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A Sequential Fractional Differential Problem Of Pantograph Type:Existence Uniqueness And Illustrations, Soumia Belarbi, Zoubir Dahmani, Mehmet Zeki̇ Sarikaya
A Sequential Fractional Differential Problem Of Pantograph Type:Existence Uniqueness And Illustrations, Soumia Belarbi, Zoubir Dahmani, Mehmet Zeki̇ Sarikaya
Turkish Journal of Mathematics
In this study, a new class of sequential fractional differential problems of pantograph type is introduced. New existence and uniqueness criteria for the existence and uniqueness of solutions are discussed. Some existence results using Darbo's fixed point and measure of noncompactness are also studied. At the end, two illustrative examples are discussed.
A Refinement Of Newton And Maclaurin Inequalities Through Abstract Convexity, Gülteki̇n Tinaztepe, Ramazan Tinaztepe
A Refinement Of Newton And Maclaurin Inequalities Through Abstract Convexity, Gülteki̇n Tinaztepe, Ramazan Tinaztepe
Turkish Journal of Mathematics
In this study, the refinements of Maclaurin's and Newton's inequalities are given. These refinements are obtained by applying the results on optimality conditions of abstract convex functions. When doing this, we obtain lower bounds for the solutions of some special rational equations.
Elliptical Kinematics Of The Accretive Surface Growth, Zehra Özdemi̇r, Gül Güner
Elliptical Kinematics Of The Accretive Surface Growth, Zehra Özdemi̇r, Gül Güner
Turkish Journal of Mathematics
The stresses within the soft tissue are not constant for some shell surfaces. They vary with position along the mantle edge. In this paper, we show that elliptical geometry is more convenient to describe this type of surface. Thus, we introduce the elliptical kinematics along an initial curve and construct some accretive surfaces with an elliptical cross-section. In fact, these surfaces are not only curves with an elliptical cross-sectional curve, but also the material points of the surface follow an elliptical trajectory during their formation. This situation can be easily explained through elliptical motion and elliptical quaternion algebra. Then, we …
Some Notes On Crossed Semimodules, Sedat Temel
Some Notes On Crossed Semimodules, Sedat Temel
Turkish Journal of Mathematics
In this paper, we introduce the notion of lifting via a homomorphism of monoids for a crossed semimodule and give some properties. Further, we characterize actions and coverings of Schreier internal categories in the category Mon of monoids and prove the natural equivalence between their categories. Then, we prove that liftings of a certain crossed semimodule are naturally equivalent to the actions of Schreier internal category in Mon, where the Schreier internal category corresponds to the crossed semimodule. Finally, we give a relation between crossed semimodules and simplicial monoids.
On Extended Interpolative Single And Multivalued $F$-Contractions, İsa Yildirim
On Extended Interpolative Single And Multivalued $F$-Contractions, İsa Yildirim
Turkish Journal of Mathematics
The main objective of this paper is to study an extended interpolative single and multivalued Hardy-Rogers type $F$-contractions in complete metric spaces. We prove some fixed point theorems for such mappings. Further, we give an application to integral equations to verify our main results. The results presented in this paper improve the recent works of Karapinar et al. [12] and Mohammadi et al. [16].
