Common Fixed Point Theorems for Expansive Type Mappings in b-Metric Spaces

ROHIT KUMAR VERMA

Abstract


Abstract- In this paper, we prove three common fixed point results for expansive type mappings in b-metric spaces. First part of our main result contains two results on weakly compatible mappings under a given expansive condition. First theorem is a generalizations of main result of Deheria et.al.[7] and a slight variation of Mohanta [13]. Second theorem is a generalization of another fixed point result of Mohanta [13]. For the second section of our main result, we have introduced f-extension condition on b-metric spaces. Suppose a mapping g:X→X doesn’t satisfy an extension condition in itself but it have a fixed point. If another mapping f:X→X is introduced such that f and g satisfy an f-extension condition and provide a common fixed point then this is called f-extension. Below, we have given examples of f-extension as well as illustrative example of our third main result.


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