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Articles 61 - 90 of 2581
Full-Text Articles in Mathematics
On Certain Subclasses Of Starlike And Convex Functions With Respect To T-Symmetric Points, Osman Altintaş, Ni̇zami̇ Mustafa
On Certain Subclasses Of Starlike And Convex Functions With Respect To T-Symmetric Points, Osman Altintaş, Ni̇zami̇ Mustafa
Turkish Journal of Mathematics
In this study, we defined for the first time a new subclass of stalike and convex functions in the open unit disk of the complex plane and we examined coefficiend upper bound estimates for this class.
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.
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.
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 …
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 …
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 …
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.
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 …
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.
On Minimal Hypersurfaces In Euclidean Spaces And Riemannian Manifolds, Josef Mikeš, Sergey Stepanov, Irina Tsyganok
On Minimal Hypersurfaces In Euclidean Spaces And Riemannian Manifolds, Josef Mikeš, Sergey Stepanov, Irina Tsyganok
Turkish Journal of Mathematics
In this paper, we present the conditions under which minimal and stable minimal hypersurfaces are as hyperplanes in Euclidean spaces ands a totally geodesic submanifolds in Riemannian manifolds.
Asymptotic Behavior Of The Kirchhoff Index For Square Lattice With Boundary Conditions, Fati̇h Ecevi̇t, Arzu Boysal
Asymptotic Behavior Of The Kirchhoff Index For Square Lattice With Boundary Conditions, Fati̇h Ecevi̇t, Arzu Boysal
Turkish Journal of Mathematics
We determine leading asymptotic behavior of the Kirchhoff index for the square lattice under free, cylindrical and toroidal boundary conditions. Our results provide correct forms of the eleven false theorems/results published in the following papers: L. Ye, On the Kirchhoff index of some toroidal lattices, Linear Multilinear Algebra, 59:6 (2011), 645--650; J.-B. Liu, X.-F. Pan, J. Cao, X. Huang, The Kirchhoff index of toroidal meshes and variant networks, Math. Probl. Eng., Article ID 286876, 8 pages (2014); J.-B. Liu, X.-F. Pan, A unified approach to the asymptotic topological indices of various lattices, Appl. Math. Comput., 270 (2015), 62--73.
The Role Of Α-Inequalities In Examining The Singular Version Of The Big Bang Model, Samane Ijadi, S. Mansour Vaezpour, Mehdi Shabibi, Shahram Rezapour
The Role Of Α-Inequalities In Examining The Singular Version Of The Big Bang Model, Samane Ijadi, S. Mansour Vaezpour, Mehdi Shabibi, Shahram Rezapour
Turkish Journal of Mathematics
In this article, by extending Friedmann's equation, we propose a singular fractional differential system for the Big Bang model. In this model, the rate of increase in the size of the universe tends to infinity at time near to zero and causes the emergence of a singular differential equation,which physically justifies the near-infinity energy of the universe in the near-zero volume of the universe in the early moments of the Big Bang. Then, we investigate this type of strong singular boundary value problem, by using $\alpha$-inequalities. In the sequel, some examples, describe the main results. Moreover, we present numerical and …
Estimates Of The Numerical Radius Utilizing Various Function Properties, Vuk Stojiljkovic, Mehmet Gürdal
Estimates Of The Numerical Radius Utilizing Various Function Properties, Vuk Stojiljkovic, Mehmet Gürdal
Turkish Journal of Mathematics
Numerous inequalities of the vector and numerical radius types have been found. We achieved several extensions of the well-known numerical radius type inequalities by using the function [[EQUATION]] described in the publication by Stojiljkovi\'{c} and Dragomir in [30] and convexity characteristics with standard operator theory approaches. In particular, the following integral type numerical radius inequality has been obtained, that is [[EQUATION]]
Properties Of Frontier, Exterior And Border In Picture Topological Spaces, Shanmugasundharam Durga, Lakshmanadas Vidyarani, Mandarasalam Vigneshwaran, Tomasz Witczak
Properties Of Frontier, Exterior And Border In Picture Topological Spaces, Shanmugasundharam Durga, Lakshmanadas Vidyarani, Mandarasalam Vigneshwaran, Tomasz Witczak
Turkish Journal of Mathematics
The paper is dedicated to picture sets. They are crisp version of Cuong's picture fuzzy sets (just like intuitionistic sets introduced by Coker are crisp version of intuitionistic fuzzy sets). We have already defined several basic topological notions in this framework and we have analyzed its algebra. Now we continue our research. We introduce the notions of border, frontier and exterior. Many properties are studied. Moreover, we point out that there are some important differences between classical and non-classical approach.
