Mathematics Commons^™

The Variation Of Eigenvalues Of The Two-Dimensional Magnetic Schrödinger Operator With Respect To The Angle Of A Flat Sector, Araz R. Aliev, Elshad H. Eyvazov

Turkish Journal of Mathematics

A two-dimensional Schrödinger operator with a spherically symmetric electric potential and an Aharonov Bohm magnetic field in a circular sector under Neumann boundary conditions is considered. The intervals of the angular variation of the flat region are found, where the eigenvalues of the Neumann problem for the Schrödinger operator with a spherically symmetric electric potential strictly decrease monotonically in the Aharonov-Bohm magnetic field.

Further Geometric Properties Of The Generalized K-Bessel Functions, Merve Görgülü, İbrahi̇m Aktaş

Turkish Journal of Mathematics

This study investigates certain geometric properties of the normalized k-Bessel function, which is a natural generalization of classical and modified Bessel functions of the first kind. These geometric properties include η-starlikeness, η-uniform convexity, starlikeness associated with exponential function and Bernoulli’s lemniscate, and convexity associated with exponential function and Bernoulli’s lemniscate. Moreover, certain corollaries related to classical and modified Bessel functions are presented by specialising parameters. In addition, some examples and their graphical representations are provided to support the findings of this study.

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Turkish Journal of Mathematics

No abstract provided.

Some Methods For Finding The Number Of Partitions Of N With M−Parts, P(N, M), Yusuf Soyvural, Ali̇ Bülent Eki̇n

Turkish Journal of Mathematics

P(n, m) denotes the number of partitions of n with m parts, while P_m(n) denotes the number of partitions of n with parts at most m. It is a well-known result that the number of partitions of n ≥ 0 into m or fewer parts is equal to P_m(n). In the literature, there are some results for P(n, m) and P_m(n) for some values of m. In this work, we give more compact results for P(n …

Representation Of Inverse Ordered Semigroups By Means Of Symmetric Inverse Semigroups On A Set, Michael Tsingelis

Turkish Journal of Mathematics

A partial one-to-one mapping on a set X is a mapping whose domain is a subset of X. The set of partial one-one mappings on a set X is an inverse semigroup (the symmetric inverse semigroup on X). An element x of an ordered semigroup (S, ·, ≤) is called an inverse element of α ∈ S if α ≤ xαx and x ≤ xαx. An inverse ordered semigroup is an ordered semigroup S for which every element of S possesses an inverse element and the inverse elements of any element of S are in …

Fubini Collocation Method For Numerical Solutions Of Differential Equations With Quadratic And Cubic Nonlinearities, Kübra Erdem Bi̇çer, Havva Türkhan

Turkish Journal of Mathematics

In this study, the Fubini collocation method is proposed for the approximate solution of nonlinear differential equations. The method utilizes fundamental relations involving Fubini polynomials and their derivatives, employing collocation points to enhance solution accuracy. Within this framework, the given differential equation is transformed into a system of nonlinear algebraic equations involving the unknown coefficients of the approximate solution. This resulting system is then solved using appropriate numerical techniques to obtain the approximate solution. The effectiveness of the proposed method is demonstrated through several test problems, with accuracy evaluated using absolute error functions. Furthermore, illustrative examples and residual-based error analysis …

Codazzi Normalized Null Hypersurfaces, Théophile Kemajou Mbiakop, Cyriaque Atindogbe, Ferdinand Ngakeu

Turkish Journal of Mathematics

We introduce a class of null hypersurfaces of Lorentzian manifolds, namely Codazzi normalized null hyper surfaces, whose (screen) shape operator associated with the rigged vector field is a Codazzi tensor. Several examples are given to support our study. Moreover, we investigate conditions implying that the induced Riemannian screen structure on a Codazzi-type normalized null hypersurface of a Lorentzian space is locally a nontrivial warped product.