Relation Between Matrices And The Suborbital Graphs By The Special Number Sequences, Ümmügülsün Akbaba, Ali̇ Hi̇kmet Değer
Relation Between Matrices And The Suborbital Graphs By The Special Number Sequences, Ümmügülsün Akbaba, Ali̇ Hi̇kmet Değer
Turkish Journal of Mathematics
under circuit and forest conditions. Special number sequences and special vertex values of minimal length paths in suborbital graphs have been associated in our previous studies. In these associations, matrix connections of the special continued fractions $\mathcal K (-1/-k)$, where $k\in \mathbb{Z}^{+}, \ k\geq 2$ with the values of the special number sequences are used and new identities are obtained. In this study, by producing new matrices, new identities related to Fibonacci, Lucas, Pell, and Pell-Lucas number sequences are found by using both recurrence relations and matrix connections of the continued fractions. In addition, the farthest vertex values of the …
A Köthe-Toeplitz Dual Of A Generalized Cesaro Difference Sequence Space, A Degenerate Lorentz Space, Their Corresponding Function Spaces And Fpp, Veysel Nezi̇r, Ni̇zami̇ Mustafa
A Köthe-Toeplitz Dual Of A Generalized Cesaro Difference Sequence Space, A Degenerate Lorentz Space, Their Corresponding Function Spaces And Fpp, Veysel Nezi̇r, Ni̇zami̇ Mustafa
Turkish Journal of Mathematics
In 1970, Cesaro sequence spaces was introduced by Shiue. In 1981, Kızmaz defined difference sequence spaces for ${\ell }^{\infty }$, ${\mathrm{c}}_0$ and $\mathrm{c}$. Then, in 1983, Orhan introduced Cesaro difference sequence spaces. Both works used difference operator and investigated the Köthe-Toeplitz dual for the new Banach spaces they introduced. Later, various authors generalized these new spaces, especially the one introduced by Orhan. In this study, first we discuss the fixed point property for these spaces and for the corresponding function space of the Köthe-Toeplitz dual. Moreover, we consider another generalized space which is a degenerate Lorentz space because the spaces …
$P$-Strong Convergence With Respect To An Orlicz Function, Ni̇lay Şahi̇n Bayram
$P$-Strong Convergence With Respect To An Orlicz Function, Ni̇lay Şahi̇n Bayram
Turkish Journal of Mathematics
The concepts of strong convergence, statistical convergence, and uniform integrability are of some interest in convergence theories. Recently Ünver and Orhan [19] have introduced the concepts of $P$-strong and $P$-statistical convergences with the help of power series methods and established a relationship between them. In the present paper, we introduce the notion of $P$-strong convergence with respect to an Orlicz function and prove that all these three concepts are boundedly equivalent provided that Orlicz function satisfies $\triangle _{2}-$condition. We also get an improvement of this result by using the concept of uniform integrability.
Non-Solvable Groups All Of Whose Indices Are Odd-Square-Free, Sajjad Mahmood Robati, Roghayeh Hafezieh Balaman
Non-Solvable Groups All Of Whose Indices Are Odd-Square-Free, Sajjad Mahmood Robati, Roghayeh Hafezieh Balaman
Turkish Journal of Mathematics
Given a finite group $G$ and $x\in G$, the class size of $x$ in $G$ is called odd-square-free if it is not divisible by the square of any odd prime number. In this paper, we show that if $G$ is a nonsolvable finite group, all of whose class sizes are odd-square-free, then we have some control on the structure of $G$, which is an answer to the dual of the question mentioned by Huppert in [5].
Minimal Generators Of Annihilators Of Even Neat Elements In The Exterior Algebra Footnotesize, Songül Esi̇n
Minimal Generators Of Annihilators Of Even Neat Elements In The Exterior Algebra Footnotesize, Songül Esi̇n
Turkish Journal of Mathematics
This paper deals with an exterior algebra of a vector space whose base field is of positive characteristic. In this work, a minimal set of generators forming the annihilator of even neat elements of such an exterior algebra is exhibited. The annihilator of some special type of even neat elements is determined to prove the conjecture established in [3]. Moreover, a vector space basis for the annihilators under consideration is calculated.
$K$-Fibonacci Numbers And $K$-Lucas Numbers And Associated Bipartite Graphs, Gwangyeon Lee
$K$-Fibonacci Numbers And $K$-Lucas Numbers And Associated Bipartite Graphs, Gwangyeon Lee
Turkish Journal of Mathematics
In [6], [8] and [10], the authors studied the generalized Fibonacci numbers. Also, in [7], the author found a class of bipartite graphs whose number of $1$-factors is the $n$th $k$-Lucas numbers. In this paper, we give a new relationship between $g_n^{(k)}$ and $l_n^{(k)}$ and the number of $1$-factors of a bipartite graph.
The Radii Of Starlikeness And Convexity Of The Functions Including Derivatives Of Bessel Functions, Sercan Kazimoğlu, Erhan Deni̇z
The Radii Of Starlikeness And Convexity Of The Functions Including Derivatives Of Bessel Functions, Sercan Kazimoğlu, Erhan Deni̇z
Turkish Journal of Mathematics
Let $J_\nu(z)$ denote the Bessel function of the first kind of order $\nu.$ In this paper, our aim is to determine the radii of starlikeness and convexity for three kind of normalization of the function $N_\nu(z)=az^{2}J_{\nu }^{\prime \prime }(z)+bzJ_{\nu }^{\prime }(z)+cJ_{\nu }(z)$ in the case where zeros are all real except for a single pair, which are conjugate purely imaginary. The key tools in the proof of our main results are the Mittag-Leffler expansion for function $N_\nu(z)$ and properties of real and complex zeros of it.
