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  • Küçük Resim
    Öğe
    On Composition Operators of Fibonacci Matrix and Applications of Hausdorff Measure of Noncompactness
    (Soc Paranaense Matematica, 2022) Das, Anupam; Hazarika, Bipan; Kara, Emrah Evren; Basar, Feyzi
    The aim of the paper is introduced the composition of the two infinite matrices Lambda = (lambda(nk)) and (F) over cap = (f(nk)). Further, we determine the alpha-, beta-, gamma-duals of new spaces and also construct the basis for the space l(p)(lambda)((F) over cap). Additionally, we characterize some matrix classes on the spaces l(infinity)(lambda) ((F) over cap) and l(p)(lambda) ((F) over cap). We also investigate some geometric properties concerning Banach- Saks type p. Finally we characterize the subclasses K(X : Y) of compact operators by applying the Hausdorff measure of noncompactness, where X is an element of{l(infinity)(lambda) ((F) over cap), l(p)(lambda) ((F) over cap)} and Y is an element of{c(0), c, l(infinity), l(1), b(v)}, and 1 <= p < infinity.
  • Küçük Resim Yok
    Öğe
    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