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Subclasses Of Uniformly Convex And Starlike Functions Associated Withbessel Functions, Muhammad Naeem, Saqib Hussain, Fethi̇ye Müge Sakar, Tahir Mahmood, Akhter Rasheed
Subclasses Of Uniformly Convex And Starlike Functions Associated Withbessel Functions, Muhammad Naeem, Saqib Hussain, Fethi̇ye Müge Sakar, Tahir Mahmood, Akhter Rasheed
Turkish Journal of Mathematics
In recent years, applications of Bessel differential equations have been commonly used in univalent functions theory. The main object of the present paper is to give some characteristic properties for some subclasses of uniformly starlike and convex functions which are defined here by means of the normalized form of the generalized Bessel function to be univalent in the open unit disc. Furthermore, we also establish some results of these subclasses related to a particular integral operator. Some corresponding consequences of our main results are also considered.
The Eternal Solution To The Cross Curvature Flow Exists In 3-Manifolds Of Negative Sectional Curvature, Weihung Liao
The Eternal Solution To The Cross Curvature Flow Exists In 3-Manifolds Of Negative Sectional Curvature, Weihung Liao
Turkish Journal of Mathematics
Given a closed 3-manifold $M^3$ endowed with a radial symmetric metric of negative sectional curvature, we define the cross curvature flow on $M^3$; using the maximum principle theorem, we demonstrated that the solution to the cross curvature flow exists for all time and converges pointwise to a hyperbolic metric.
Existence Of Solutions Of Bvps For Impulsive Fractional Langevin Equations Involving Caputo Fractional Derivatives, Yuji Liu, Ravi Agarwal
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.
Some Properties For A Class Of Analytic Functions Defined By A Higher-Order Differential Inequality, Oqlah Alrefai
Some Properties For A Class Of Analytic Functions Defined By A Higher-Order Differential Inequality, Oqlah Alrefai
Turkish Journal of Mathematics
Let $\mathcal{B}_p(\alpha,\beta, \lambda;j)$ be the class consisting of functions $f(z)= z^p+\sum_{k=p+1}^{\infty}a_k z^{k},\; p\in \mathbb{N}$ which satisfy $ \mathrm{Re}\left\{\alpha\frac{f^{(j)}(z)}{z^{p-j}}+\beta\frac{f^{(j+1)}(z)}{z^{p-j-1}}+\left(\frac{\beta-\alpha}{2}\right)\frac{f^{(j+2)}(z)}{z^{p-j-2}}\right\}>\lambda,\;\;(z\in \mathbb{U}=\{z:\; z (5-12\ln 2)/(44-48\ln 2)\approx -0.309$ is sufficient condition for any normalized analytic function $f$ to be starlike in $\mathbb{U}$. The results improve and include a number of known results as their special cases.
A Remark On A Paper Of P. B. Djakov And M. S. Ramanujan, Eli̇f Uyanik, Murat Hayretti̇n Yurdakul
A Remark On A Paper Of P. B. Djakov And M. S. Ramanujan, Eli̇f Uyanik, Murat Hayretti̇n Yurdakul
Turkish Journal of Mathematics
Let $\ell$ be a Banach sequence space with a monotone norm in which the canonical system $(e_{n})$ is an unconditional basis. We show that if there exists a continuous linear unbounded operator between $\ell$-Köthe spaces, then there exists a continuous unbounded quasidiagonal operator between them. Using this result, we study the corresponding Köthe matrices when every continuous linear operator between $\ell$-Köthe spaces is bounded. As an application, we observe that the existence of an unbounded operator between $\ell$-Köthe spaces, under a splitting condition, causes the existence of a common basic subspace.
The Generalized Picard Groups For Finite Dimensional $C^*$-Hopf Algebra Coactions On Unital $C^*$-Algebras, Kazunori Kodaka
The Generalized Picard Groups For Finite Dimensional $C^*$-Hopf Algebra Coactions On Unital $C^*$-Algebras, Kazunori Kodaka
Turkish Journal of Mathematics
We shall generalize the notion of the strong Morita equivalence for coactions of a finite dimensional $C^*$-Hopf algebra on a unital $C^*$-algebra and define the Picard groups with respect to the generalized strong Morita equivalence. We call them the generalized Picard groups for coactions of a finite dimensional $C^*$-Hopf algebra on a unital $C^*$-algebra. We shall investigate basic properties of the generalized Picard groups and clarify the relation between the generalized Picard groups and the Picard groups for unital inclusions of unital $C^*$-algebras.