On Almost Kenmotsu Manifolds Admitting Nearly Vacuum Static Equations With Applications, Uday Chand De, Krishnendu De, Sudhakar Kumar Chaubey

Turkish Journal of Mathematics

In this article, we study certain characteristics of nearly vacuum static equations on almost Kenmotsu manifolds. It is established that an η-Einstein almost Kenmotsu manifold allowing nearly vacuum static equations is of constant scalar curvature and either the solution is trivial or, the manifold reduces to an Einstein manifold. Next,  nearly vacuum static equations on (κ,μ)-almost Kenmotsu manifolds and generalized (κ,μ)'-nullity distribution are considered and we obtain several interesting results. Moreover, we illustrate that if a 3-dimensional Kenmotsu manifold allows nearly vacuum static equations, then the manifold is locally isometric to the hyperbolic space Η3(-1). After that, we investigate a …

Cospectrality Results For Signed Graphs With Two Eigenvalues Unequal To ±1, Willem H. Haemers, Hati̇ce Topcu

Turkish Journal of Mathematics

Recently the collection G of all signed graphs for which the adjacency matrix has all but at most two eigenvalues equal to ±1 has been determined. Here we investigate G for cospectral pairs, and for signed graphs determined by their spectrum (up to switching). If the order is at most 20, the outcome is presented in a clear table. If the spectrum is symmetric we find all signed graphs in G determined by their spectrum, and we obtain all signed graphs cospectral with the bipartite double of the complete graph. In addition we determine all signed graphs cospectral with the …

On The Existence Of Solutions For Nonlinear Third-Order Q-Difference Equations With Boundary Conditions Involving Q-Integrals, İlker Gençtürk

Turkish Journal of Mathematics

In this research, we focus on investigating the existence of solutions for a q-integral boundary value problem associated with third-order nonlinear q-difference equations. To achieve this, we employ two fundamental mathematical tools: the Banach contraction principle and Krasnoselskii’s fixed point theorem, which provide the theoretical framework for our analysis. Furthermore, to illustrate the applicability and robustness of our results, we present and discuss several concrete examples that highlight the practical implications of the proposed methods.

Classifications Of Gradient Almost Ricci Solitons Within The Framework Of Closed Conformal Vector Fields, Akram Ali, Fatemah Mofarreh, Jae Won Lee

Turkish Journal of Mathematics

In this paper, we consider gradient almost Ricci solitons with nonparallel closed conformal vector fields. We classify gradient almost Ricci solitons and show that a complete, noncompact gradient almost Ricci soliton admitting a nonparallel closed conformal vector field, is locally a warped product with Einstein fibers, while in the second case, under additional hypothesis, gradient almost Ricci soliton is totally umbilical if and only if it has constant scalar curvature.

On Trinomial Units Of The Group Ring RcN, César A. Hernandez Melo, Fernanda Diniz De Melo Hernandez, Patricia Massae Kitani

Turkish Journal of Mathematics

Let R be an associative ring with identity, C_n be the cyclic group of order n, and g be a generator of C_n. In this manuscript, for i ∈ N such that 1 ≤ i < n and gcd(i, n) = 1, the algebraic properties of the trinomial elements h_i = -1 + g + g^-i in the group ring RC_n are investigated. More precisely, necessary and sufficient conditions are given for an element h_i to be a unit in RC_n. When h_i is a unit, explicit formulas for computing …

End-Regular Flower Graphs CR,S, Joerg Koppitz, Suparat Phantukang, Phurinut Srisawad, Somnuek Worawiset

Turkish Journal of Mathematics

In the present paper, we study the regularity of the endomorphism monoid of a class of graphs, which generalizes the cycle graph. We give a complete list of all end-regular r × s flower graphs. In particular, for an odd integer s ≥ 3, the s × s flower graph Cs,s has a regular endomorphism monoid, i.e., Cs,s is end-regular. For Cs,s, s ≥ 3 odd, we determine the cardinality and the rank of its endomorphism monoid (including a generating set of minimal size).

Generalized Szász–Mirakyan Operators In The Variation Seminorm, Sare Yumruçali, Harun Karsli, Fatma Taşdelen Yeşi̇ldal

Turkish Journal of Mathematics

The aim of the present paper is to introduce generalized Szász–Mirakyan operators. This article studies the property of variation seminorm and some approximation properties of generalized Szász–Mirakyan operators not only in normed spaces but also in variation seminorm. We obtain convergence properties of our operators using of Korovkin’s theorem and the order of convergence by using a classical approach, the second modulus of continuity and Peetre’s K functional. We also give asymptotic formula and the convergence of the derivatives for these operators. We investigate the variation detracting property of generalized Szász–Mirakyan operators. We show the convergence of generalized Szász–Mirakyan operators …

Some Properties Of Nabla Laplace Transform On Isolated Time Scales, Müfi̇t Şan, Huri̇ye Dağ, Manuel D. Ortigueira

Turkish Journal of Mathematics

This study presents the properties of the bilateral and unilateral nabla Laplace transform, defined on isolated time scales. Furthermore, it explores the nabla Laplace transforms of several elementary functions, employing various proof techniques from real and complex analysis. The findings are illustrated with examples, demonstrating the applicability of these definitions.

