Some Extensions of Banach's Contraction Principle in Complete Cone Metric Spaces

Abstract

In this paper we consider complete cone metric spaces. We generalize some definitions such as c-nonexpansive and c, λ-uniformly locally contractive functions f-closure, c-isometric in cone metric spaces, and certain fixed point theorems will be proved in those spaces. Among other results, we prove some interesting applications for the fixed point theorems in cone metric spaces.

Fixed point theorems for w-cone distance contraction mappings in tvs-cone metric spaces

“…Hence, we get p(z, Tz) = θ. ■ The following theorem extends and unifies Theorem 2 of [6] and results of ( [1,18]). Theorem 14.…”

A generalised fixed point theorem of presic type in cone metric spaces and application to markov process

“…In [5], Di Bari and Vetro obtained results on points of coincidence and common fixed points in non-normal cone metric spaces. Further results on fixed point theorems in such spaces were obtained by several authors, see [5][6][7][8][9][10][11][12][13][14][15].…”

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“…Also we have proved some new fixed point results in p-quasi-metric spaces using a comparison functionand the normality of cone which generalize the results of Raja and Vaezpour [1]. We give some basic notations in the section below PRELIMINARIES Definition 1.…”