A Geometric Description For Simple And Damped Harmonic Oscillators, Zahi̇de Ok Bayrakdar, Tuna Bayrakdar
A Geometric Description For Simple And Damped Harmonic Oscillators, Zahi̇de Ok Bayrakdar, Tuna Bayrakdar
Turkish Journal of Mathematics
In this work we consider the Riemannian geometry associated with the differential equations of one dimensional simple and damped linear harmonic oscillators. We show that the sectional curvatures are completely determined by the oscillation frequency and the friction coefficient and these physical constants can be thought as obstructions for the manifold to be flat. Moreover, equations of simple and damped harmonic oscillators describe nonisomorphic solvable Lie groups with nonpositive scalar curvature.
Near-Vector Spaces Determined By Finite Fields And Their Fibrations, Karin-Therese Howell
Near-Vector Spaces Determined By Finite Fields And Their Fibrations, Karin-Therese Howell
Turkish Journal of Mathematics
In this paper we study near-vector spaces constructed from copies of finite fields. We show that for these near-vector spaces regularity is equivalent to the quasikernel being the entire space. As a second focus, we study the fibrations of near-vector spaces. We define the pseudo-projective space of a near-vector space and prove that a special class of near-vector spaces, namely those constructed using finite fields, always has a fibration associated with them. We also give a formula for calculating the cardinality of the pseudo-projective space for this class of near-vector spaces.
The Exponential Diophantine Equation $(3am^2-1)^X+(A(A-3)M^2+1)^Y=(Am)^Z$, Nai-Juan Deng, Dan-Yao Wu, Ping-Zhi Yuan
The Exponential Diophantine Equation $(3am^2-1)^X+(A(A-3)M^2+1)^Y=(Am)^Z$, Nai-Juan Deng, Dan-Yao Wu, Ping-Zhi Yuan
Turkish Journal of Mathematics
Let $a,\ m$ be positive integers such that $am\not\equiv0\pmod{3}, 2\nmid a$, and $a>3$. We prove that the exponential Diophantine equation $(3am^2-1)^x+(a(a-3)m^2+1)^y=(am)^z$ has only the positive integer solution $(x,y,z)=(1,1,2)$.
Fekete-Szegö Problem For A General Subclass Of Analytic Functions, Nesli̇han Uyanik
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.
On Factorials In Perrin And Padovan Sequences, Nuretti̇n Irmak
On Factorials In Perrin And Padovan Sequences, Nuretti̇n Irmak
Turkish Journal of Mathematics
Assume that $w_n$ is the $n$th term of either Padovan or Perrin sequence. In this paper, we solve the equation $w_n=m!$ completely.
Ricci-Yamabe Maps For Riemannian Flows And Their Volume Variation And Volume Entropy, Si̇nem Güler, Mircea Crasmareanu
Ricci-Yamabe Maps For Riemannian Flows And Their Volume Variation And Volume Entropy, Si̇nem Güler, Mircea Crasmareanu
Turkish Journal of Mathematics
The aim of this short note is to produce new examples of geometrical flows associated to a given Riemannian flow $g(t)$. The considered flow in covariant symmetric $2$-tensor fields will be called Ricci-Yamabe map since it involves a scalar combination of Ricci tensor and scalar curvature of $g(t)$. Due to the signs of considered scalars the Ricci-Yamabe flow can be also a Riemannian or semi-Riemannian or singular Riemannian flow. We study the associated function of volume variation as well as the volume entropy. Finally, since the two-dimensional case was the most commonly addressed situation we express the Ricci flow equation …
On Congruences For $Q$-Analogues Of Ballot Numbers, Si̇bel Koparal
On Congruences For $Q$-Analogues Of Ballot Numbers, Si̇bel Koparal
Turkish Journal of Mathematics
In this paper, we examine some congruences with $q$-analogues of ballot numbers. For example, for $n>1$ and $% d=0,1,...,n-1$, \begin{eqnarray*} &&\sum\limits_{k=1}^{n-d}q^{k}B_{k,d}^{q}\equiv -2+\left( -1\right) ^{n-d}\left( \frac{n-d+1}{3}\right) q^{-\frac{1}{3}\binom{n-d}{2}}-\left( \frac{n-d-1% }{3}\right) q^{d+1-\frac{1}{3}\binom{n-d-2}{2}} \pmod{\Phi _{n}\left( q\right)} , \end{eqnarray*}% with the Legendre symbol $\left( \frac{.}{3}\right) ,~$the$~q$-analogue of ballot number $B_{n,d}^{q}$, and the $n$th cyclotomic polynomial $% \Phi _{n}\left( q\right) $.
