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

Abstract

In this paper, we introduce the T-Reich contraction under the concept of c-distance in cone metric spaces. Then, we prove the existence and uniqueness of the fixed point in some type of mappings which satisfy the T-Reich contraction under the concept of c-distance in cone metric spaces. The presented theorem extends and generalizes several well-known comparable results in literature.

NEW FIXED POINT RESULTS FOR T-CONTRACTIVE MAPPING WITH c-DISTANCE IN CONE METRIC SPACES

“…Recently, Cho et al [3] introduced the concept of c-distance in a cone metric spaces and proved some fixed point results in ordered cone metric spaces. Afterward, many authors have generalized and studied fixed point theorems under c-distance in cone metric spaces (see [1,7,8,9,10,11,14,15,16]). In 2009, Beiranvand et al [2] introduced new classes of contractive functions and established the Banach principle.…”

“…In 2009, Beiranvand et al [2] introduced new classes of contractive functions and established the Banach principle. Since then, fixed point theorems for T -contraction mapping on cone metric spaces have been appeared, see for instance [4,5,6] and [11].…”