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Öğe RECONSTRUCTION OF A STURM-LIOUVILLE OPERATOR WITH SOME NONLOCAL BOUNDARY CONDITIONS(2023) Özkan, A.SinanIn the present paper, a Sturm-Liouville equation and two nonlocal boundary conditions which are generalized versions of Bitsadze-Samarskii-type conditions are considered. The main goal of this paper is to obtain the uniqueness and the recovering algorithm of the operator via nodal points.Öğe EIGENVALUES OF THE DIRAC OPERATOR WITH NONLOCAL BOUNDARY CONDITIONS ON TIME SCALES(2023) Özkan, A.SinanIn this paper, a Dirac system under some integral type nonlocal boundary conditions on a discrete set is considered. A formulation for the number of eigenvalues of the problem is obtained and a method for calculation of eigenvalues of the problem according to known coefficients is given.Öğe A Note on Pseudoparallel Submanifolds of Lorentzian para-Kenmotsu Manifolds(Published by Faculty of Sciences and Mathematics, 2023) Mert, Tuğba; Atçeken, MehmetIn this article,pseudoparallel submanifolds for Lorentzianpara Kenmotsu manifolds are investigated.The Lorentzian para-Kenmotsu manifoldis considered on the W1−curvature tensor.Submanifolds of these manifolds with properties such as W1−pseudoparallel,W1−2pseudoparallel,W1−Riccigeneralized pseudoparallel,and W1−2Ricci generalized pseudoparallel has been characterized.Öğe Inverse nodal problem for the quadratic pencil of the Sturm-Liouville equations with parameter-dependent nonlocal boundary condition(Tubitak, 2023) Keskin, Baki; Çakmak, YaşarIn this paper, we consider the inverse nodal problem for a quadratic pencil of the Sturm$-$Liouville equations with parameter-dependent Bitsadze$-$Samarskii type nonlocal boundary condition and we give an algorithm for the reconstruction of the potential functions by obtaining the asymptotics of the nodal points.Öğe A partial inverse problem for non-self-adjoint Sturm–Liouville operators with a constant delay(De Gruyter, 2023) Wang, Yu Ping; Keskin, Baki; Shieh, Chung-TsunIn this paper, we study a partial inverse spectral problem for non-self-adjoint Sturm–Liouville operators with a constant delay and show that subspectra of two boundary value problems with one common boundary condition are sufficient to determine the complex potential. We developed the Horváth’s method in [M. Horváth, On the inverse spectral theory of Schrödinger and Dirac operators, Trans. Amer. Math. Soc. 353 2001, 10, 4155–4171] for the self-adjoint Sturm–Liouville operator without delay into the non-self-adjoint Sturm–Liouville differential operator with a constant delay.Öğe SOME ALGEBRAIC PROPERTIES OF GENERALIZED q? CESARO MATRIX C_g (q)(2023) Yazarlı, HasretIn this paper, we define the generalized q-Cesaro matrix by using generalized Cesaro matrix and q-Cesaro matrix. We investigate normality, self-adjointedness and Hilbert-Schmidt properties of generalized q-Cesaro matrices.Öğe Inverse problems for discontinuous Dirac operator with eigenparameter dependent boundary and transmission conditions(Wiley, 2023) Güldü, Yalçın; Arslantaş, MerveIn this study, we consider the discontinuous Dirac equationssystem with eigenparameter dependent boundary and finitenumber of transmission conditions. First, the space thatcorresponds to problem is introduced, the norm on thisspace is defined and the operator model that correspondsto the given problem is constructed on this space. Thenthe integral equations and asymptotics of eigenfunctionsof the problem are obtained. The characteristic functionis defined and the asymptotic formula of the character-istic function is given by using obtained asymptotics ofeigenfunctions. After the Weyl solution and the Weylfunction of the problem are formed. Finally, some unique-ness theorems are proved by using Weyl function and somespectral data.Öğe Terminal value problem for neutral fractional functional differential equations with Hilfer-Katugampola fractional derivative(Published by Faculty of Sciences and Mathematics, 2023) Bouriah, Soufyane; Benchohra, Mouffak; Gülyaz Özyurt, SelmaIn this paper, we establish the existence of solutions for a class of nonlinear neutral fractional differential equations with terminal condition and Hilfer-Katugampola fractional derivative. The arguments are based upon the Banach contraction principle, and Krasnoselskii’s fixed point theorem. An example is included to show the applicability of our results.Öğe Some Classification Theorems and Endomorphisms in New Classes(MDPI, 2023) Alnoghashi, Hafedh); Alali, Amal S.; Koç Sögütcü, Emine; Rehman, Nadeem ur; Alqarni, Faez A.Let ℧ be a prime ring of char(℧) not equal 2 with its center Z. This article introduces new classes of endomorphisms and investigates how they relate to antiautomorphisms of prime rings and the commutativity of prime rings. Additionally, we fully describe and classify some of these endomorphisms. We also give examples to prove the necessity of the numerous restrictions included in the hypotheses of our results.Öğe Note on Lie ideals with symmetric bi-derivations in semiprime rings(Springer, 2023) Koç Sögütcü, Emine; Huang, ShuliangLet R be a semiprime ring, U a square-closed Lie ideal of R and D : R x R -> R a symmetric bi-derivation and d be the trace of D. In the present paper, we prove that the R contains a nonzero central ideal if any one of the following holds: i) d (x) y +/- xg(y) is an element of Z, ii)[d(x), y] = +/-[x, g(y)], iii) d(x) o y = +/- x o g(y), iv) [d(x), y] = +/- x o g(y), v)d([x, y]) = [d(x), y]+[d(y), x], vi) d(xy)+/- xy is an element of Z, vii) d(xy) +/- yx is an element of Z, viii) d(xy) +/- [x, y] is an element of Z, ix) d(xy) +/- x o y is an element of Z, x) g(xy) + d(x)d(y) +/- xy is an element of Z, xi) g(xy) + d(x)d(y) +/- yx is an element of Z, xii) g([x, y]) + [d(x), d(y)] +/- [x, y] is an element of Z, xiii) g(x o y) + d(x) o d(y) +/- x o y is an element of Z, for all x, y is an element of U, where G : R x R -> R is symmetric bi-derivation such that g is the trace of G.