Some Compatible and Weakly-Compatible Four Self-Mapping Results Approach to Nonlinear Integral Equations in Fuzzy Cone Metric Spaces

This paper is aimed at proving some unique common fixed point theorems by using the compatible and weakly-compatible four self-mappings in fuzzy cone metric (FCM) space. We prove the results under the generalized rational contraction conditions in FCM spaces with the help of one self-map are continuous. Furthermore, we prove some rational contraction results with the weaker condition of the self-mapping continuity. Ultimately, our theoretical work has been utilized to prove the existence solution of the two nonlinear integral equations. This is an illustrative application of how FCM spaces can be used in other integral type operators.

Unique Common Fixed Point Result for Rational Contraction in Complex valued Metric Space

In this paper, we prove some unique common fixed point theorem for two pairs of weakly compatible mappings, satisfying the rational contraction conditions in complex valued metric space. The proved result, generalize and extend some known results in the literature. Finally, The main result is the application of the Urysohn integral equations to derive the existence theorem for a general solution. AMS(MOS) Subject Classification Codes: 47H10, 54H25.

Fixed point results for rational contraction in function weighted dislocated quasi-metric spaces with an application

The objective of this article is to introduce function weighted L-R-complete dislocated quasi-metric spaces and to present fixed point results fulfilling generalized rational type F-contraction for a multivalued mapping in these spaces. A suitable example confirms our results. We also present an application for a generalized class of nonlinear integral equations. Our results generalize and extend the results of Karapınar et al. (IEEE Access 7:89026–89032, 2019).

Solving Integral Equations by Common Fixed Point Theorems on Complex Partial b -Metric Spaces

In this paper, we prove some common fixed point theorems for rational contraction mapping on complex partial b -metric space. The presented results generalize and expand some of the literature’s well-known results. We also explore some of the applications of our key results.

Some Existence Results for a System of Nonlinear Fractional Differential Equations

In this paper, we show that a sequence satisfying a Suzuki-type JS-rational contraction or a generalized Suzuki-type Ćirić JS-contraction, under some conditions, is a Cauchy sequence. This paper presents some common fixed point theorems and an application to resolve a system of nonlinear fractional differential equations. Some examples and consequences are also given.