An Affirmative Result on Banach Space

The aim of this paper is to establish a common fixed point theorem on Banach space using occasionally weakly compatible (OWC) mappings.

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.

Common fixed point of four maps in Sm-metric space

In this paper, first, we deal with new metric space Sm-metric space that combines multiplicative metric space and S-metric space. We generate a common fixed point theorem in a Sm-metric space using the notions of reciprocally continuous mappings, faintly compatible mappings and occasionally weakly compatible mappings (OWC). We are also studying the well-posedness of Sm metric space. Further, some examples are presented to support our outcome.

Some Results by Using CLR’s-Property in Probabilistic 2-Metric Space

The aim of this paper is to generate two fixed point theorems in probabilistic 2-metric space by applying CLR’S-property and occasionally weakly compatible mappings (OWC), these two results generalize the theorem proved by V. K. Gupta, Arihant Jain and Rajesh Kumar. Further these results are justified with suitable examples.

Relative Gorenstein Dimensions over Triangular Matrix Rings

Let A and B be rings, U a (B,A)-bimodule, and T=A0UB the triangular matrix ring. In this paper, several notions in relative Gorenstein algebra over a triangular matrix ring are investigated. We first study how to construct w-tilting (tilting, semidualizing) over T using the corresponding ones over A and B. We show that when U is relative (weakly) compatible, we are able to describe the structure of GC-projective modules over T. As an application, we study when a morphism in T-Mod is a special GCP(T)-precover and when the class GCP(T) is a special precovering class. In addition, we study the relative global dimension of T. In some cases, we show that it can be computed from the relative global dimensions of A and B. We end the paper with a counterexample to a result that characterizes when a T-module has a finite projective dimension.