scholarly journals Coupled fixed point theorems for contractive mappings involving new function classes and applications

Filomat ◽  
2017 ◽  
Vol 31 (7) ◽  
pp. 1893-1907 ◽  
Author(s):  
Arslan Ansari ◽  
Hüseyin Işik ◽  
Stojan Radenovic
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Nonlinear Integral Equations ◽  
Existence Of A Solution ◽  
Ordered Metric Spaces ◽  
Contractive Mappings ◽  
Function Classes

The aim of this paper is to introduce the notions of ?-(F,H)-(?,?) and ?-(F,H)-(?,?) contractions and present several coupled fixed point theorems for this type of contractions in the set of ordered metric spaces. Several examples are offered to illustrate the validity of the obtained results. As an application, the existence of a solution of Fredholm nonlinear integral equations are also investigated.

scholarly journals Coupled fixed point analysis in fuzzy cone metric spaces with an application to nonlinear integral equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Gui-Xiu Chen ◽  
Shamoona Jabeen ◽  
Saif Ur Rehman ◽  
Ahmed Mostafa Khalil ◽  
Fatima Abbas ◽  
...  
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Nonlinear Integral Equations ◽  
Cone Metric Spaces ◽  
Contraction Mappings ◽  
Point Analysis ◽  
Cone Metric

AbstractIn this paper, we introduce the concept of coupled type and cyclic coupled type fuzzy cone contraction mappings in fuzzy cone metric spaces. We establish some coupled fixed point results without the mixed monotone property, and also present some coupled fixed results using the partial order metric in the said space. We present some strong coupled fixed point theorems using cyclic coupled type fuzzy cone contraction mappings in fuzzy cone metric spaces. Moreover, we present an application of nonlinear integral equations for the existence of a unique solution to support our work.

scholarly journals An Extended b -Metric-Type Space and Related Fixed Point Theorems with an Application to Nonlinear Integral Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Kushal Roy ◽  
Sayantan Panja ◽  
Mantu Saha ◽  
Vahid Parvaneh
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Topological Properties ◽  
Nonlinear Integral Equations ◽  
Type Space ◽  
Contractive Mappings ◽  
Underlying Space

In this paper, the concept of sequential p -metric spaces has been introduced as a generalization of usual metric spaces, b -metric spaces and specially of p -metric spaces. Several topological properties of such spaces have been discussed here. In view of this notion, we prove fixed point theorems for some classes of contractive mappings over such spaces. Supporting examples have been given in order to examine the validity of the underlying space and in respect to our proven fixed point theorems.

scholarly journals Fixed Point Theorems for Geraghty Contraction Type Mappings in b-Metric Spaces and Applications

Axioms ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 34 ◽  
Author(s):  
Hamid Faraji ◽  
Dragana Savić ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Nonlinear Integral Equations ◽  
Contractive Mappings ◽  
Contraction Type

In this paper, some new results are given on fixed and common fixed points of Geraghty type contractive mappings defined in b-complete b-metric spaces. Moreover, two examples are represented to show the compatibility of our results. Some applications for nonlinear integral equations are also given.

scholarly journals Some New Coupled Coincidence Point and Coupled Fixed Point Results in Partially Ordered Metric-Like Spaces and an Application

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Min Liang ◽  
Chuanxi Zhu ◽  
Zhaoqi Wu ◽  
Chunfang Chen
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Coincidence Point ◽  
Coupled Fixed Point ◽  
Coupled Coincidence Point ◽  
Nonlinear Integral Equations ◽  
Partially Ordered ◽  
Coupled Coincidence

Some new coupled coincidence point and coupled fixed point theorems are established in partially ordered metric-like spaces, which generalize many results in corresponding literatures. An example is given to support our main results. As an application, we discuss the existence of the solutions for a class of nonlinear integral equations.

scholarly journals Fixed-Point Results for Generalized α -Admissible Hardy-Rogers’ Contractions in Cone b 2 -Metric Spaces over Banach’s Algebras with Application

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Ziaul Islam ◽  
Muhammad Sarwar ◽  
Manuel de la Sen
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Infinite System ◽  
Metric Spaces ◽  
Existence Of A Solution ◽  
System Of Integral Equations

In the current manuscript, the notion of a cone b 2 -metric space over Banach’s algebra with parameter b ≻ ¯ e is introduced. Furthermore, using α -admissible Hardy-Rogers’ contractive conditions, we have proven fixed-point theorems for self-mappings, which generalize and strengthen many of the conclusions in existing literature. In order to verify our key result, a nontrivial example is given, and as an application, we proved a theorem that shows the existence of a solution of an infinite system of integral equations.

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