Generalized Normed Spaces and Fixed Point Theorems


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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ISRP Style

Kamran Alam Khan, Generalized Normed Spaces and Fixed Point Theorems, Journal of Mathematics and Computer Science, 13 (2014), no. 2, 157-167

AMA Style

Khan Kamran Alam, Generalized Normed Spaces and Fixed Point Theorems. J Math Comput SCI-JM. (2014); 13(2):157-167

Chicago/Turabian Style

Khan, Kamran Alam. "Generalized Normed Spaces and Fixed Point Theorems." Journal of Mathematics and Computer Science, 13, no. 2 (2014): 157-167


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