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The Generalization Of Rectifying Helices, Bülent Altunkaya
The Generalization Of Rectifying Helices, Bülent Altunkaya
Turkish Journal of Mathematics
This work establishes connections between different classes of arbitrary speed rectifying helices. We further analyze how the involute of a space curve can exhibit spherical helicity and how the evolute can inherit rectifying properties, thereby providing an alternative characterization of these helices. These relationships, along with their interplay with involutes and evolutes, are supported by illustrative examples that offer deeper insights into their geometric properties.
Applications Of A New Linear Operator Involving Dziok-Srivastava Operator And Bessel Function Of The First Kind, Daniela Andrada Bardac-Vlada, Georgia Irina Oros
Applications Of A New Linear Operator Involving Dziok-Srivastava Operator And Bessel Function Of The First Kind, Daniela Andrada Bardac-Vlada, Georgia Irina Oros
Turkish Journal of Mathematics
This study introduces a new linear operator constructed from the well-known Dziok–Srivastava linear hypergeometric operator, the Bessel function of the first kind, and convolution. Applying the new operator, a class of functions with positive real part is defined and investigated concerning inclusion relations, the necessary and sufficient conditions for functions to belong to this class, as well as starlikeness and convexity conditions. The properties of the new class to be convex of a certain order, close-to-convex and starlike of a certain order are highlighted and examples are also included to prove that the new outcome is applicable. The methods employed …
The Geometry Of Semislant Submersions Whose Total Manifolds Are Locally Conformal Kähler Manifolds, Çağrihan Çi̇men, Hakan Mete Taştan
The Geometry Of Semislant Submersions Whose Total Manifolds Are Locally Conformal Kähler Manifolds, Çağrihan Çi̇men, Hakan Mete Taştan
Turkish Journal of Mathematics
We study semislant submersions whose total manifolds are locally conformal Kähler manifolds. We provide conditions for the total geodesicity and integrability of the distributions involved in the definition. Next, we establish a condition under which such a submersion is a Clairaut submersion. Finally, we obtain some optimal inequalities for a semislant submersion whose total manifold is Hopf space form.
Some Properties Of Rescaled Sasaki Type Metric On The Coframe Bundle, Habil Fattayev, Arif Salimov
Some Properties Of Rescaled Sasaki Type Metric On The Coframe Bundle, Habil Fattayev, Arif Salimov
Turkish Journal of Mathematics
In this paper we introduce the rescaled Sasaki type metric on the coframe bundle of a Riemannian manifold and investigate the Levi-Civita connection, curvature tensor, paracomplex structures of coframe bundle with this metric
Janowski Close-To-Convexity Harmonic Mappings, Bushra Arif, Jacek Dziok, Wasim Ul Haq, Mohsan Raza
Janowski Close-To-Convexity Harmonic Mappings, Bushra Arif, Jacek Dziok, Wasim Ul Haq, Mohsan Raza
Turkish Journal of Mathematics
In the present work we introduce harmonic univalent functions related to Janowski close-to-convexity and we provide their necessary and sufficient criteria. The extreme points and topological features of such harmonic mappings will also be investigated. By applying extreme points theory, we obtain integral mean inequalities, distortion theorems, and coefficient estimates for families of harmonic functions.
Approximate Controllability Of Fractional Backward Stochastic Differential Inclusions With Order 1/2 < P < 1, Müberaa Selah
Approximate Controllability Of Fractional Backward Stochastic Differential Inclusions With Order 1/2 < P < 1, Müberaa Selah
Turkish Journal of Mathematics
In this paper, fractional backward stochastic differential equations are extended to multivalued forms. Since the problem of approximate controllability of the obtained fractional backward stochastic differential inclusions has not yet been addressed in the literature, we focus on the approximate controllability of these systems. The study’s main results, such as existence of the mild solution and approximate controllability for fractional backward stochastic differential inclusions, have been proven through fractional calculus, Bohnenblust-Karlin Theorem, and appropriate conditions.
