Generalized Normed Spaces and Fixed Point Theorems

Volume 13, Issue 2, pp 157-167 http://dx.doi.org/10.22436/jmcs.013.02.07

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Authors

Kamran Alam Khan - Department of Mathematics, V. R. A. L. Govt. Girls P. G. College, Bareilly (U.P.)-INDIA

Abstract

Gähler ([4], [5]) introduced and investigated the notion of 2-metric spaces and 2-normed spaces in sixties. These concepts are inspired by the notion of area in two dimensional Euclidean space. In this paper, we choose a fundamentally different approach and introduce a possible generalization of usual norm retaining the distance analogue properties. This generalized norm will be called as G-norm. We show that every G-normed space is a G-metric space and therefore, a topological space and develop the theory for G-normed spaces. We also introduce G-Banach spaces and obtain some fixed point theorems.

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Keywords

• Linear 2-normed space
• invex set
• G-normed space
• G-metric space
• Fixed point theorem

MSC

•  46B20
•  47H10

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