Properties Of Abelian-By-Cyclic Shared By Soluble Finitely Generated Groups, Fares Gherbi, Nadir Trabelsi
Properties Of Abelian-By-Cyclic Shared By Soluble Finitely Generated Groups, Fares Gherbi, Nadir Trabelsi
Turkish Journal of Mathematics
Our main result states that if $G$ is a finitely generated soluble group having a normal Abelian subgroup $A$, such that $G/A$ and $\left\langle x,a\right\rangle $ are nilpotent (respectively, finite-by-nilpotent, periodic-by-nilpotent, nilpotent-by-finite, finite-by-supersoluble, supersoluble-by-finite) for all $(x,a)\in G\times A$, then so is $G$. We deduce that if $\mathfrak{X}$ is a subgroup and quotient closed class of groups and if all $2$-generated Abelian-by-cyclic groups of $\mathfrak{X}$ are nilpotent (respectively, finite-by-nilpotent, periodic-by-nilpotent, nilpotent-by-finite, finite-by-supersoluble, supersoluble-by-finite), then so are all finitely generated soluble groups of $\mathfrak{X}$. We give examples that show that our main result is not true for other classes of groups, …
Two Classes Of Permutation Polynomials With Niho Exponents Over Finite Fields With Even Characteristic, Qian Liu
Turkish Journal of Mathematics
In this paper, by transforming the permutation problem into the root distribution problem in the unit circle of certain quadratic and cubic equations, we investigate the permutation behavior of the type $f(x)=x+x^{2^{3m}-2^m+1}+x^{2^{4m}-2^{3m}+2^m}$ over $F_{2^{4m}}$ and $f(x)=x+x^{2^m}+x^{2^{m+1}-1}+ax^{2^{2m}-2^m+1}$ over $F_{2^{2m}}$, respectively.
On A Class Of Generalized Humbert-Hermite Polynomials Via Generalized Fibonacci Polynomials, Mahmood Ahmad Pathan, Wassem Ahmad Khan
On A Class Of Generalized Humbert-Hermite Polynomials Via Generalized Fibonacci Polynomials, Mahmood Ahmad Pathan, Wassem Ahmad Khan
Turkish Journal of Mathematics
A unified presentation of a class of Humbert's polynomials in two variables which generalizes the well known class of Gegenbauer, Humbert, Legendre, Chebycheff, Pincherle, Horadam, Kinney, Horadam-Pethe, Djordjevi${\acute{c}}$, Gould, Milovanovi${\acute{c}}$ and Djordjevi${\acute{c}}$, Pathan and Khan polynomials and many not so called 'named' polynomials has inspired the present paper. We define here generalized Humbert-Hermite polynomials of two variables. Several expansions of Humbert-Hermite polynomials, Hermite-Gegenbaurer (or ultraspherical) polynomials
Construction Of Minimal Linear Codes With Few Weights From Weakly Regular Plateaued Functions, Ahmet Sinak
Construction Of Minimal Linear Codes With Few Weights From Weakly Regular Plateaued Functions, Ahmet Sinak
Turkish Journal of Mathematics
The construction of (minimal) linear codes from functions over finite fields has been greatly studied in the literature, since determining the parameters of codes based on functions is rather easy due to the nice structures of functions. In this paper, we derive $3$-weight and $4$-weight linear codes from weakly regular plateaued functions in the recent construction method of linear codes over the odd characteristic finite fields. The Hamming weights and weight distributions for codes are, respectively, determined by using the Walsh transform values and Walsh distributions of the employed functions. We also derive projective $3$-weight punctured codes with good parameters …
Multiplicative Conformable Fractional Dirac System, Sertaç Göktaş, Hi̇kmet Kemaloğlu, Emrah Yilmaz
Multiplicative Conformable Fractional Dirac System, Sertaç Göktaş, Hi̇kmet Kemaloğlu, Emrah Yilmaz
Turkish Journal of Mathematics
In multiplicative fractional calculus, the well-known Dirac system in fractional calculus is redefined. The aim of this study is to analyze some spectral properties such as self-adjointness of the operator, structure of all eigenvalues, orthogonality of distinct eigenfunctions, etc. for this system. Moreover, Green's function in multiplicative case is reconstructed for this system.