The Circular Sum Of Points Of An Affine Segment, Mircea Crasmareanu, Marius Munteanu
The Circular Sum Of Points Of An Affine Segment, Mircea Crasmareanu, Marius Munteanu
Turkish Journal of Mathematics
This note introduces a sum for two interior points of an affine segment [AB] based on a trigonometric approach. Some properties of this operation, along with general examples (including squares of endpoints, the midpoint, and the centroid), are discussed. A main result is that the midpoint of a segment is the circular sum of the points dividing the segment with the ratios 4 and 9. In addition, we completely solve a Diophantine equation associated with the circular sum in order to identify all points with integer ratio whose circular sum is a point with integer ratio.
Weighted Inequalities For Discrete Bilinear Hardy-Type Operator With A Matrix, Nazerke Zhangabergenova, Ainur Temirkhanova
Weighted Inequalities For Discrete Bilinear Hardy-Type Operator With A Matrix, Nazerke Zhangabergenova, Ainur Temirkhanova
Turkish Journal of Mathematics
In this paper, we consider a new discrete bilinear inequality of Hardy-type involving a matrix operator. We establish weight characterizations of this inequality under some conditions on the matrix entries.
New Characterizations Of Weights In Dynamic Inequalities Of Hardy's Type On Time Scales, Mario Krnic, Mahmoud M. Osman, Samir H. Saker
New Characterizations Of Weights In Dynamic Inequalities Of Hardy's Type On Time Scales, Mario Krnic, Mahmoud M. Osman, Samir H. Saker
Turkish Journal of Mathematics
The main aim of this paper is to establish some new characterizations of the weights in Hardy-type dynamic inequality, dual Hardy-type inequality, andreverse Hardy-type dynamic inequality on time scales. Some integral and discrete inequalities due to Copson, Leindler, and Hyun and Kim will bededuced as special cases. Moreover, new dynamic inequalities via convexity are proved.
Analytical Solution And Stability Of Ψ-Prabhakar Delayed Systems: Application To Antibiotic Production, Mustafa Aydin
Analytical Solution And Stability Of Ψ-Prabhakar Delayed Systems: Application To Antibiotic Production, Mustafa Aydin
Turkish Journal of Mathematics
The analytical solution of the linear ψ -Prabhakar delay differential equations is explored using the method of variation of parameters, in which a ψ -general delayed exponential matrix function is introduced. The ψ -Prabhakar calculus is enhanced in terms of the semi-group property, inversion results, and several simplified calculations and relations. The system's stability is analyzed within the framework of Ulam-Hyers stability. Finally, the theoretical findings are validated through an application to antibiotic production.
Integral Extensions On Growth And Higher Derivatives Of A Polynomial, Nirmal Kumar Singha, Fahreddi̇n G. Abdullayev, Barchad Chanam
Integral Extensions On Growth And Higher Derivatives Of A Polynomial, Nirmal Kumar Singha, Fahreddi̇n G. Abdullayev, Barchad Chanam
Turkish Journal of Mathematics
A well-known theorem due to Ankeny and Rivlin states that if p(z) is a polynomial of degree n such that p(z) has no zero in |z| < 1, then
max|z|=R≥1 |p(z)| ≤ (Rn + 1 / 2) max|z|=1 |p(z)|.
This research examines the polynomial p(z), ensuring that it has no zero in the disk |z| < k, where k ≥ 1. At the same time, we investigate the sth derivative of this polynomial, where 0 ≤ s < n. In our effort to establish integral formulations of the inequalities related to the derivatives of this class of polynomials, we have successfully extended and generalized Ankeny and Rivlin’s inequality to integral settings. Additionally, part of our findings provides integral analogs of results by Mir [J. Anal., 27 (2019), 851−857]. Moreover, another aspect of our work leads to an improvement in the result of Jain [Turk. J. Math., 31 (2007), 89−94], which we have also verified using an example. We have also compared our results with a previously known result using this numerical example, where the bounds that are in terms of integral means are estimated numerically by numerical integration using Simpson’s 1/3rd rule and illustrate graphically the obtained inequalities as regards sharpness.