From Rough Categories To Rough Groupoids, Mehmet Mustafa Beydaği, Abdullah Fati̇h Özcan, İlhan İçen

Turkish Journal of Mathematics

In this study, we introduce the concepts of rough category and rough groupoid by combining the concepts of category theory and groupoid with rough set theory. We present some properties and examples of these concepts, which are discussed for the first time. Additionally, by defining a rough functor among the rough categories, the category of rough categories were created. Moreover, rough groupoid homomorphism, rough action groupoid, and category of the rough groupoids have been examined algebraically and introduced to the literature.

An Investigation Of New Associated Curves Of A Frenet Curve In Euclidean N-Space, Bedi̇a Meri̇h Özçeti̇n

Turkish Journal of Mathematics

In this study, we introduce the V2-direction curve, Vn−1-direction curve and Vn-direction curve of a Frenet curve in n-dimensional Euclidean space. We provide characterizations and investigate the relationships between the Frenet apparatus of the principal curve and the corresponding apparatus of the direction curves. We also present an application for all direction curves with the results shown using computer code implemented in MATLAB.

New Structures Of Golden Type On The Tangent Bundle, Simona-Luiza Druta-Romaniuc, Cristina-Elena Hretcanu, Aydin Gezer

Turkish Journal of Mathematics

The aim of our paper is to prove the existence of some types of almost (α, p)–golden structures, obtained as general natural lifts of the Riemannian metric from the base manifold M to the total space TM of the tangent bundle. We show that TM, endowed with a general natural almost (α, p)–golden structure (which is a generalisation of the golden structure) and with a general natural metric, is an almost (α, p)–golden Riemannian manifold if and only if the function coefficients of the almost (α, p)–golden structure are related to …

Corrigendum To “ Improved Berezin Radius Inequalities For Functional Hilbert Space Operators” [Turkish Journal Of Mathematics 49 (5) 2025 545-561], Mojtaba Bakherad, Ulaş Yamanci, Mohammad W. Alomari

Turkish Journal of Mathematics

In the article entitled Improved Berezin radius inequalities for functional Hilbert space operators, published in the Turkish Journal of Mathematics, [49 (5): 545-561. https://doi.org/10.55730/1300-0098.3607], the affiliation of the author MOHAMMAD W. ALOMARI was published incorrectly due to an error at the submission stage. The incorrect affiliation was Department of Mathematics, Faculty of Science and Information Technology, Irbid National University, Irbid, Jordan T he correct affiliation is Department of Mathematics, Faculty of Science, Jadara University, Irbid, Jordan T he authors apologize for any inconvenience caused.

The original article can be accessed at: https://doi.org/10.55730/1300-0098.3607

Monotone Positive Solutions Of Impulsive Differential Equations Asymptotic To Nonprincipal Solutions, Si̇bel Doğru Akgöl, Ağacik Zafer

Turkish Journal of Mathematics

This study investigates the asymptotic behavior of monotone positive solutions for a general class of nonlinear second-order impulsive differential equations. By employing the principal and nonprincipal solutions of the associated homogeneous equation, we establish the existence of a monotone positive solution asymptotic to a nonprincipal solution at infinity. To achieve this, we also prove a compactness criterion for an effective use of Schauder’s fixed-point theorem. Under suitable conditions, similarly to the classical case, it is demonstrated that a monotone positive solution asymptotic to a nonprincipal solution exists. A concrete example is given to illustrate the results.

Majorization Properties For Analytic Functions With Positive Real Part, Oya Mert

Turkish Journal of Mathematics

The majorization feature is important when investigating analytical functions’ geometric properties. The present work focuses on the majorization property for a general Ma-Minda type function class S^*_φ(γ, λ) of starlike functions of complex order, which is described with the Ruscheweyh differential operator. In the context of the main theorem, consequences are presented for various special functions φ having a positive real part. Furthermore, the Ruscheweyh differential operator extends a representation formula and investigates an upper-bound formula. Examples of upper bounds for analytic functions are also presented.

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.

The Action Of The Superposition Operator On Weighted Banach Sequence Spaces LP,Σ, Nermin Okičić, Fehim Dedagić

Turkish Journal of Mathematics

We consider a nonlinear superposition operator on weighted Banach spaces l_p,σ, where σ is the weighted function with the property that (∀n ∈ ℕ) σ(n) ≥ 1. We present the necessary and sufficient conditions for the action of the superposition operator from l_p,σ to l_q,τ, 1 ≤ p, q ≤ ∞, as well as the L-characteristic of the action of the considered operator.

