Common fixed point under contractive condition of Ćirić’s type on cone metric type spaces

Abstract

The purpose of this article is to generalize common fixed point theorems under contractive condition of Ćirić's type on a cone metric type space. We give basic facts about cone metric type spaces, and we prove common fixed point theorems under contractive condition of Ćirić's type on a cone metric type space without assumption of normality for cone. As special cases we get the corresponding fixed point theorems on a cone metric space with respect to a solid cone. Obtained results in this article extend, generalize, and improve, well-known comparable results in the literature.

Common fixed point theorems for cyclic contractive mappings in partial cone b-metric spaces and applications to integral equations

“…Taking α(x, y) ≡ 1 in Corollary 1, it extends and generalizes Theorem 3.3 of[32] and so also the famous Hardy and Rogers fixed point theorem to that in the setting of partial cone b-metric spaces. Let E = R 2 , P = {(x, y) ∈ E: x, y 0}, and X = R + .…”

“…Such an approach allows the investigation of the case that the cone is not necessarily normal. Since then, there were many references concerned with fixed point results in cone spaces (see [3,13,16,20,25,26,29,[32][33][34]). In 2011, Malhotra et al [19] and Sonmez [31] defined a partial cone metric space; Hussain and Shah [12] introduced a cone b-metric space and established some topological properties in such spaces.…”

On some new fixed point results in b-rectangular metric spaces

“…Also, there are some important generalizations of usual metric spaces. Three well known generalizations of (usual) metric spaces are b−metric spaces [3,6] or metric type spaces-MTS by some authors ( [13,15,20,31]), generalized metric spaces (g.m.s.) [5] or rectangular metric spaces ( [9,11,16,17,18,21,23,24], [27]- [32]) and rectangular b−metric space [10] or a b−generalized metric space (b−g.m.s.)…”

Common Fixed Points for Two Mappings With Expansive Properties on Complex Valued Metric Spaces

“…Wang, Li and Gao ( [17]) obtained important fixed point theorems in complete real metric spaces for the above expansive type maps, and the authors in ( [5,6,8,9,12,13]) obtained coincidence point and common fixed point theorems for two maps with expansive conditions in real metric spaces, cone metric spaces and CMTS( [4,16]) respectively, widely generalized and improved the corresponding results in ( [17]). …”