On The Solutions Of Difference Equations Of The Volterra Type, Hakan Adigüzel
On The Solutions Of Difference Equations Of The Volterra Type, Hakan Adigüzel
Turkish Journal of Mathematics
In this paper, we conduct a thorough analysis of the qualitative behavior of solutions to three different types of difference equations of the Volterra type. Utilizing the principles of discrete calculus and various well-known inequalities, we have presented our findings. To conclude our theoretical findings, we provide several examples that illustrate full alignment with the findings.
Pointwise Slant Riemannian Maps From Almost Contact Metric Manifolds With Horizontal Reeb Vector Field ˆΞ, Ramazan Demi̇r, Cumali̇ Yildirim
Pointwise Slant Riemannian Maps From Almost Contact Metric Manifolds With Horizontal Reeb Vector Field ˆΞ, Ramazan Demi̇r, Cumali̇ Yildirim
Turkish Journal of Mathematics
This paper introduces the notion of pointwise slant Riemannian maps, which extend the concept of slant submanifolds, pointwise slant submanifolds, slant submersions, pointwise slant submersions, and slant Riemannian maps. These maps are defined from almost contact metric manifolds to Riemannian manifolds with horizontal Reeb vektor field . Furthermore, we present examples and investigate the fundamental properties of such maps. Also we explore the geometry of the foliations induced by pointwise slant Riemannian maps and establish decomposition theorems related to their existence.
On The Invariant Integration Of A Vector In Some Problems In Mechanics, Saad Bin Mansoor
On The Invariant Integration Of A Vector In Some Problems In Mechanics, Saad Bin Mansoor
Turkish Journal of Mathematics
Invariant integration of vectors and tensors over manifolds was introduced around fifty years ago by V.N. Folomeshkin, though the concept appears to not have attracted much attention among researchers. Although it is a sophisticated concept, the operation of the invariant integration of vectors is actually required to correctly solve some problems in mechanics. Two such problems are discussed in the present exposition, in the context of a two-dimensional Euclidean space covered by a polar coordinate system. The notion of invariant integration becomes necessary when the space is described without any reference to a Cartesian coordinate system.
On Cesàro And Abel-Poisson Means Of Hexagonal Fourier Series, Ali̇ Güven
On Cesàro And Abel-Poisson Means Of Hexagonal Fourier Series, Ali̇ Güven
Turkish Journal of Mathematics
Approximation properties of Ces`aro and Abel-Poisson means of hexagonal Fourier series are studied. The degree of approximation by these means of hexagonal Fourier series of functions, which are continuous and periodic with respect to the hexagon lattice, is estimated in terms of modulus of continuity of functions.
The Concept Of T-Basis And Vector-Valued Hardy Classes, Bilal Bilalov, Sabina Rahib Sadigova
The Concept Of T-Basis And Vector-Valued Hardy Classes, Bilal Bilalov, Sabina Rahib Sadigova
Turkish Journal of Mathematics
This paper introduces the concept of a t-basis generated by some bilinear mapping t(·;·). It is considered the vector-valued class Lp(X) := Lp(J; X), 1 ≤ p < +∞, where J = [−π, π] and X is a Banach space with the UMD property, and it is proven that the classical system of exponents {eint}n∈ℤ forms a t-basis for Lp(X), 1 < p < +∞. Using this fact, the Hardy vector classes nHp±(X), 1 < p < +∞, different from the classical ones, are defined, and an equivalent definition of these classes is given and some of their properties are studied. In addition, the concept of t-Riesz property of a system of exponentials is introduced in Lp(X), 1 < p < +∞, and it is proved that this system has the t-Riesz property. A new method is given for establishing the Plemelj–Sokhotski formulas for X-valued Cauchy type integrals when X has the UMD property. An abstract analogue of the “1/4-Kadets” theorem is obtained for …
On The Images Of N-Ellipses Under The Möbius Transformations, Ni̇hal Özgür
On The Images Of N-Ellipses Under The Möbius Transformations, Ni̇hal Özgür
Turkish Journal of Mathematics
In this paper, we examine the images of n-ellipses under the Möbius transformations (linear fractional transformations) for n ≥ 3. As a result of this investigation, we present a new and generalized version (called n-generalized Apollonius circle) of the concept of an Apollonius circle in the plane.
