On the Cesaro summability for functions of two variables

WOS: 000458493700035For a continuous function f(T, S) on R-+(2) = [0,infinity) x [0,infinity), we define its integral on R-+(2) by F(T, S) = integral(T)(0) integral(S)(0) f(t,s)dt ds, and its (C, alpha, beta) mean by sigma(alpha, beta)(T,S) = integral(T)(0) integral(S)(0)(1-t/T)(alpha) (1-s/S)(beta) f(t,s)dt ds, where alpha > -1, and beta > -1. We say that integral(infinity)(0)integral(infinity)(0) f(t,s)dt ds is (C, alpha, beta) integrable to L if lim(T,S ->infinity)sigma(alpha,beta)(T,S) = L exists. We prove that if lim(T,S ->infinity)sigma(alpha,beta)(T,S) = L exists for some alpha > -1 and beta > -1, then lim(T,S ->infinity)sigma(alpha+h, beta+k)(T,S) = L exists for all h > 0 and k > 0. Next, we prove that if integral(infinity)(0)integral(infinity)(0) f(t,s) dtds is (C, 1, 1) integrable to L and T integral(S)(0) f(T,s)ds = O(1) and S integral(T)(0) f(t,S)ds = O(1) then lim(T,S ->infinity)F(T,S) = L exists

SOME CONDITIONS UNDER WHICH SLOW OSCILLATION OF A SEQUENCE OF FUZZY NUMBERS FOLLOWS FROM CESARO SUMMABILITY OF ITS GENERATOR SEQUENCE

WOS: 000342330600002Let (u(n)) be a sequence of fuzzy numbers. We recover the slow oscillation of (u(n)) of fuzzy numbers from the Cesaro summability of its generator sequence and some additional conditions imposed on (u(n)). Further, fuzzy analogues of some well known classical Tauberian theorems for Cesaro summability method are established as particular cases

HOLDER SUMMABILITY METHOD OF FUZZY NUMBERS AND A TAUBERIAN THEOREM

WOS: 000342330600007In this paper we establish a Tauberian condition under which convergence follows from Holder summability of sequences of fuzzy numbers

Preface Analysis and Functional Analysis

3rd International Conference of Mathematical Sciences, ICMS 2019 -- 4 September 2019 through 8 September 2019 -- -- 155611[No abstract available

Hölder summability method of fuzzy numbers and a tauberian theorem

In this paper we establish a Tauberian condition under which convergence follows from Hölder summability of sequences of fuzzy numbers. © 2014, University of Sistan and Baluchestan. All rights reserved

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

4th International Conference of Mathematical Sciences, ICMS 2020 -- 17 June 2020 through 21 June 2020 -- -- 1675532-s2.0-85102307914In 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

A tauberian theorem for the weighted mean method of summability

In this paper we obtain a Tauberian condition in terms of the weighted classical control modulo for the weighted mean method of summability. Some additional results are also given

On a Tauberian theorem for the weighted mean method of summability

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