Common fixed point theorems for Geraghty’s type contraction mappings using the monotone property with two metrics

Juan Martínez-Moreno,Yeol Je Cho,Wutiphol Sintunavarat

doi:10.1186/s13663-015-0426-y

Abstract

AbstractThe main aim of this paper is to obtain some new common fixed point theorems for Geraghty’s type contraction mappings using the monotone property with two metrics and to give some examples to illustrate the main results. Further, by using our main results, we prove some results about multidimensional common fixed points. Our results generalize and extend some recent results given by Kadelburg et al. (Fixed Point Theory Appl. 2015:27, 2015) and Choudhurya and Kundu (J. Nonlinear Sci. Appl. 5:259-270, 2012).

Highlights

Introduction and preliminariesLet denote the class of real functions θ : [, ∞) → [, ) satisfying the following condition:θ → ⇒ tn → .An example of a function in may be given by θ (t) = e– t for all t > and θ ( ) ∈ [, )
The aim of this paper is to study some new common fixed point theorems for Geraghty’s type contraction mappings using the monotone property with two metrics, which is an important advantage to compare with well known fixed point theorems in metric spaces
2 Main results we prove some fixed point results for generalized contractions on spaces with two metrics

Summary

Introduction

In each of the following two cases, the mapping f has at least one fixed point in X: ( ) f is continuous or ( ) for any non-decreasing sequence {xn} in X, if xn → x ∈ X as n → ∞, xn x for all n ≥ .

Objectives

Results

Conclusion