On Cr-Structures On The Null Tangent Bundle, Mohamed Tahar Kadaoui Abbassi, Cornelia-Livia Bejan, Khadija Boulagouaz
On Cr-Structures On The Null Tangent Bundle, Mohamed Tahar Kadaoui Abbassi, Cornelia-Livia Bejan, Khadija Boulagouaz
Turkish Journal of Mathematics
The null tangent bundle of an indefinite pseudo-Riemannian manifold is a lightlike hypersurface of the tangent bundle which inherits a CR-structure from the almost Hermitian structure defined by Oproiu on the tangent bundle. We investigate the properties of this structure in relation to the choice of the screen distribution and the geometry of the base manifold.
Discrete Dirac Equations, Bilender Paşaoğlu Allahverdiev, Hüseyi̇n Tuna
Discrete Dirac Equations, Bilender Paşaoğlu Allahverdiev, Hüseyi̇n Tuna
Turkish Journal of Mathematics
In this paper, regular discrete Dirac systems are considered. Some fundamental properties are studied concerning self-adjointness, orthogonality of eigenfunctions, and eigenfunction expansions.
Lancret-Type Results For A New Family Of Curves In Minkowski 3-Space, Héctor Guerrero Mora, Willy Sierra
Lancret-Type Results For A New Family Of Curves In Minkowski 3-Space, Héctor Guerrero Mora, Willy Sierra
Turkish Journal of Mathematics
In this article, using the concept of a Killing vector field along a curve, we extend certain results concerning a family of curves—previously studied in three-dimensional Euclidean space—to the setting of three-dimensional Minkowski space. Depending on the causal character of the curve, we derive Lancret-type results that establish the necessary and sufficient conditions for the existence of this family in three-dimensional Minkowski space. We determine the intrinsic equation of this family in three cases: (i) when the curve is nonnull with a nonnull acceleration vector, (ii) when the curve is spacelike with a null acceleration vector, and (iii) when the …
Geometry Of Conformally Flat Harmonic Nearly Trans-Sasakian Manifolds, Aligadzhi Rabadanovich Rustanov, Svetlana Vladimirovna Kharitonova
Geometry Of Conformally Flat Harmonic Nearly Trans-Sasakian Manifolds, Aligadzhi Rabadanovich Rustanov, Svetlana Vladimirovna Kharitonova
Turkish Journal of Mathematics
Conformally flat harmonic nearly trans-Sasakian manifolds are studied. In the space of adjoint G-structure, components of the Weyl tensor of the conformal curvature are calculated, identities for this tensor are found, and also some conformal invariants of harmonic nearly trans-Sasakian manifold are provided. An exhaustive description of the class W1 of such manifolds is obtained. It is proved that this class is locally equivalent to the product of a complex Euclidean space and a real line. Complete local characteristic of harmonic nearly trans-Sasakian manifolds of the class W6, which are Einstein manifolds, is obtained. Full classification of conformally flat harmonic …
Biquandle Power Brackets Of Oriented Links, Nesli̇han Gügümcü, Sam Nelson
Biquandle Power Brackets Of Oriented Links, Nesli̇han Gügümcü, Sam Nelson
Turkish Journal of Mathematics
In this paper, we introduce biquandle power brackets, an infinite family of invariants of oriented links containing the classical skein invariants and the quandle and biquandle 2-cocycle invariants as special cases. Biquandle power brackets are generalizations of biquandle brackets in which the values of Kauffman states also depend on the biquandle colors they admit. We provide example computations and discuss the relationship between these new invariants and the previous cases.
