New Fixed Point Results of Single‐Valued Mapping for c‐Distance in Cone Metric Spaces

Abstract

A new concept of thec-distance in cone metric space has been introduced recently in 2011. The aim of this paper is to extend and generalize some fixed point results in literature forc-distance in cone metric spaces by replacing the constants in contractive conditions with functions. Some supporting examples are given.

T-Reich contraction and fixed point results in cone metric spaces with c-distance

“…In 2011, Cho et al [1] introduced the concept of the c-distance in cone metric spaces. Then, many authors studied the existence and uniqueness of the fixed point, common fixed point, coupled fixed point and common coupled fixed point problems using this distance in cone metric spaces and ordered cone metric spaces; see for example [5][6][7][8][9][10][11][12][13][14].…”

Some fixed point results of single-valued mapping for c-distance in tvs-cone metric spaces

“…This is cone metric version of w-distance of Kada et al [19]. Then several authors have proved fixed point theorems for c-distance in cone metric spaces (see [10], [11], [12], [13], [14], [15], [26], [27]).…”

“…In [10], Fadail et al proved the following theorems for c-distance in cone metric spaces-Theorem 1. Let (X, d) be a complete cone metric space and q is a c-distance on X.…”

Tripled fixed point theorems in cone metric spaces under F -invariant set and c -distance

“…After that, a large number of articles have appeared in studying fixed point, common fixed point, coupled fixed point, common coupled fixed point, tripled fixed point and tripled coincidence point theorems in cone metric spaces under c-distance idea. The reader may see [5,15,17,18,19,42].…”