Fixed point theorems for convex contractions on cone 2-metric space over Banach algebra

P Rama Bhadra Murthy ,M Rangamma

doi:10.28919/afpt/3434

Abstract

In 2007, B.Singh, S Jain and P Bhagat introduced cone 2-metric space and proved some fixed point theorems of certain contractive mappings while Tao Wang, Jiangdong Yin, and Qi Yan introduced cone 2-metric spaces over Banach algebra and established some existence and uniqueness theorems of fixed points for some contractive mappings. In this paper, we extended some results of Istra{\c{t}}escu's convex contractions to cone 2-metric space over Banach algebra and presented two fixed point theorems. Examples are given showing the significance of our results.

Highlights

In 1962, Gahler [6] introduced 2-metric space with area of triangle as an underlying example
We extended some results of Istratescu’s convex contractions to cone 2-metric space over Banach algebra and presented two fixed point theorems
Among many other generalizations of an ordinary metric, 2-metric has not been known to be topologically equivalent to an ordinary metric and there was no easy relationship between the results obtained in 2-metric spaces and ordinary metric spaces

Summary

Introduction

In 1962, Gahler [6] introduced 2-metric space with area of triangle as an underlying example. We extended some results of Istratescu’s convex contractions to cone 2-metric space over Banach algebra and presented two fixed point theorems. We have presented cone convex contractions on cone 2-metric space over Banach algebras and proved some fixed theorems.

Results

Conclusion