Improved Berezin Radius Inequalities For Functional Hilbert Space Operators, Mojtaba Bakherad, Ulaş Yamanci, Mohammad W. Alomari

Turkish Journal of Mathematics

The Berezin number of an operator S is defined by ber(S) = sup_λ∈Θ |Ŝ(λ)| = sup_λ∈Θ |⟨Sĸ̂_λ, ĸ̂_λ⟩|, where Ŝ(λ) = ⟨Sĸ̂_λ, ĸ̂_λ⟩ (λ ∈ Θ) is the Berezin transform of an operator S on the functional Hilbert space ℋ = ℋ(Θ) and ĸ̂_λ = ĸ_λ / ‖ĸ_λ‖ is the normalized reproducing kernel of ℋ. In this paper, we show an improvement of the classical Cauchy–Schwarz inequality involving the Berezin number. Moreover, some Berezin numbers inequalities are proven for invertible operators.

On Multiplicative Order Convergence And Multiplicative Order Continuous Operators, Hüma Gürkök, Bahri̇ Turan

Turkish Journal of Mathematics

Let A and B be two f-algebras. This paper establishes the theoretical framework for multiplicative order convergence, clarifying its definition, properties, and relations to other convergence types. This includes a detailed discussion on the conditions under which multiplicative order convergence and order convergence, as well as unbounded order convergence, mutually imply each other. We establish an extension theorem for multiplicative order continuous operators, similar to Veksler’s theorem for order continuous operators. As a result of this theorem, we derive the order structure of the space of multiplicative order continuous operators. We show that the space L_mo(A, …

Nonoscillatory Solutions Of Third-Order Nonlinear Dynamic Equations: Existence And Nonexistence, Özkan Öztürk, Elvan Akin, Nesli̇han Nesli̇ye Pelen

Turkish Journal of Mathematics

This paper investigates a third-order nonlinear dynamic equation on arbitrary time scales, a nonempty closed subset of the real numbers, unifying continuous and discrete analyses. We study the qualitative behavior of nonoscillatory solutions and their quasi-derivatives, focusing on their limiting behaviors. The existence of such solutions are established using improper integral criteria and Schauder’s and Knaster’s fixed point theorems. In addition, we establish the criteria for the nonexistence of nonoscillatory solutions. Furthermore, we prove the existence of Kneser-type solutions of the corresponding linear dynamic equation on isolated time scales, addressing an open problem in the literature. Several examples of theoretical …

Structural Stability For Damped Nonlinear Wave Equations, Sevda Isayeva, Varga Kalantarov

Turkish Journal of Mathematics

We study the problem of continuous dependence on parameters for solutions to initial-boundary value problems for nonlinear strongly damped wave equations. Specifically, we consider three classes of equations: a strongly damped wave equation with a nonlinear damping term; a strongly damped wave equation incorporating both a nonlinear damping term and a nonlinear source term; and a strongly damped wave equation with a nonlinear source term and a linear weak damping term. For each class, we establish structural stability results, showing that the solutions depend continuously on the relevant parameters.

Application On Convolution For Fuzzy Differential Subordination Of Meromorphic Functions, Kholood Mohamed Alsager, Fethi̇ye Müge Sakar, Alina Alb Lupas, Sheza Mohamed El-Deeb

Turkish Journal of Mathematics

This paper investigates fuzzy differential subordinations involving meromorphic functions defined in the punctured unit disk. A novel operator based on the Hadamard product (also known as convolution) is introduced to establish new results in the theory of fuzzy differential subordination. This operator provides a generalized framework that extends classical analytic methods to the fuzzy setting, offering new insights into the geometric behavior of meromorphic functions under fuzzy conditions. Several sufficient conditions for fuzzy differential subordination are derived, and their connections to existing results are discussed. The findings contribute to the growing body of literature at the intersection of classical geometric …

(Α, Β)-Normal Differential Operators For First Order In Hilbert Spaces Of Vector-Functions, Zameddin I. Ismailov, Pembe İpek Al

Turkish Journal of Mathematics

In this article, the relationships between (α, β)-normality properties of the extensions of the minimal operator generated by the first-order differential operator expression in the Hilbert spaces of vector-functions in a finite interval and the variable operator coefficients of this differential operator expression are investigated. Then, the general form of all (α, β)-normal extensions of the minimal operator in these spaces is determined under the constraints obtained for the coefficient operators.

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 …