ON ASYMPTOTICALLY LACUNARY STATISTICAL EQUIVALENT SEQUENCES IN PROBALISTIC NORMED SPACE

Esi Esi

doi:10.3844/jmssp.2013.144.148

Abstract

In this study we study the new concept of asymptotically lacunary statistical convergent sequences in probabilistic normed spaces and prove some basic properties.

Highlights

Marouf (1993) presented definitions for asymptotically equivalent sequences and asymptotic regular matrices. Patterson (2003), extended those concepts by presenting an asymptotically statistical equivalent analog of these definitions and natural regularity conditions for non-negative sum ability matrices
In this study we study the new concept of asymptotically lacunary statistical convergent sequences in probabilistic normed spaces and prove some basic properties
An interesting and important generalization of the notion of metric space was introduced by Menger (1942) under the name of statistical metric, which is called probabilistic metric space

Summary

INTRODUCTION

Marouf (1993) presented definitions for asymptotically equivalent sequences and asymptotic regular matrices. Patterson (2003), extended those concepts by presenting an asymptotically statistical equivalent analog of these definitions and natural regularity conditions for non-negative sum ability matrices. This study extends the definitions presented in (Patterson and Savas, 2006) to lacunary sequences in probabilistic normed space. Probabilistic normed spaces (briefly, PN-spaces) are linear spaces in which the norm of each vector is an appropriate probability distribution function rather than a number. Such spaces were introduced by Serstnev (1963). In this study we study the concept of asymptotically lacunary statistical convergent sequences on probabilistic normed spaces. Since the study of convergence in PNspaces is fundamental to probabilistic functional analysis, we feel that the concept of symptotically lacunary statistical convergent sequences in a PN-space would provide a more general framework for the subject

Prelimiaries

Asymptotically Lacunary Convergence on PN-Spaces

CONCLUSION