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    Approximation properties of Bernstein-Stancu operators preserving e?2x
    (University of Nis, 2023) Usta, Fuat; Mursaleen, M.; Çakır, İ.
    Bernstein-Stancu operators are one of the most powerful tool that can be used in approximation theory. In this manuscript, we propose a new construction of Bernstein-Stancu operators which preserve the constant and e?2x, x > 0. In this direction, the approximation properties of this newly defined operators have been examined in the sense of different function spaces. In addition to these, we present the Voronovskaya type theorem for this operators. At the end, we provide two computational examples to demonstrate that the new operator is an approximation procedure. © 2023, University of Nis. All rights reserved.
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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