Fixed point results under c-distance in tvs-cone metric spaces

Abstract

Fixed point and common fixed point results for mappings in tvs-cone metric spaces (with the underlying cone which is not normal) under contractive conditions expressed in the terms of c-distance are obtained. Respective results concerning mappings without periodic points are also deduced. Examples are given to distinguish these results from the known ones. Mathematics Subject Classification (2010) 47H10, 54H25

Ordered weak $\varphi$-contractions in cone metric spaces over Banach algebras and fixed point theorems

“…Define B (x n , c) = {x ∈ X : d(x n , x) c, x n x}, n ≥ n 1 , then obviously B (x n , c) = ∅. Choose x ∈ B (x n , c) with n ≥ n 1 , tnen by (5) and the definition of B (x n , c) we get…”

Topological Properties of E-Metric Spaces with Applications to Fixed Point Theory

“…Motivated by the concept of c-sequence from [15], we introduce the concept of the e-sequence in E-metric space as follows.…”

Fixed Point Results for Weakφ-Contractions in Cone Metric Spaces over Banach Algebras and Applications

“…In [4], Huang and Zhang introduced cone metric space and generalized Banach fixed point theorem in such spaces. Subsequently, many people were interested in fixed point results in cone metric spaces (see [5][6][7][8][9][10] and the references therein). In [11][12][13], Rus and Berinde introduced the notion of -contraction and also generalized Banach fixed point theorem in usual metric spaces.…”

“…Definition 7 (see [8]). A sequence { } in a Banach algebra A is said to be a -sequence if, for each ≫ , there exists ∈ N such that ≪ for all > .…”