Order Structure Of Order-To-Topological Continuous Operator, Gül Si̇nem Keleş, Bahri̇ Turan, Bi̇rol Altin
Order Structure Of Order-To-Topological Continuous Operator, Gül Si̇nem Keleş, Bahri̇ Turan, Bi̇rol Altin
Turkish Journal of Mathematics
Let J be a vector lattice, and W be a topological vector space. An operator K: J → W is called an order-to-topological continuous operator if uα → 0 in J implies K(uα) → 0 in W for each net (uα) in J. In this study, we examine the order structure of the space of order-to-topological continuous operators in general and the order structure of order-to-norm continuous operators in particular. We study the relationships between order-to-topology continuous operators and other classes of operators, such as order weakly compact and order continuous operators. Moreover, we give …
Fractional Equivalent Of Fourth-Order Laguerre And Chebyshev Polynomials, Zahra Kavousi, Kazem Ghanbari
Fractional Equivalent Of Fourth-Order Laguerre And Chebyshev Polynomials, Zahra Kavousi, Kazem Ghanbari
Turkish Journal of Mathematics
Orthogonal polynomials have very useful properties in the solution of mathematical and physical problems. In the last few years, there has been considerable interest in the properties of orthogonal polynomials satisfying differential equations (DE) of order greater than two, their connection to singular boundary value problems, their generalizations, and their classification as solutions of second-order DE. In this paper, we develop a fractional analog of the fourth-order Laguerre differential equation on the interval [0, ∞) and, in addition, we develop a fractional analog of the fourth-order Chebyshev differential equation on a symmetric interval [−α, α], where α is the order …
Continuous Dependence Of Thermoelasticity Problem, Müge Meyvaci, Şevket Gür
Continuous Dependence Of Thermoelasticity Problem, Müge Meyvaci, Şevket Gür
Turkish Journal of Mathematics
The current study considers the initial boundary value problem for the thermoelastic model. The model in which heat conduction is given by Green and Naghdi's theory is called Type II. It is increasingly accepted that studying the structural stability of the initial boundary value problem is crucial. This is because even minor changes in the equation or its coefficients can lead to significant variations in the solution of the problem. From this point of view, we analyze the structural stability of the solutions, specifically examining the continuous dependence of the solutions on all the coefficients of the thermoelastic system, using …
A Note On A Novel Type Of Alster Covering Property In Bitopological Setting, Necati̇ Can Açikgöz, Ceren Sultan Elmali
A Note On A Novel Type Of Alster Covering Property In Bitopological Setting, Necati̇ Can Açikgöz, Ceren Sultan Elmali
Turkish Journal of Mathematics
In this paper, we introduce a new type of Alster covering property in bitopological setting. We investigate its relations with other existing covering properties. By giving counterexamples, we indicate that our new property is different than other mentioned properties. We also construct some conditions for equivalences of those properties with the corresponding property. We also consider the preservation of this new form of bitopological Alster covering property. We investigate the productivity of bitopological nearly Lindelöfness and bitopological nearly Mengerness.
Improving Upper Bounds Of Berezin Number Inequalities Using Convex Function, Sana Khan, Mehmet Gürdal, Muhammad Saeed Akram
Improving Upper Bounds Of Berezin Number Inequalities Using Convex Function, Sana Khan, Mehmet Gürdal, Muhammad Saeed Akram
Turkish Journal of Mathematics
In this research article, new upper bounds are established for the Berezin number of bounded linear operators within the context of functional Hilbert space using the convex function. These bounds are achieved by exploiting an extension of Furuta's inequality and an extension of Kato's inequality. These Berezin number bounds are refinements of already existing bounds found in the literature.