Coupled fixed point theorems in G b -metric space satisfying some rational contractive conditions

Abstract

In this paper we prove the existence and uniqueness of couple fixed point theorems for three mappings satisfying some new rational contractive conditions. We prove our results in the frame work of Gb-metric space which is recently introduced by Aghajani et al. (Filomat 28(6):1087–1101, 2014). Illustrative example is also given to support our result.

Unique Common Tripled Fixed Point for Three Mappings in <img src=image/13424616_01.gif> Spaces

“…In 2014, Aghajani et al [2]introduced a G b -metric space as a different generalization of metric space using the concepts of b-metric space and G -metric space. The goal of this study is to show that unique common tripled fixed point theorems for three mappings via rational type contractive conditions which are broaden and extrapolate the paradigm of the results of Khomadram et al [14] in the setting of G b -metric spaces. Metric spaces are the medium where a significant amount of functional analysis ideas and conclusions are articulated.…”

FIXED POINT THEOREMS OF (α, ψ)-RATIONAL TYPE CONTRACTIVE MAPPINGS IN RECTANGULAR b-METRIC SPACE LANGPOKLAKPAM PREMILA DEVI AND LAISHRAM SHAMBHU SINGH

“…al. [5] For more results on rectangular b-metric space and other generalized forms of metric space one can see research paper s in [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] and references therein. Following definitions will be needed in the sequel: Definition 1.4 [5] Let (X, d) be a rectangular b-metric space.…”

Some Coupled fixed point theorems in partially ordered A_b-metric space

“…Mention can be made about G b -metric space, S b -metric space, b 2 -metric space, cone b-metric space, partial b-metric space, fuzzy b-metric space, rectangular b-metric space etc. Some results about generalized metric space can be seen in [1,5,8,12,[15][16][17][18][19][21][22][23] and references there in.…”