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 first introduce some types of generalized $alpha$-Meir-Keeler contractions in $b$-metric-like spaces and then we establish some fixed point results for these types of contractions. Also, we present a new fixed point theorem for a Meir-Keeler contraction through rational expression. Finally, we give some examples to illustrate the usability of the obtained results.

This paper is concerned with the revision of beliefs in the face of new and possibly contradicting information. In the Logic of Theory Change developed by Alchourron, Gärdenfors and Makinson this nonmonotonic process consists of a contraction and an expansion of a set of formulas. To achieve minimal change they formulated widely accepted postulates that rational contractions have to fulfill. Co...

In this paper, we present some fixed and coincidence point theorems for hybrid rational Geraghty contractive mappings in partially ordered $b$-metric spaces. Also, we derive certain coincidence point results for such contractions. An illustrative example is provided here to highlight our findings.

Abstract In this paper, we improve the Proinov theorem by adding certain rational expressions to definition of corresponding contractions. After that, prove fixed point theorems for these modified contractions in framework dislocated b -metric spaces. We show some illustrative examples indicate validity main results.

Samet et al. in [S. Samet, C. Vetro, H. Yazidi, J. Nonlinear Sci. Appl., 6 (2013), 162–169] proved some fixed point theorem for contractions of rational type. In order to clarify the mathematical structure of contractions of rational type, we generalize this theorem in a general setting.

Abstract The aim of this paper is to investigate the interpolative contractions involving rational forms in framework b -metric spaces. We prove existence a fixed point such mapping with different combinations forms. A certain example considered indicate validity observed result.

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.