Öğe Multiplicative (generalized)-reverse derivations in rings and Banach algebras(De Gruyter, 2023) Koç Sögütcü, EmineIn this work, the subject of ideal in a semiprime ring with multiplicative (generalized)- reverse derivations studied is included. We give new essential results for researchers in this field and generalize some results found in the literature. Also, the application of continuous reverse derivations in Banach algebras is discussed for the first time.Öğe Best Proximity Point Results for Gamma Class of Mappings(Yokohama Publishers, 2022) Sakthi, Ramalingam, Gülyaz Özyurt, Selma and Karpagam, SaravananIn this manuscript, we define the class of Γ consist of p-cyclic mapping with certain assumptions. We investigate the existence and uniqueness of a best proximity point in the setting of a metric space with an additional condition p-completeness. Further, we examine the both existence and uniqueness a best proximity point for the mapping that lies in this class in the context of strictly convex normed linear space.Öğe Trace Formulae for a Conformable Fractional Diffusion Operator(Filomat, 2022) Çakmak, YaşarIn this paper, we obtain the regularized trace formulae for a diffusion operator, which includes conformable fractional derivatives of order α (0 < α ≤ 1) instead of the ordinary derivatives in a traditional diffusion operator by the contour integration method. The results of this paper are of great importance in solving inverse problems and can be considered as partial fractional generalizations.Öğe SPECTRA AND FINE SPECTRA OF THE GENERALIZED UPPER DIFFERENCE OPERATOR WITH TRIPLE REPETITION (D_3)^ab ON THE HAHN SEQUENCE SPACE(2022) Durna, Nuh; Mursaalen, Muhammed; Kılıç, RabiaThe goal of this paper is to obtain the spectra and fi ne spectra of the matrix (D_3)^ab on the Hahn space. Also, we explore some ideas of how to study the problem for a general form of the matrix, namely, the matrix (D_n)^ab where the non-zero diagonals are the entries of a n-ary repetition sequence.Öğe Inverse Nodal Problems for Dirac- Type Integro-Differential Operators with Linear Functions in the Boundary Condition(Taylor&Francis, 2022) Keskin, Baki; Tel, H. DilaraIn this article, Dirac-type integro-differential operator with linear functions in the boundary condition is considered. We obtain asymptotic expressions for the solution of the differential system and derive the large eigenvalues and nodal points. We also give a constructive procedure for solving an inverse nodal problem. We prove that a dense subset of the nodes determines the coefficients of the differential part of the operator and gives partial information for the integral part of it.Öğe Inverse nodal problems for Dirac type integro differential system with a nonlocal boundary condition(TUBİTAK, 2022) Keskin Baki; Keskin, BakiIn this paper, the Dirac-type integro differential system with a nonlocal integral boundary condition is considered. First, we derive the asymptotic expressions for the solutions and large eigenvalues. Second, we provide asymptotic expressions for the nodal points and prove that a dense subset of nodal points uniquely determines the boundary condition parameter and the potential function of the considered differential system. We also provide an effective procedure for solving the inverse nodal problem.Öğe Spectra and fine spectra of the generalized upper difference operator with triple repetition ?_3^ab on the Hahn sequence space(De Gruyter, 2022) Nuh Durna, Mursaleen Muhammed, Kılıç RabiaThe goal of this paper is to obtain the spectra and ne spectra of the matrix D_3âb on the Hahn space. Also, we explore some ideas of how to study the problem for a general form of the matrix, namely, the matrix D_3âb where the non-zero diagonals are the entries of a n-ary repetition sequence.Öğe Half inverse problem for diffusion operators with jump conditions dependent on the spectral parameter(2022) Ergün, Abdullah; Amirov, RaufIn this paper, half inverse problem for diffusion operators with jump conditions dependent on the spectral parameter is considered. The half inverse problems is studied of determining the coefficient and potential functions of the value problem from its spectrum by using the Yang–Zettl and Hocstadt–Lieberman methods. We show that if the functions p(x) and q(x) are prescribed over the semi-interval, then potential functions are determined uniquely by one spectrum on the over interval.Öğe Some properties and Vajda theorems of split dual Fibonacci and split dual Lucas octonions(AIMS Mathematics, 02 March 2022) Tokeşer, Ümit; Mert, Tuğba; Dündar, YakupIn this paper, we introduce split dual Fibonacci and split dual Lucas octonions over the algebra O(a; b; c), where a; b and c are real numbers. We obtain Binet formulas for these octonions. Also, we give many identities and Vajda theorems for split dual Fibonacci and split dual Lucas octonions including Catalan’s identity, Cassini’s identity and d’Ocagne’s identity.Öğe On a Classification of Almost C(?)-Manifolds(Hindawi, Journal of Mathematics, 2022) Mert, TuğbaIn this paper, pseudosymmetric and Ricci pseudosymmetric almost C(/alpha)-manifold are studied. For an almost C(/alpha)-manifold, Riemann pseudosymmetric, Riemann Ricci pseudosymmetric, Ricci pseudosymmetric, projective pseudosymmetric, projective Ricci pseudosymmetric, concircular pseudosymmetric, and concircular Ricci pseudosymmetric cases are considered and new results are obtained.
