Fixed point results for weak contractions in partially ordered b-metric space

Abstract

Objectives We explore the existence of a fixed point as well as the uniqueness of a mapping in an ordered b-metric space using a generalized $$({\check{\psi }}, \hat{\eta })$$ ( ψ ˇ , η ^ ) -weak contraction. In addition, some results are posed on a coincidence point and a coupled coincidence point of two mappings under the same contraction condition. These findings generalize and build on a few recent studies in the literature. At the end, we provided some examples to back up our findings. Result In partially ordered b-metric spaces, it is discussed how to obtain a fixed point and its uniqueness of a mapping, and also investigated the existence of a coincidence point and a coupled coincidence point for two mappings that satisfying generalized weak contraction conditions.

Variations of generalized weak contractions in partially ordered b-metric space

“…In the present work, we proved some fixed point results for the self mappings satisfying a generalized weak contractive condition in a complete partially ordered b -metric space. The obtained results generalized and extended the results of [ 12 , 28 , 32 , 33 ] and some existing results in the literature. A few examples are illustrated to support findings.…”

“…[ 33 ] If the metric d is complete then is called complete partially ordered b -metric space (CPO b -MS).…”

“…[ 33 ] Let be a partially ordered set and let are two mappings. Then is called a monotone non-decreasing, if for all with .…”

“…Later, there has been a lot of generalizations and extensions for the results of coupled fixed points and coupled coincidence points in various ordered spaces, some of such works can be found from the articles [ 4 – 6 , 9 , 14 , 15 , 17 – 19 , 25 – 27 ]. Recently, some results on fixed point, coincidence point and coupled coincidence points for the mappings satisfying generalized weak contraction contractions in the context of partially ordered b -metric space with topological properties have been investigated by Belay Mituku et al [ 12 ], Seshagiri Rao et al [ 28 , 32 , 33 ]. In [ 2 ] Aftab Alam et al have generalized some frequently used metrical notations such as completeness, continuity, compatibility etc.…”

Generalized fixed point results of rational type contractions in partially ordered metric spaces

“…rkA lot of work on the results of fixed points, common fixed points, coupled fixed points in partly ordered metric spaces with different topological properties involved can be found from [ 29 – 41 ]. Some generalized fixed points results of monotone mappings in partially ordered b -metric spaces have been investigated by Seshagiri Rao et al [ 43 , 46 , 47 ], Kalyani et al [ 42 , 45 , 48 ] and Belay Mitiku et al [ 44 ]. Acar [ 49 ] explored some fixed point results of F -contraction for multivalued integral type mapping on a complete metric space.…”