Berezin Symbol Inequalities Via Grüss Type Inequalities And Related Questions, Rami̇z Tapdigoğlu, Mübari̇z Garayev, Najla Altwaijry
Berezin Symbol Inequalities Via Grüss Type Inequalities And Related Questions, Rami̇z Tapdigoğlu, Mübari̇z Garayev, Najla Altwaijry
Turkish Journal of Mathematics
We prove some new inequalities for Berezin symbols of operators via classical Grüss type inequalities. Some other related questions are also discussed.
Compact Matrix Operators On Banach Space Of Absolutely $K$-Summable Series, Fadi̇me Gökçe
Compact Matrix Operators On Banach Space Of Absolutely $K$-Summable Series, Fadi̇me Gökçe
Turkish Journal of Mathematics
In a more recent paper [23], Banach spaces of absolutely $k$-summable series $\left\vert T_{\phi }\right\vert _{k}$ have been introduced and studied by Sarıgöl and Agarwal. In this paper, we characterize matrix and compact operators from the space $\left\vert T_{\phi }\right\vert _{k}$ to the classical spaces $c_{0},c$ and $l_{\infty },$ by determining identities or estimates for operator norms and the Hausdorff measure of noncompactness.
Clairaut Invariant Riemannian Maps With Kahler Structure, Akhilesh Yadav, Kiran Meena
Clairaut Invariant Riemannian Maps With Kahler Structure, Akhilesh Yadav, Kiran Meena
Turkish Journal of Mathematics
In this paper, we study Clairaut invariant Riemannian maps from Kahler manifolds to Riemannian manifolds, and from Riemannian manifolds to Kahler manifolds. We find necessary and sufficient conditions for the curves on the total spaces and base spaces of invariant Riemannian maps to be geodesic. Further, we obtain necessary and sufficient conditions for invariant Riemannian maps from Kahler manifolds to Riemannian manifolds to be Clairaut invariant Riemannian maps. Moreover, we obtain a necessary and sufficient condition for invariant Riemannian maps from Riemannian manifolds to Kahler manifolds to be Clairaut invariant Riemannian maps. We also give nontrivial examples of Clairaut invariant …
Metric Connection On Tangent Bundle With Berger-Type Deformed Sasaki Metric, Lokman Bi̇len
Metric Connection On Tangent Bundle With Berger-Type Deformed Sasaki Metric, Lokman Bi̇len
Turkish Journal of Mathematics
Let $TM$ be the tangent bundle over an almost antipara-Hermitian manifold endowed with Berger-type deformed Sasaki metric $% ^{BS}g$. In this paper, we introduce the deformed Sasaki metric which Berger-type and study the metric connection of this metric on the tangent bundle. We give some curvature properties of this metric and characterization of projective vector field which preserving the fiber of $\left( TM, ^{BS}g\right) $. Next, we present some geometric results concerning them.
Some Properties Of The Matrix Wiener Transform With Related Topics On Hilbert Space, Hyun Soo Chung
Some Properties Of The Matrix Wiener Transform With Related Topics On Hilbert Space, Hyun Soo Chung
Turkish Journal of Mathematics
Main purpose of this paper is to obtain fundamental relationships for the integrals and the matrix Wiener transforms on Hilbert space. Using some technics and properties of matrices of real numbers, we state some algebraic structure of matrices. We then establish evaluation formulas with examples. Furthermore, we define the matrix Wiener transform, and investigate some properties of the matrix Wiener transform. Finally, we establish relationships for the matrix Wiener transform.
Application Of Gegenbauer Polynomials For Biunivalent Functions Defined By Subordination, Fethi̇ye Müge Sakar, Saqib Hussain, Ibrar Ahmad
Application Of Gegenbauer Polynomials For Biunivalent Functions Defined By Subordination, Fethi̇ye Müge Sakar, Saqib Hussain, Ibrar Ahmad
Turkish Journal of Mathematics
We present and investigate a new subclass of biunivalent functions by applying Gegenbouer polynomials in this paper. Also, we find nonsharp estimates on the first two coefficients $\left \vert b_{0}\right \vert $ and $% \left \vert b_{1}\right \vert $ for functions belonging to this subclass. Furthermore, the Fekete-Szegö inequality $\left \vert b_{1}-\eta b_{0}^{2}\right \vert $ for this subclass is obtained. We also point out some consequences of results.
