra Moranjkic, Zehra Nurkanovic
Turkish Journal of Mathematics
We investigate the global asymptotic stability of the difference equation of the form \begin{equation*} x_{n+1}=\frac{A x_{n}^{2}+F}{a x_{n}^{2}+e x_{n-1}}, \quad n=0,1,\ldots, \end{equation*}% with positive parameters and nonnegative initial conditions such that $x_0 + x_{-1}>0$. The map associated to this equation is always decreasing in the second variable and can be either increasing or decreasing in the first variable depending on the parametric space. In some cases, we prove that local asymptotic stability of the unique equilibrium point implies global asymptotic stability.
Additive Derivative And Multiplicative Coderivative Operators On Mv-Algebras, Ahmet Hamal
Additive Derivative And Multiplicative Coderivative Operators On Mv-Algebras, Ahmet Hamal
Turkish Journal of Mathematics
In this paper we introduce derivative MV-algebras (or MV-algebras with additive derivative operators). We indicate that the derivative MV-algebras are generalizations of closure MV-algebras. Then we investigate the connection between additive derivative operators on MV-algebras and the derivative operators on the greatest Boolean subalgebras of MV-algebras. Finally, we study some properties of the derivative MV-algebras.
On Band Operators, Bahri̇ Turan, Kazim Özcan
On Band Operators, Bahri̇ Turan, Kazim Özcan
Turkish Journal of Mathematics
Let $G$ and $H$ be Archimedean Riesz spaces. We study the properties of band operators and inverse band operators from $G$ to $H$ and investigate their relations to some well-known classes of operators. Then, we show that under some assumptions on the Riesz spaces $G$ or $H$, if $S$ is a bijective band operator from $G$ into $H$ then $S^{-1}:H\rightarrow G$ is a band operator. Additionally, we give some conditions under which a band operator becomes order bounded.
Coefficient Bounds And Distortion Theorems For The Certain Analytic Functions, Osman Altintaş, Ni̇zami̇ Mustafa
Coefficient Bounds And Distortion Theorems For The Certain Analytic Functions, Osman Altintaş, Ni̇zami̇ Mustafa
Turkish Journal of Mathematics
In this paper, we introduce and investigate an analytic function class $% P_{q}(\lambda,A,B)$ that we call the class of $q-$starlike and $q-$convex functions with respect to the parameter $\lambda $. We give coefficient bounds estimates, distortion bound and growth theorems for the functions belonging to this class.
On The Divisors Of Shifted Primes, Jean Marie De Koninck, Imre Katai
On The Divisors Of Shifted Primes, Jean Marie De Koninck, Imre Katai
Turkish Journal of Mathematics
Let $\tau(n)$ stand for the number of positive divisors of $n$. Given an additive function $f$ and a real number $\alpha\in [0,1)$, let $\displaystyle{h_n(\alpha):= \frac 1{\tau(n)} \sum_{d\mid n \atop \{f(d)\}
Study On The Existence Of Solutions To Two Specific Types Of Differential-Difference Equations, Qiong Wang, Qiongyan Wang
Study On The Existence Of Solutions To Two Specific Types Of Differential-Difference Equations, Qiong Wang, Qiongyan Wang
Turkish Journal of Mathematics
This paper concerns the description of the entire or meromorphic solutions to two certain types of differential-difference equations under some certain conditions. The significance of our results lies in that we find the entire solutions of the second type equation with the form $f=Ae^{Bz}$, where $A,B$ are constants that are completely determined only by coefficients and correlated indices. Our results are accurate in a certain sense and are supplemented by an example. In particular, our results generalize and improve a result of Zhang and Huang, and they are closely related to recent results by Dong and Liao.