Local Dynamic Analysis Of The Covid-19 Mathematical Model Based On Discrete-Time Predator-Prey Population Model, Fi̇gen Kangalgi̇l, Ni̇lüfer Topsakal, Özge Kuzucu
Local Dynamic Analysis Of The Covid-19 Mathematical Model Based On Discrete-Time Predator-Prey Population Model, Fi̇gen Kangalgi̇l, Ni̇lüfer Topsakal, Özge Kuzucu
Turkish Journal of Mathematics
In this article, the local dynamics of a discrete-time Covid-19 pandemic model based on the Lotka Volterra model with topological classifications, bifurcation analysis and chaos control are investigated. It is shown that under some parametric conditions, the discrete-time Covid-19 pandemic model has two equilibrium points. With linear stability theory, local dynamics are investigated with topological classifications about the equilibrium points of the discrete-time Covid-19 epidemic model. In addition, the existence of a Neimark-Sacker bifurcation at the internal equilibrium point is proved and this bifurcation is analysed using explicit criteria. Furthermore, the chaos in the discrete Covid-19 pandemic model is also …
Generalization Of Dual Numbers And Dual Euclidean 3-Space, Şükran Duygu Soylu, Harun Bariş Çolakoğlu, Mustafa Özdemi̇r
Generalization Of Dual Numbers And Dual Euclidean 3-Space, Şükran Duygu Soylu, Harun Bariş Çolakoğlu, Mustafa Özdemi̇r
Turkish Journal of Mathematics
In this study, we consider the generalized dual numbers and determine their algebraic and geometric properties. Then we generalize the well-known D3 module and introduce the generalized dual Euclidean 3-space with its scalar product and norm. After determining the conditions for being a unit generalized dual Euclidean vector, we derive the generalized Euclidean Study map, which states that there is a bijective correspondence between directed lines of the space and the elements of the unit generalized dual Euclidean sphere. Finally, we define the dual Euclidean angle between two generalized dual Euclidean vectors.
Nearly Toric Varieties Of Type A, Mahi̇r Bi̇len Can, Nestor Fernando Diaz Morera
Nearly Toric Varieties Of Type A, Mahi̇r Bi̇len Can, Nestor Fernando Diaz Morera
Turkish Journal of Mathematics
A notion of a nearly toric variety is introduced. The examples of nearly toric varieties in the context of Schubert varieties are discussed. In particular, combinatorial characterizations of the smooth and singular nearly toric Schubert varieties are found. Furthermore, the counts and generating series are determined. Additionally, a connection between Dyck paths and a certain family of nearly toric Schubert varieties is established.
Inverse Ordered Semigroups, Michael Tsingelis
Inverse Ordered Semigroups, Michael Tsingelis
Turkish Journal of Mathematics
Ένα στοιχείο x μιας διατεταγμένης ημιομάδας [[EQUATION]] ονομάζεται αντίστροφο στοιχείο του [[EQUATION]]if [[EQUATION]]και [[EQUATION]]. Μια αντίστροφη διατεταγμένη ημιομάδα είναι μια διατεταγμένη ημιομάδα S για την οποία κάθε στοιχείο του S έχει ένα αντίστροφο στοιχείο και τα αντίστροφα στοιχεία οποιουδήποτε στοιχείου του S βρίσκονται στην ίδια συνδεδεμένη συνιστώσα του διαγράμματος Hasse της σχέσης τάξης του. Παρουσιάζουμε ιδιότητες που ικανοποιούνται από αντίστροφα διατεταγμένες ημιομάδες και χαρακτηρίζουμε αντίστροφα διατεταγμένες ημιομάδες με βάση την έννοια της κανονικότητας των διατεταγμένων ημιομάδων, το σύνολο των αδυναμιών τους και τις σχέσεις του Green. Επίσης αποδεικνύουμε ότι η αντιστρεψιμότητα των διατεταγμένων ημιομάδων διατηρείται από ομομορφισμούς.
On The Connection Between Σϵ(A1 ⊗ A2) And Σϵ(A1), Σϵ(A2) For Certain Specialoperators, Fati̇h Yilmaz
On The Connection Between Σϵ(A1 ⊗ A2) And Σϵ(A1), Σϵ(A2) For Certain Specialoperators, Fati̇h Yilmaz
Turkish Journal of Mathematics
In this paper, the connection between the ϵ -pseudospectrum of the tensor product operator A1 ⊗ A2 andthe ϵ -pseudospectrums of operators A1 and A2 has been investigated and some results are given about this connectionunder certain conditions.
Ideals In Semigroups Of Partial Transformations With Invariant Set, Jitsupa Srisawat, Yanisa Chaiya
Ideals In Semigroups Of Partial Transformations With Invariant Set, Jitsupa Srisawat, Yanisa Chaiya
Turkish Journal of Mathematics
This paper explores the ideals and their structural properties in two generalizations of the partial transformationsemigroup. Furthermore, principal, maximal, and minimal ideals within these semigroups are elucidated.
A Non-Newtonian Conics In Multiplicative Analytic Geometry, Aykut Has, Beyhan Yilmaz
A Non-Newtonian Conics In Multiplicative Analytic Geometry, Aykut Has, Beyhan Yilmaz
Turkish Journal of Mathematics
In this study, conics (circle, ellipse, hyperbola) are characterized by taking into account basic multiplicationoperations in multiplicative space. For this purpose, firstly multiplicative axes and regions are introduced. Additionally,the multiplicative cone definition is given and visualized on the figure. General definitions and theorems of non-Newtonianconics are given. Additionally, examples were given and drawings were made to make the resulting characterizations andtheorems more memorable.