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

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.

Probabilistic $ (\omega, \gamma, \phi) $-contractions and coupled coincidence point results

<abstract><p>In this paper, we introduce the notion of probabilistic $ (\omega, \gamma, \phi) $-contraction and establish the existence coupled coincidence points for mixed monotone operators subjected to the introduced contraction in the framework of ordered Menger $ PM $-spaces with Had${\rm{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}} \over z} }}$ić type $ t $-norm. As an application, a corresponding result in the setup of fuzzy metric space is also obtained.</p></abstract>

Some fixed point results of generalized $$(\phi , \psi )$$-contractive mappings in ordered b-metric spaces

Objectives The aim of this paper is to establish some fixed point, coincidence point and, coupled coincidence and coupled common fixed point results for generalized $$(\phi , \psi )$$ ( ϕ , ψ ) -contractive mappings in partially ordered b-metric spaces. Our results generalize, extend and unify most of the fundamental metrical fixed point theorems in the existing literature. Few examples are illustrated to justify our results. Result The existence and uniqueness theorems for a fixed point and coincidence point, coupled coincidence point and coupled common fixed points for two mappings satisfying generalized $$(\phi , \psi )$$ ( ϕ , ψ ) -contractive conditions in complete partially ordered b-metric spaces are proved. These results generalize several comparable results in the existing literature.

Upper class of type I on coupled coincidence point results for some contractions in partially ordered JS-metric spaces

In this research work, the necessary and sufficient conditions of a coupled coincidence point of certain type of generalized contractions are explored. These results are considered under JS-metric spaces equipped with a partial order. Moreover, examples satisfying theorems are given. Finally, an application to a system of integral equations is obtained using our results. In addition, an example of the system is provided.

Coupled coincidence point results for contraction of $C$-class mappings in ordered uniform spaces

In the literature there is a lot of works related to fixed point theory. The theory has many applications and some authors are interested in these applications in various spaces. In 2009, Altun I. and Imdad M. defined the order relation on uniform spaces and the concept of compatibility of mappings. Later Ansari A.H. defined the $C$-class function concept. In this paper, we take some ultra altering distance and $C$-class functions, then we prove some coupled coincidence point theorems for a mapping providing mixed $g$-monotonicity property in ordered uniform spaces. We also give the appropriate examples.