Yazar "Kara, Merve Ilkhan" seçeneğine göre listele

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    Certain domains of a new matrix constructed by Euler totient and its summation function
    (Amer Inst Mathematical Sciences-Aims, 2025) Kara, Merve Ilkhan; Aydin, Dilek
    With the aid of the Euler totient function phi and its summation function inverted perpendicular, a new matrix O(phi, inverted perpendicular) = (delta(phi, inverted perpendicular)nk), where delta(phi, inverted perpendicular)(nk) = {(-1)n-k inverted perpendicular(k)/ O-phi(n) , n - 1 <= k <= n, 0, otherwise is constructed to define the domains l(p)(O(phi, inverted perpendicular)), l(infinity)(O(phi, inverted perpendicular)), and l(1)(O(phi, inverted perpendicular)). After obtaining the norms on these domains, it is proved that these spaces are linearly isomorphic to classical ones. Also, their dual spaces are determined. Finally, characterizations of several matrix mappings are stated and proved.
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    The Cesaro-Gamma operator and its associated sequence space
    (Springer Basel Ag, 2021) Kara, Merve Ilkhan; Roopaei, Hadi
    In this paper, we introduce Cesaro-Gamma matrix that exhibits the structure of both the Cesaro and Gamma matrices. We study the domain of this new matrix in the space l(p) (1 <= p <= infinity). By this new matrix, we obtain a factorization for the infinite Hilbert matrix, based on the Cesaro matrix of order lambda, of the form H = (BC lambda)-C-lambda. As a second application of this operator, we obtain a factorization for the Cesaro matrix of order lambda of the form C lambda+(lambda) over tilde = (R lambda,(lambda) over tilde +1C(lambda) over tilde), which results in a factorization for the Cesaro matrices of the form C-lambda = (SC(lambda) over tilde)-C-lambda,(lambda) over tilde.
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    Matrix transformations and compact operators on Catalan sequence spaces
    (Academic Press Inc Elsevier Science, 2021) Kara, Merve Ilkhan; Kara, Emrah Evren
    This paper is devoted to the study of domain of a recently defined conservative matrix in the spaces of p-absolutely summable sequences and bounded sequences. The aforementioned matrix is obtained by using the fascinating Catalan numbers. After determining the beta-duals of the newly defined Banach spaces, the characterization of some matrix operators are obtained. Finally, the characterization of certain compact operators is presented by utilizing the Hausdorff measure of non-compactness. (C) 2021 Elsevier Inc. All rights reserved.
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    Negative Difference Operator and Its Associated Sequence Space
    (Taylor & Francis Inc, 2021) Roopaei, Hadi; Kara, Merve Ilkhan
    Let Delta(-n) be the backward difference operator of order -n. In this paper, we study some properties of the matrix domain associated with this operator and after computing alpha-, beta-, gamma-duals, we characterize some matrix classes on this space. Moreover, we investigate the problem of finding the norm of well-known operators such as Cesaro and Hilbert from l(p)(Delta(-n)) into l(p).
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    New Banach Sequence Spaces Defined by Jordan Totient Function
    (Emrah Evren KARA, 2023) Devletli, Uskan; Kara, Merve Ilkhan
    In this study, a special lower triangular matrix derived by combining Riesz matrix and Jordan totient matrix is used to construct new Banach spaces. $\alpha-$,$\beta-$,$\gamma-$duals of the resulting spaces are obtained and some matrix operators are characterized.
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    ON SEQUENCE SPACES DEFINED BY THE DOMAIN OF TRIBONACCI MATRIX IN c(0) AND c
    (Kangwon-Kyungki Mathematical Soc, 2021) Yaying, Taja; Kara, Merve Ilkhan
    In this article we introduce tribonacci sequence spaces c(0)(T) and c(T) derived by the domain of a newly defined regular tribonacci matrix T. We give some topological properties, inclusion relations, obtain the Schauder basis and determine alpha-, beta- and gamma- duals of the spaces c(0)(T) and c(T). We characterize certain matrix classes (c(0)(T), Y) and (c(T), Y), where Y is any of the spaces c(0), c or l(infinity). Finally, using Hausdorff measure of non-compactness we characterize certain class of compact operators on the space c(0)(T).
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    q-Schroder sequence spaces and Schroder core
    (Univ Nis, Fac Sci Math, 2025) Ellidokuzoglu, Hacer Bilgin; Demiriz, Serkan; Kara, Merve Ilkhan
    This research employs the q-Schroder matrix to create the sequence spaces c(0)((S) over tilde (q)), c((S) over tilde (q)),l(infinity)((S) over tilde (q)) and l(p)((S) over tilde (q)) where (1 <= p < infinity). We demonstrate certain topological features, derive Schauder bases, calculate the alpha, beta and gamma duals of new sequence spaces, build some matrix classes, and finally show some topological properties. In addition, we give Schroder's core of complex valued sequences and define various inclusion theorems for the new core type.