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JOURNALS // Problemy Analiza — Issues of Analysis // Archive

Probl. Anal. Issues Anal., 2023 Volume 12(30), Issue 1, Pages 72–86 (Mi pa369)

This article is cited in 2 papers

A new approach to Egorov's theorem by means of $\alpha\beta$-statistical ideal convergence

Sonali Sharma, Kuldip Raj

School of Mathematics, Shri Mata Vaishno Devi University, Katra-182320, J&K, India

Abstract: In this work, we introduce the $\alpha\beta$-statistical pointwise ideal convergence, $\alpha\beta$-statistical uniform ideal convergence, and $\alpha\beta$-equi-statistical ideal convergence for sequences of fuzzy-valued functions. With the help of some examples, we present the relationship between these convergence concepts. Moreover, we give the $\alpha\beta$-statistical ideal version of Egorov's theorem for the sequences of fuzzy valued measurable functions.

Keywords: Egorov's theorem, $\alpha\beta$-statistical pointwise ideal convergence, $\alpha\beta$-statistical uniform ideal convergence, $\alpha\beta$-statistical equi-ideal convergence.

UDC: 510.22

MSC: 40A05, 40A30, 46S40, 47S40

Received: 26.05.2022
Revised: 06.10.2022
Accepted: 12.10.2022

DOI: 10.15393/j3.art.2023.11890



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© Steklov Math. Inst. of RAS, 2024