Radii Of Starlikeness And Convexity Of $Q$-Mittag-Leffler Functions, Evri̇m Toklu
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.
Derivations Of Generalized Quaternion Algebra, Eyüp Kizil, Yasemi̇n Alagöz
Derivations Of Generalized Quaternion Algebra, Eyüp Kizil, Yasemi̇n Alagöz
Turkish Journal of Mathematics
The purpose of this paper is to determine derivations of the algebra $H_{\alpha ,\beta }$ of generalized quaternions over the reals and hence to obtain the algebra $Der(H_{\alpha ,\beta })$ of derivations of $H_{\alpha ,\beta }$. Once we know derivations we might decompose $Der(H_{\alpha ,\beta })$ in terms of its inner and/or central derivations whenever they exist. Apart from $Der(H_{\alpha ,\beta })$ we would also be able to obtain generalized derivations, which have been studied by analysts in the context of algebras of some normed spaces, and of prime and semiprime rings.
Automorphisms Of Free Metabelian Leibniz Algebras Of Rank Three, Tuba Taş Adiyaman, Zeynep Özkurt
Automorphisms Of Free Metabelian Leibniz Algebras Of Rank Three, Tuba Taş Adiyaman, Zeynep Özkurt
Turkish Journal of Mathematics
In this work, we determine the structure of the automorphism group of the free metabelian Leibniz algebra of rank three over a field K of characteristic zero.
On The N-Strong Drazin Invertibility In Rings, Honglin Zou, Dijana Mosic, Kezheng Zuo, Yinlan Chen
On The N-Strong Drazin Invertibility In Rings, Honglin Zou, Dijana Mosic, Kezheng Zuo, Yinlan Chen
Turkish Journal of Mathematics
Let R be a ring and n be a positive integer. In this paper, further results on the n-strong Drazin inverse are obtained in a ring. We prove that a ∈ R is n-strongly Drazin invertible if and only if a-an+1 is nilpotent. In terms of this characterization, the extensions of Cline's formula and Jacobson's lemma for this inverse are proved. Moreover, the n-strong Drazin invertibility for the sums of two elements is considered. We prove that a,b ∈ R are n-strongly Drazin invertible if and only if a + b is n-strongly Drazin invertible, under the condition ab = …
Sherman's Inequality And Its Converse For Strongly Convex Functions Withapplications To Generalizedf-Divergences, Slavica Ivelic Bradanovic
Sherman's Inequality And Its Converse For Strongly Convex Functions Withapplications To Generalizedf-Divergences, Slavica Ivelic Bradanovic
Turkish Journal of Mathematics
Considering the weighted concept of majorization, Sherman obtained generalization of majorization inequality for convex functions known as Sherman's inequality. We extend Sherman's result to the class of n-strongly convex functions using extended idea of convexity to the class of strongly convex functions. We also obtain upper bound for Sherman's inequality, called the converse Sherman inequality, and as easy consequences we get Jensen's as well as majorization inequality and their conversions for strongly convex functions. Obtained results are stronger versions for analogous results for convex functions. As applications, we introduced a generalized concept of f-divergence and derived some reverse relations for …
Study On The Q-Analogue Of A Certain Family Of Linear Operators, Shujaat Ali Shah, Khalida Inayat Noor
Study On The Q-Analogue Of A Certain Family Of Linear Operators, Shujaat Ali Shah, Khalida Inayat Noor
Turkish Journal of Mathematics
Inthispaper, weintroducetheq-analogueofacertainfamilyoflinearoperatorsingeometricfunctiontheory. Our main purpose is to define some subclasses of analytic functions by means of the q-analogue of linear operators and investigate various inclusion relationships with integral preserving properties.