Oscillation Criteria For Third-Order Neutral Differential Equations With Unbounded Neutral Coefficients And Distributed Deviating Arguments, Yibing Sun, Yige Zhao, Qiangqiang Xie
Oscillation Criteria For Third-Order Neutral Differential Equations With Unbounded Neutral Coefficients And Distributed Deviating Arguments, Yibing Sun, Yige Zhao, Qiangqiang Xie
Turkish Journal of Mathematics
This paper focuses on the oscillation criteria for the third-order neutral differential equations with unbounded neutral coefficients and distributed deviating arguments. Using comparison principles, new sufficient conditions improve some known existing results substantially due to less constraints on the considered equation. At last, two examples are established to illustrate the given theorems.
On The Paper "Generalized Hyperideals In Locally Associativeleft Almost Semihypergroups", Niovi Kehayopulu
On The Paper "Generalized Hyperideals In Locally Associativeleft Almost Semihypergroups", Niovi Kehayopulu
Turkish Journal of Mathematics
This note is written to show that the definition of the ${\cal L}{\cal A}$-semihypergroup by V. Amjad, K. Hila and F. Yousafzai "Generalized hyperideals in locally associative left almost semihypergroups, New York J. Math. 2014" should be corrected and that it is not enough to replace the multiplication "$\cdot$" of an ${\cal L}{\cal A}$-semigroup by the hyperoperation "$\circ$" to pass from an ${\cal L}{\cal A}$-semigroup to an ${\cal L}{\cal A}$-semihypergroup. The two examples of the paper based on the definition of the ${\cal L}{\cal A}$-semihypergroup are wrong that is a further indication that this definition needs correction. According to the …
On The Inclusion Properties For $\Vartheta $-Spirallike Functions Involving Both Mittag-Leffler And Wright Function, Şahsene Altinkaya
On The Inclusion Properties For $\Vartheta $-Spirallike Functions Involving Both Mittag-Leffler And Wright Function, Şahsene Altinkaya
Turkish Journal of Mathematics
By making use of the both Mittag-Leffler and Wright function, we establish a new subfamily of the class $S_{\vartheta }$ of $\vartheta $-spirallike functions. The main object of the paper is to provide sufficient conditions for a function to be in this newly established class and to discuss subordination outcomes.
Boundedness For Variable Fractional Integral Operators And Their Commutators On Herz-Hardy Spaces With Variable Exponent, Yinping Xin
Turkish Journal of Mathematics
Let $E\subset\mathbb{R}^n$ be a bounded open set. In this paper, we establish the boundedness of variable fractional integral operators and their commutators on variable Herz-Hardy spaces $H\dot{K}^{\alpha(\cdot),q(\cdot)}_{p(\cdot)}(E)$ with three variable exponents by using the atomic decomposition.
On Hom-F-Manifold Algebras And Quantization, Abdelkader Benhassine, Taoufik Chtioui, Mohamed Ali Maalaoui, Sami Mabrouk
On Hom-F-Manifold Algebras And Quantization, Abdelkader Benhassine, Taoufik Chtioui, Mohamed Ali Maalaoui, Sami Mabrouk
Turkish Journal of Mathematics
The notion of a $F$-manifold algebras is an algebraic description of a $F$-manifold. In this paper, we introduce the notion of Hom-$F$-manifold algebras which is generalisation of $F$-manifold algebras and Hom-Poisson algebras. We develop the representation theory of Hom-$F$-manifold algebras and generalize the notion of Hom-pre-Poisson algebras by introducing the Hom-pre-$F$-manifold algebras which give rise to a Hom-$F$-manifold algebra through the subadjacent commutative Hom-associative algebra and the subadjacent Hom-Lie algebra. Using Ο-operators on a Hom-$F$-manifold algebras we construct a Hom-pre-$F$-manifold algebras on a module. Then, we study Hom-pre-Lie formal deformations of commutative Hom-associative algebra and we prove that Hom-$F$-manifold algebras …
Rough Approximations Based On Different Topologies Via Ideals, Ayşegül Çaksu Güler, Esra Dalan Yildirim, Oya Özbakir
Rough Approximations Based On Different Topologies Via Ideals, Ayşegül Çaksu Güler, Esra Dalan Yildirim, Oya Özbakir
Turkish Journal of Mathematics
In this paper, we generalize the notations of rough sets based on the topological space. Firstly, we produce various topologies by using the concept of ideal, $C_j$-neighbourhoods and $P_j$-neighbourhoods. When we compare these topologies with previous topologies, we see that these topologies are more general. Then we introduce new methods to find the approximations by using these generated topologies. When we compare these methods with the previous methods, we see that these methods are more accurate.