Yazar "Ilkhan, Merve" seçeneğine göre listele

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    Almost convergence and Euler totient matrix
    (Springer Basel Ag, 2020) Demiriz, Serkan; Ilkhan, Merve; Kara, Emrah Evren
    This paper is devoted to study the almost convergent sequence space c(F) derived by the Euler totient matrix. It is proved that the space c(F) and the space of all almost convergent sequences are linearly isomorphic. Further, the ss-dual of the space c(F) is determined and Euler totient core of a complex-valued sequence has been defined. Finally, inclusion theorems related to this new type of core are obtained.
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    Compact operators on the Jordan totient sequence spaces
    (Wiley, 2021) Ilkhan, Merve; Kara, Evren Emrah; Usta, Fuat
    The necessary and sufficient conditions for compactness of a matrix operator between Banach spaces is obtained by utilizing the concept of the Hausdorff measure of noncompactness. This is one of the most interesting application in the theory of sequence spaces. In this paper, the compact operators are characterized on Jordan totient sequence spaces by using the concept of the Hausdorff measure of noncompactness.
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    FIXED POINTS OF (alpha, phi)-MEIR-KEELER CONTRACTIVE MAPPINGS IN GENERALIZED RECTANGULAR b-METRIC SPACES
    (Mili Publ, 2019) Ozcelik, Reyhan; Ilkhan, Merve; Kara, Emrah Evren
    The main objective of this work is to develop fixed point results for (alpha, phi)-Meir-Keeler contractive mappings in generalized rectangular b-metric spaces and to investigate the uniqueness of fixed points.
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    Matrix Domain of a Regular Matrix Derived by Euler Totient Function in the Spaces c(0) and c
    (Springer Basel Ag, 2020) Ilkhan, Merve
    The main purpose of this manuscript is to introduce Banach spaces c(0)(Phi) and c(Phi) as the matrix domain of a regular matrix Phi derived by the Euler totient function. These spaces consist of phi-convergent to zero and phi-convergent sequences, respectively. After determining alpha-, beta- and gamma-duals of these spaces, some matrix classes are characterized. Finally, using the Hausdorff measure of noncompactness, the characterization of some classes of compact operators on the space c(0)(Phi) is given.
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    A new conservative matrix derived by Catalan numbers and its matrix domain in the spaces c and c(0)
    (Taylor & Francis Ltd, 2020) Ilkhan, Merve
    The main purpose of this paper is to define a new conservative matrix by means of the fascinating sequence of Catalan numbers and study the matrix domain of this newly introduced matrix in the classical sequence spaces c and . Additionally, after determining the Kothe-Toeplitz dual, generalized Kothe-Toeplitz dual and Garling dual, certain matrix transformations and compact operators are characterized on the new Banach spaces.
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    A NEW PARANORMED SERIES SPACE USING EULER TOTIENT MEANS AND SOME MATRIX TRANSFORMATIONS
    (Kangwon-Kyungki Mathematical Soc, 2020) Gulec, G. Canan Hazar; Ilkhan, Merve
    Paranormed spaces are important as a generalization of the normed spaces in terms of having more general properties. The aim of this study is to introduce a new paranormed space vertical bar phi(z)vertical bar (p) over the paranormed space l(p) using Euler totient means, where p = (p(k)) is a bounded sequence of positive real numbers. Besides this, we investigate topological properties and compute the alpha-, beta-, and gamma duals of this paranormed space. Finally, we characterize the classes of infinite matrices (vertical bar phi(z)vertical bar (p) , lambda) and (lambda, vertical bar phi(z)vertical bar (p)), where lambda is any given sequence space.
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    A new regular infinite matrix defined by Jordan totient function and its matrix domain in l(p)
    (Wiley, 2021) Ilkhan, Merve; Simsek, Necip; Kara, Emrah Evren
    In this paper, we first define a new regular matrix by using the arithmetic function called Jordan totient function and study the matrix domain of this newly introduced matrix in the Banach space l(p). After computing the dual spaces of this new space, we characterize certain matrix mappings related to this space.
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    On Lacunary ideal convergence of some sequences
    (Biska Bilişim, 2017) Kara, Emrah Evren; Dastan, Mahmut; Ilkhan, Merve
    In this paper, new classes of lacunary ideal convergent and lacunary ideal bounded sequences combining an infinite matrix and an Orlicz function are defined. Some properties of these spaces are investigated and also some inclusion relations are obtained.
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    POISSON LIKE MATRIX OPERATOR AND ITS APPLICATION IN p-SUMMABLE SPACE
    (Walter De Gruyter Gmbh, 2021) Yaying, Taja; Hazarika, Bipan; Ilkhan, Merve; Mursaleen, M.
    The incomplete gamma function (a, u) is defined by Gamma(a, u) = integral(infinity)(u) t(a-1)e(-t) dt, where u > 0. Using the incomplete gamma function, we define a new Poisson like regular matrix beta(mu) = (p(nk)(mu)) given by p(nk)(mu) = {n!/Gamma(n+1, mu) e(-mu)mu(k)/k! (0 <= k <= n), 0 (k > n), where mu > 0 is fixed. We introduce the sequence space l(p) (beta(mu)) for 1 <= p <= 1 and some topological properties, inclusion relations and generalized duals of the newly defined space are discussed. Also we characterize certain matrix classes and compact operators related to the space l(p) (beta(mu)). We obtain Gurarii's modulus of convexity and investigate some geometric properties of the new space. Finally, spectrum of the operator beta(mu) on sequence space c(0) has been investigated. (C) 2021 Mathematical Institute Slovak Academy of Sciences