Fixed Point Theorems in General Metric Space with an Application

يهدف هذا البحث إلى إثبات مبرهنة وجود لمعادلة من نوع فولتيرا في تعميم فضاء G- متري يسمى  فضاء   -  المتري, حيث تتم مناقشة مبرهنة النقطة الصامدة في فضاء   -  المترية وتطبيقها. أولاً ، تم تقديم انكماش جديد من نوع هاردي روجيس ثم تم كذلك إنشاء مبرهنة النقطة الصامدة لهذه الانكماشات في حالة فضاء   -  المترية. كتطبيق ، تم الحصول على نتيجة وجود معادلة فولتيرا التكاملية.   This paper aims to prove an existence theorem for Voltera-type equation in a generalized G- metric space, called the -metric space, where the fixed-point theorem in - metric space is discussed and its application.  First, a new contraction of Hardy-Rogess type is presented and also then fixed point theorem is established for these contractions in the setup of -metric spaces. As application, an existence result for Voltera integral equation is obtained.

A Weak Tripled Contraction for Solving a Fuzzy Global Optimization Problem in Fuzzy Metric Spaces

In the setting of fuzzy metric spaces (FMSs), a global optimization problem (GOP) obtaining the distance between two subsets of an FMS is solved by a tripled fixed-point (FP) technique here. Also, fuzzy weak tripled contractions (WTCs) for that are given. This problem was known before in metric space (MS) as a proximity point problem (PPP). The result is correct for each continuous τ —norms related to the FMS. Furthermore, a non-trivial example to illustrate the main theorem is discussed.This work was supported in part by the Basque Government under Grant IT1207-19

Multivalued Fixed Point Results for Two Families of Mappings in Modular-Like Metric Spaces with Applications

The aim of this research work is to find out some results in fixed point theory for a pair of families of multivalued mappings fulfilling a new type of U-contractions in modular-like metric spaces. Some new results in graph theory for multigraph-dominated contractions in modular-like metric spaces are developed. An application has been presented to ensure the uniqueness and existence of a solution of families of nonlinear integral equationsThe authors thank the Basque Government for supporting this work through Grant IT1207-19

Common fixed point results of generalized almost rational contraction mappings with an application

In this paper, we introduce the notion of generalized almost rational contraction with respect to a pair of self mappings on a complete metric space. Several common xed point results for such mappings are proved. Our results extend and unify various results in the existing literature. An example and application to obtain the existence of a common solution of the system of functional equations arising in dynamic programming are also given in order to illustrate the e ectiveness of the presented results.This article was funded by the Deanship of Scienti c Research (DSR), King Abdulaziz University, Jeddah.http://www.tjnsa.comhb2016Mathematics and Applied Mathematic

Theory and Application of Fixed Point

In the past few decades, several interesting problems have been solved using fixed point theory. In addition to classical ordinary differential equations and integral equation, researchers also focus on fractional differential equations (FDE) and fractional integral equations (FIE). Indeed, FDE and FIE lead to a better understanding of several physical phenomena, which is why such differential equations have been highly appreciated and explored. We also note the importance of distinct abstract spaces, such as quasi-metric, b-metric, symmetric, partial metric, and dislocated metric. Sometimes, one of these spaces is more suitable for a particular application. Fixed point theory techniques in partial metric spaces have been used to solve classical problems of the semantic and domain theory of computer science. This book contains some very recent theoretical results related to some new types of contraction mappings defined in various types of spaces. There are also studies related to applications of the theoretical findings to mathematical models of specific problems, and their approximate computations. In this sense, this book will contribute to the area and provide directions for further developments in fixed point theory and its applications

Exciting Fixed Point Results under a New Control Function with Supportive Application in Fuzzy Cone Metric Spaces

The objective of this paper is to present a new notion of a tripled fixed point (TFP) findings by virtue of a control function in the framework of fuzzy cone metric spaces (FCM-spaces). This function is a continuous one-to-one self-map that is subsequentially convergent (SC) in FCM-spaces. Moreover, by using the triangular property of a FCM, some unique TFP results are shown under modified contractive-type conditions. Additionally, two examples are discussed to uplift our work. Ultimately, to examine and support the theoretical results, the existence and uniqueness solution to a system of Volterra integral equations (VIEs) are obtained.This work was supported in part by the Basque Government under Grant IT1207-19