Unbounded Absolutely Weak Dunford-Pettis Operators, Nazi̇fe Erkurşun Özcan, Ni̇yazi̇ Anil Gezer, Omid Zabeti
Unbounded Absolutely Weak Dunford-Pettis Operators, Nazi̇fe Erkurşun Özcan, Ni̇yazi̇ Anil Gezer, Omid Zabeti
Turkish Journal of Mathematics
In the present article, we expose various properties of unbounded absolutely weak Dunford?Pettis and unbounded absolutely weak compact operators on a Banach lattice E. In addition to their topological and lattice properties, we investigate relationships between M-weakly compact operators, L-weakly compact operators, and order weakly compact operators with unbounded absolutely weak Dunford-Pettis operators. We show that the square of any positive uaw-Dunford-Pettis (M-weakly compact) operator on an order continuous Banach lattice is compact. Many examples are given to illustrate the essential conditions.
The Intrinsic Metric And Geodesics On The Sierpinski Gasket Sg(3), Yunus Özdemi̇r
The Intrinsic Metric And Geodesics On The Sierpinski Gasket Sg(3), Yunus Özdemi̇r
Turkish Journal of Mathematics
We give an explicit expression for the intrinsic metric on the Sierpinski gasket SG(3) (the mod-3 Sierpinski gasket) via code representation of its points. We also investigate the geodesics of SG(3) and determine the number of geodesics between two points.
On The Regularity Of The Solution Map Of The Euler-Poisson System, Hasan İnci̇
On The Regularity Of The Solution Map Of The Euler-Poisson System, Hasan İnci̇
Turkish Journal of Mathematics
In this paper we consider the Euler--Poisson system (describing a plasma consisting of positive ions with a negligible temperature and massless electrons in thermodynamical equilibrium) on the Sobolev spaces $H^s(\mathbb{R}^3)$, $s > 5/2$. Using a geometric approach we show that for any time $T > 0$ the corresponding solution map, $(\rho_0,u_0) \mapsto (\rho(T),u(T))$, is nowhere locally uniformly continuous. On the other hand it turns out that the trajectories of the ions are analytic curves in $\mathbb{R}^3$.
Classifying Semisymmetric Cubic Graphs Of Order 20p, Mohsen Shahsavaran, Mohammad Reza Darafsheh
Classifying Semisymmetric Cubic Graphs Of Order 20p, Mohsen Shahsavaran, Mohammad Reza Darafsheh
Turkish Journal of Mathematics
A simple graph is called semisymmetric if it is regular and edge-transitive but not vertex-transitive. In this paper we classify all connected cubic semisymmetric graphs of order 20p, p prime.
Minimal Free Resolutions Of The Tangent Cones For Gorenstein Monomial Curves, Pinar Mete, Esra Emi̇ne Zengi̇n
Minimal Free Resolutions Of The Tangent Cones For Gorenstein Monomial Curves, Pinar Mete, Esra Emi̇ne Zengi̇n
Turkish Journal of Mathematics
We study the minimal free resolution of the tangent cone of Gorenstein monomial curves in affine 4-space. We give the explicit minimal free resolution of the tangent cone of noncomplete intersection Gorenstein monomial curve whose tangentcone has fiveminimal generators and showthat the possible Betti sequences are (1,5,6,2) and (1,5,5,1). Moreover, we compute the Hilbert function of the tangent cone of these families as a result.
