Mathematics and Computer Science, Volume 1

7Some Fixed Point and Coincidence Point Results Involving G_α-Type Weakly Commuting Mappings

Krishna Kanta Sarkar¹*, Krishnapada Das² and Abhijit Pramanik¹

¹Department of Mathematics, Brainware University, Ramkrishnapur Road, Barasat, Kolkata, West Bengal, India

²Department of Mathematics, Sarojini Naidu College for Women, Jessore Road, Dum Dum, Kolkata, West Bengal, India

Abstract

G-metric spaces appeared in analysis as a generalization of metric spaces. D-metric and 2-metric are also generalized by G-metric. G-fuzzy metric spaces may be treated as fuzzy version of G-metric. Commuting mapping and weakly commuting mappings are very much important for the study of fixed points. We have established some results for coincidence point in G-fuzzy metric spaces and some results for common fixed point. Here we have deduced some corollaries to our theorems and our theorems are also supported by examples.

Keywords: G-fuzzy metric, G-Cauchy sequence, altering distance function

AMS classification of subject: 54H25, 54E70, 47H10

7.1 Introduction

S. Banach [4] initiated the study of fixed point (fp) theory by his seminal work in 1922. This theory of fp generalized by researcher in many directions. With the help of commuting mappings Jungck [17] established a result on common fixed point (cfp) in the year 1976. This notion further generalized to mappings with weakly, R-weakly type, compatible, weakly compatible, R-weakly compatible type and many more. Some authors also interested to find ...