In 2014, Zead Mustafa introduced $b_2$-metric spaces, as a generalization of both $2$-metric and $b$-metric spaces. Then new fixed point results for the classes of  rational Geraghty contractive mappings of type I,II and III in the setup of $b_2$-metric spaces are investigated. Then, we prove some fixed point theorems under various contractive conditions in partially ordered $b_2$-metric spaces...

The aim of this paper is to prove some common fixed point theorems for four  mappings satisfying $(psi,varphi)$-weak contractions involving rational expressions in ordered partial metric spaces. Our results extend, generalize and improve some well-known results in the literature. Also, we give two examples to illustrate our results.

In this paper we define weak $F$-contractions on a‎ ‎metric space into itself by extending $F$-contractions‎ ‎introduced by D‎. ‎Wardowski (2012) and provide some fixed point‎ ‎results in complete metric spaces and in partially ordered complete ‎generalized metric spaces‎. ‎Some relationships between weak‎ ‎$F$-contractions and $Fi$-contractions are highlighted‎. ‎We also ‎give some application...

In this paper, we introduce the concept of generalized quasi-contractions in the setting of cone $b$-metric spaces over Banach algebras. By omitting the  assumption of normality we establish common fixed point theorems for the generalized quasi-contractions  with the spectral radius $r(lambda)$ of the quasi-contractive constant vector $lambda$ satisfying $r(lambda)in [0,frac{1}{s})$  in the set...

The aim of this paper is to prove some common fixed point theorems for four  mappings satisfying $(psi,varphi)$-weak contractions involving rational expressions in ordered partial metric spaces. Our results extend, generalize and improve some well-known results in the literature. Also, we give two examples to illustrate our results.

In this paper, we obtain a unique common fixed point results by using Suzuki - $(\mathcal{Z}_{\psi}(\alpha,\beta))$ type rational contractive mappings in metric spaces. Also give an example which supports our main theorem.

in this paper we define weak $f$-contractions on a‎ ‎metric space into itself by extending $f$-contractions‎ ‎introduced by d‎. ‎wardowski (2012) and provide some fixed point‎ ‎results in complete metric spaces and in partially ordered complete ‎generalized metric spaces‎. ‎some relationships between weak‎ ‎$f$-contractions and $fi$-contractions are highlighted‎. ‎we also ‎give some application...

the aim of this paper is to prove some common fixed point theorems for four  mappings satisfying $(psi,varphi)$-weak contractions involving rational expressions in ordered partial metric spaces. our results extend, generalize and improve some well-known results in the literature. also, we give two examples to illustrate our results.