Abstract
Abstract In this study, using the notion of ( V , λ ) -summability and λ-statistical convergence, we introduce the concepts of strong ( V , λ , p ) -summability and λ-statistical convergence of order α of real-valued functions which are measurable (in the Lebesgue sense) in the interval ( 1 , ∞ ) . Also some relations between λ-statistical convergence of order α and strong ( V , λ , p ) -summability of order β are given. MSC:40A05, 40C05, 46A45.
Highlights
1 Introduction The idea of statistical convergence was given by Zygmund [ ] in the first edition of his monograph published in Warsaw in
Generalizations of statistical convergence have appeared in the study of strong integral summability and the structure of ideals of bounded continuous functions on locally compact spaces
Statistical convergence and its generalizations are connected with subsets of the Stone-Čech compactification of the natural numbers
Summary
The idea of statistical convergence was given by Zygmund [ ] in the first edition of his monograph published in Warsaw in. A real-valued function x(t), measurable (in the Lebesgue sense) in the interval ( , ∞), is said to be strongly summable to L = Lx if lim n x(t) – L p dt = ,
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