In this article, we deal with dual spaces and the Hahn-Banach Theorem. At the first, we defined dual spaces of real linear spaces and proved related basic properties. Next, we defined dual spaces of real normed spaces. We formed the definitions based on dual spaces of real linear spaces. In addition, we proved properties of the norm about elements of dual spaces. For the proof we referred to de...

* Correspondence: [email protected] Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India Full list of author information is available at the end of the article Abstract Recently, the concepts of statistical convergence, ideal convergence and lacunary statistical convergence have been studied in intuitionistic fuzzy normed spaces. In this article, we study the concepts ...

The main aim of this work is to investigate some important properties statistical convergence sequence in non-Archimedean fields. Statistical has been discussed various fields mathematics namely approximation theory, measure probability trigonometric series, number etc. concept summability over valued a significant area that many applications analytic continuation, quantum mechanics, Fourier an...

in this paper we define intuitionistic fuzzy metric and normedspaces. we first consider finite dimensional intuitionistic fuzzy normed spacesand prove several theorems about completeness, compactness and weak convergencein these spaces. in section 3 we define the intuitionistic fuzzy quotientnorm and study completeness and review some fundamental theorems. finally,we consider some properties of...

Stochastic processes on manifolds over non-Archimedean fields and with transition measures having values in the field C of complex numbers are studied. Stochastic antideriva-tional equations (with the non-Archimedean time parameter) on manifolds are investigated. 1. Introduction. Stochastic processes and stochastic differential equations on real Banach spaces and manifolds on them were intensiv...

This paper generalizes the Aleksandrov problem, the Mazur–Ulam theorem and Benz theorem on n-normed spaces. It proves that a one-distance preserving mapping is an nisometry if and only if it has the zero-distance preserving property, and two kinds of n-isometries on n-normed spaces are equivalent.

In this paper we introduce the sequence spaces χM (p, q, u), using an modulus function M and defined over a semi normed space (X, q), semi normed by q. We study some properties of these sequence spaces and obtain some inclusion relations.

Recently in [22], Mursaleen introduced the concept of statistical convergence in random 2-normed spaces. In this paper, we define and study the notion of lacunary ∆-statistical convergence and lacunary ∆-statistical Cauchy sequences in random 2-normed spaces using lacunary density and prove some interesting theorems. Subjclass [2000] : Primary 40A05; Secondary 46A70, 40A99, 46A99.

w0-Nearest Points and w0-Farthest Point in Normed Linear Spaces