Some fixed point theorems for contractive maps in N-cone metric spaces

Jerolina Fernandez,Geeta Modi,Neeraj Malviya

doi:10.1007/s40096-015-0145-x

Abstract

In present paper, we prove unique fixed point theorems for contractive maps in \(N\)-cone metric spaces. Our results extend and generalize some well-known results of (Banach, Fund Math 3:133–181 1992; Chatterjee, Rend Acad Bulgare Sci 25:727–730 1972; Kannan, Bull Calcutta Math Soc 60:71–76 1968; Rezapour and Hamlbarani, J Math Anal Appl 345:719–724 2008) in the setting of \(N\)-cone metric spaces.

Highlights

Introduction and preliminariesThe notion of cone metric space was introduced in [7]
In present paper, we prove unique fixed point theorems for contractive maps in N-cone metric spaces
Our results extend and generalize some well-known results of (Banach, Fund Math 3:133–181 1992; Chatterjee, Rend Acad Bulgare Sci 25:727–730 1972; Kannan, Bull Calcutta Math Soc 60:71–76 1968; Rezapour and Hamlbarani, J Math Anal Appl 345:719–724 2008) in the setting of Ncone metric spaces

Summary

Introduction

Introduction and preliminariesThe notion of cone metric space was introduced in [7]. In this paper, Huang and Zhang replace the real numbers by ordering Banach space and define cone metric space. Abstract In present paper, we prove unique fixed point theorems for contractive maps in N-cone metric spaces. Keywords N-cone metric space Á Fixed point Á Contractive map Mathematics Subject Classification 54H25 Á 47H10 Malviya and Fisher [13] introduced the notion of N-cone metric space and proved fixed point theorems for asymptotically regular maps and sequence.

Results

Conclusion