Multiplicative Normed Linear Space and its Topological Properties

Renu Chugh; Ashish Nandal  and Naresh Kumar

doi:10.17485/ijst/2017/v10i10/74294

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Multiplicative Normed Linear Space and its Topological Properties

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Indian Journal of Science and Technology

DOI: 10.17485/ijst/2017/v10i10/74294

Year: 2017, Volume: 10, Issue: 10, Pages: 1-9

Original Article

Multiplicative Normed Linear Space and its Topological Properties

Renu Chugh, Ashish Nandal^* and Naresh Kumar

Department of Mathematics, M. D. University, Rohtak - 124001, Haryana, India; [email protected], [email protected], [email protected]

*Author for correspondence
Ashish Nandal
Department of Mathematics, M. D. University, Rohtak - 124001, Haryana, India; [email protected]

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

The aim of this article is to propose a new space called multiplicative normed linear space and discuss different topological properties of this space. We establish equivalence between multiplicative compactness and multiplicative sequentially compactness. Some examples are given which demonstrate the validity of our results. Further we apply our results to prove fixed point existence theorems.

Keywords: Multiplicative Continuous Function, Multiplicative Convergent Sequence, Fixed Point Existence Theorems, Multiplicative Normed Linear Space. Mathematics Subject Classification (2010): 46B20, 46B50, 47H10