The Relation Between B-Weakly Compact Operator And Kb-Operator, Bahri̇ Turan, Bi̇rol Altin
The Relation Between B-Weakly Compact Operator And Kb-Operator, Bahri̇ Turan, Bi̇rol Altin
Turkish Journal of Mathematics
Our aim is to solve the problem asked by Bahramnezhad and Azar in "KB-operators on Banach lattices and their relationships with Dunford-Pettis and order weakly compact operators". We show that a continuous operators R from a Banach lattice N into a Banach space M is a b-weakly compact operator if and only if R is a KB-operator.
Extended S-Supplement Submodules, Yilmaz Durğun
Extended S-Supplement Submodules, Yilmaz Durğun
Turkish Journal of Mathematics
In this paper, we introduced and studied extended S-supplement submodules. A submodule U of a module V is called extended S-supplement submodule in V if there exists a submodule T of V such that V = T + U and U ∩ T is Goldie torsion. Extended S-supplement submodule is a dual notion of extended S-closed submodule. The class of extended S-supplement sequences is a proper class which is generated by nonsingular modules injectively. We studied coinjective objects of this class. Moreover, extended S-supplemented modules are also investigated. We present new characterizations of Z2(RR) -semiperfect rings and SI-rings by extended …
Some Properties Of Riemannian Geometry Of The Tangent Bundle Of Lie Groups, Davood Seifipour, Esmaeil Peyghan
Some Properties Of Riemannian Geometry Of The Tangent Bundle Of Lie Groups, Davood Seifipour, Esmaeil Peyghan
Turkish Journal of Mathematics
We consider a bi-invariant Lie group (G, g) and we equip its tangent bundle TG with the left invariant Riemannian metric introduced in the paper of Asgari and Salimi Moghaddam. We investigate Einstein-like, Ricci soliton, and Yamabe soliton structures on TG. Then we study some geometrical tensors on TG such as Cotton, Schouten, Weyl, and Bach tensors, and we also compute projective and concircular and m-projective curvatures on TG. Finally, we compute the Szabo operator and Jacobi operator on the tangent Lie group TG.
Coefficient Estimates For A New Subclasses Of Λ-Pseudo Biunivalent Functions Withrespect To Symmetrical Points Associated With The Horadam Polynomials, Adnan Alamoush
Turkish Journal of Mathematics
In the present article, we introduce two new subclasses of λ-pseudo biunivalent functions with respect to symmetrical points in the open unit disk U defined by means of the Horadam polynomials. For functions belonging to these subclasses, estimates on the Taylor -Maclaurin coefficients ja2j and ja3j are obtained. Fekete-Szegö inequalities of functions belonging to these subclasses are also founded. Furthermore, we point out several new special cases of our results.
Tauberian Conditions Under Which Convergence Follows From Summability By Thediscrete Power Series Method, Sefa Anil Sezer, İbrahi̇m Çanak
Tauberian Conditions Under Which Convergence Follows From Summability By Thediscrete Power Series Method, Sefa Anil Sezer, İbrahi̇m Çanak
Turkish Journal of Mathematics
In this paper, we obtain Tauberian conditions to recover convergence of a series from its discrete power series summability under certain conditions. As special cases of our main results, we get discrete analogues of some well-known Tauberian theorems in the literature.
A Metric Invariant Of Möbius Transformations, Teerapong Suksumran, Oğuzhan Demi̇rel
A Metric Invariant Of Möbius Transformations, Teerapong Suksumran, Oğuzhan Demi̇rel
Turkish Journal of Mathematics
The complex unit disk $\mathbb{D} = \{z\in\mathbb{C}\colon z < 1\}$ is endowed with Möbius addition $\oplus_M$ defined by $$ w\oplus_M z = \dfrac{w+z}{1+\overline{w}z}. $$ We prove that the metric $d_T$ defined on $\mathbb{D}$ by $d_T(w, z) = \tan^{-1} -w\oplus_M z $ is an invariant of Möbius transformations carrying $\mathbb{D}$ onto itself. We also prove that $(\mathbb{D}, d_T)$ and $(\mathbb{D}, d_P)$, where $d_P$ denotes the Poincaré metric, have the same isometry group and then classify the isometries of $(\mathbb{D}, d_T)$.