Ordered Sp -metric spaces and some fixed point theorems for contractive mappings with application to periodic boundary value problems

In this paper, we introduce the structure of Sp-metric spaces as a generalization of both S-metric and Sb-metric spaces. Also, we present the notions of S?-contractive mappings in the setup of ordered Sp-metric spaces and investigate the existence of a fixed point for such mappings under various contractive conditions. We provide examples to illustrate the results presented herein. An application to periodic boundary value problems is presented. - 2019, The Author(s).The publication of this article funded by the Qatar National Library.Scopu

Rational Geraghty Contractive Mappings and Fixed Point Theorems in Ordered b2b_2-metric Spaces

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. These include Geraghty-type conditions, conditions that use comparison functions and almost generalized weakly contractive conditions. Berinde in [17-20] initiated the concept of almost contractions and obtained many interesting fixed point theorems. Results with similar conditions were obtained, textit{e.g.}, in [21] and [22]. In the last section of the paper, we define the notion of almost generalized $(psi ,varphi )_{s,a}$-contractive mappings and prove some new results. In particular, we extend Theorems 2.1, 2.2 and 2.3 of  Ciric et.al. in [23] to the setting of $b_{2}$-metric spaces. Also, some examples are provided to illustrate the results presented herein and several interesting consequences of our theorems are also provided. The findings of the paper are based on generalization and modification of some recently reported theorems in the literature

Solving existence problems via F-contraction in modified b-metric spaces

In this paper, we introduce a new abstract structure, expanded b-metric, as an natural extension of b-metric. We also define basic topological notions in expanded bmetric to able to investigate the existence of fixed point for such mappings under various F-contractive conditions. We provide example to illustrate the results presented herein

Existence of common fixed point for b-metric rational type contraction

The necessary conditions for existence of a common fixed point of two mappings satisfying generalized b-order contractive condition in the setting of a partially ordered b-complete b-metric space are presented. Also, we study well-posedness of common fixed point problem for generalized b-order contractive mappings. We employ our result to establish an existence of a solution of an integral equation.http://www.pmf.ni.ac.rs/filomatam2017Mathematics 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

Fixed point results for a pair of fuzzy mappings and related applications in b-metric like spaces

AbstractThis paper is devoted to finding out some realization of the concept of b-metric like space. First, we attain a fixed point for two fuzzy mappings satisfying a suitable requirement of contractiveness. Subsequently, we apply such a result to graphic contractions. Also, we attain a unique solution for a system of integral equations, and lastly we give an application to ensure that there exists a common bounded solution of a suitable functional equation in dynamic programming

Some coupled coincidence and common fixed point results for a hybrid pair of mappings in 0-complete partial metric spaces

In this paper we extend some coupled coincidence and common fixed point theorems for a hybrid pair of mappings obtained by Abbas et al. (Fixed Point Theory Appl. 2012:4, 2012, doi:10.1186/1687-1812-2012-4) from the complete metric space to 0-complete partial metric spaces. An example showing that this extension is proper is given

New Fixed Point Results via a Graph Structure

The main aim of this paper is to introduce and study some fixed point results for rational multivalued G-contraction and F-Khan-type multivalued contraction mappings on a metric space with a graph. At the end, we give an illustrative example.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