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Öğe On a Tauberian theorem for the weighted mean method of summability(University of Kuwait, 2015) Sezer S.A.; Canak I.We investigate conditions needed for a weighted mean summable series to be convergent by using Kloosterman's method. The results of this paper generalize the well known results of Landau and Hardy.Öğe On converse theorems for the discrete Bürmann power series method of summability(Maejo University, 2016) Sezer S.A.; Canak I.In this communication we recover ordinary convergence of a series from its summability by the discrete Bürmann power series method under certain conditions. © 2016 by Maejo University.Öğe Revisited tauberian theorem for which slow decrease with respect to a weight function is a tauberian condition for the weighted mean summability of integrals over r(American Institute of Physics Inc., 2021) Canak I.In this extended abstract, we present an alternative proof of a Tauberian theorem of slowly decreasing type with respect to the weight function due to Karamata [5] for the weighted mean summable real-valued integrals over R+ := [0,?). Some particular choices of weight functions provide alternative proofs of some well-known Tauberian theorems given for several important summability methods. © 2021 American Institute of Physics Inc.. All rights reserved.Öğe Some Tauberian theorems for weighted means of double integrals on R + 2(American Institute of Physics Inc., 2019) Flndlk G.; Canak I.Let p(x) and q(y) be nondecreasing continuous functions on [0, 8) such that p(0) = q(0) = 0 and p(x), q(y) › 8 as x, y › 8. For a locally integrable function R+2 = [0,8) × [0,8), we denote its double integral by F(x,y)=?0x?0yf(t,s)dtds and its weighted mean of type (?, ß) by t?,ß(x,y)=?0x?0y(1-p(t)p(x))?(1-q(s)q(y))ßf(t,s)dtds where ? > -1 and ß > -1. We say that ?08?08f(t,s)dtds is integrable to L by the weighted mean method of type (?, ß) determined by the functions p(x) and q(x) if lim x,y›8 t ?,ß (x, y) = L exists. We prove that if lim x,y›8 t ?,ß (x, y) = L exists and t ?,ß (x, y) is bounded on R+2 for some ? > -1 and ß > -1, then lim x,y›8 t ?+h,ß+k (x, y) = L exists for all h > 0 and k > 0. Finally, we prove that if ?08?08f(t,s)dtds is integrable to L by the weighted mean method of type (1, 1) determined by the functions p(x) and q(x) and conditions (x)p'(x)?0yf(x,s)ds=O(1)andq(y)q'(y)?0xf(t,y)dt=O(1) hold, then lim x,y›8 F(x, y) = L exists. © 2019 Author(s).Öğe Statistical extensions of Tauberian theorems for the weighted mean method of summability in two-normed spaces(American Institute of Physics Inc., 2021) Bakicierler H.; Canak I.In this extended abstract, we first define the concept of statistical summability (N, p) in 2-normed spaces and then present necessary and/or sufficient Tauberian conditions for statistical summability (N, p) in 2-normed spaces. © 2021 American Institute of Physics Inc.. All rights reserved.Öğe A Tauberian theorem for Cesro summability of integrals(2011) Canak I.; Totur Ü.In this paper we give a proof of the generalized Littlewood Tauberian theorem for Cesro summability of improper integrals. © 2010 Elsevier Ltd. All rights reserved.
