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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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    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