Common fixed point theorem satisfying rational contraction in complexvalued dislocated metric space

J Uma Maheswari,A Anbarasan,Lakshmi Narayan Mishra,Vishnu Narayan Mishra

doi:10.26637/mjm904/006

Abstract

Common fixed point theorem satisfying rational contraction in complexvalued dislocated metric space

Highlights

In this article we introduce a notion of fixed point theorem satisfying rational contraction in complex valued dislocated metric space and support our main theorem to provide an example
Consider (H, γd) be a complex valued dislocated metric space and define a sequence {un} in H for each u ∈ H (i)let the sequence {un} be convergent to u in (H, γd) is said to be complex valued dislocated metric space for each > 0 we can find n0 ∈ N such that γd(un, u) < for each n > n0 which is denoted by un → u (ii)Consider the sequence {un} be cauchy sequence in (H, γd) is called complex valued dislocated metric space if limn→∞γd(un, un+b) = 0 for each b > 0 (iii)Let (H,γd) be a complex valued complete dislocated metric space if every complex valued cauchy sequence in H converges to some u ∈ H
We prove the theorem by using new rational contraction mapping in complex valued dislocated metric space

Summary

Introduction

In this article we introduce a notion of fixed point theorem satisfying rational contraction in complex valued dislocated metric space and support our main theorem to provide an example. We define a complex valued dislocated metric space

Results

Conclusion