Best approximation and fixed points for rational-type contraction mappings

2019 ◽  
Vol 25 (2) ◽  
pp. 205-209
Author(s):  
Sumit Chandok
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Best Approximation ◽  
Contraction Mapping ◽  
Metric Spaces ◽  
Contraction Mappings ◽  
Invariant Approximation ◽  
Frame Work ◽  
Rational Type ◽  
Type Contraction

AbstractIn this paper, we prove a fixed point theorem for a rational type contraction mapping in the frame work of metric spaces. Also, we extend Brosowski–Meinardus type results on invariant approximation for such class of contraction mappings. The results proved extend some of the known results existing in the literature.

scholarly journals Some common fixed point theorems for Ciric type contraction mappings

2012 ◽  
Vol 43 (2) ◽  
pp. 187-202
Author(s):  
Sumit Chandok
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contraction Mappings ◽  
Invariant Approximation ◽  
Convex Metric Spaces ◽  
Common Fixed Point Theorems ◽  
Type Contraction

Some common fixed point theorems for \'{C}iri\'{c} type contraction mappings have been obtained in convex metric spaces. As applications, invariant approximation results for these type of mappings are obtained. The proved results generalize, unify and extend some of the results of the literature.

scholarly journals Fixed Point Results Satisfying Rational Type Contraction inG-Metric Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Branislav Z. Popović ◽  
Muhammad Shoaib ◽  
Muhammad Sarwar
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Unique Fixed Point ◽  
Contractive Condition ◽  
Fixed Point Result ◽  
Rational Type ◽  
Type Contraction

A unique fixed point theorem for three self-maps under rational type contractive condition is established. In addition, a unique fixed point result for six continuous self-mappings through rational type expression is also discussed.

scholarly journals Some Rational Coupled Fuzzy Cone Contraction Theorems in Fuzzy Cone Metric Spaces with an Application

2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Saif Ur Rehman ◽  
Muhammad Talha Waheed ◽  
Naeem Jan ◽  
Abdu Gumaei ◽  
Mabrook Al-Rakhami
Keyword(s):  
Fixed Point ◽  
Contraction Mapping ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Integral Type ◽  
Cone Metric Spaces ◽  
Cone Metric ◽  
Rational Type ◽  
Type Contraction

In this paper, we establish the new concept of rational coupled fuzzy cone contraction mapping in fuzzy cone metric spaces and prove some unique rational-type coupled fixed-point theorems in the framework of fuzzy cone metric spaces by using “the triangular property of fuzzy cone metric.” To ensure the existence of our results, we present some illustrative unique coupled fixed-point examples. Furthermore, we present an application of a Lebesgue integral-type contraction mapping in fuzzy cone metric spaces and to prove a unique coupled fixed-point theorem.

scholarly journals On a fixed point theorem with application to functional equations

2019 ◽  
Vol 17 (1) ◽  
pp. 1724-1736
Author(s):  
Muhammad Nazam ◽  
Muhammad Arshad ◽  
Choonkil Park ◽  
Hasan Mahmood
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Partial Metric ◽  
Ordered Metric Spaces ◽  
Partial Metric Spaces ◽  
Rational Type ◽  
Type Contraction

Abstract The purpose of this paper is to study behavior of a rational type contraction introduced in [A fixed point theorem for contractions of rational type in partially ordered metric spaces, Ann. Univ. Ferrara, 2013, 59, 251–258] in context of ordered dualistic partial metric spaces and to investigate sufficient conditions for the existence of a fixed point in this space. These results extend various comparable results, existing in the literature. We give examples to explain our findings. We apply our result to prove the existence of the solution of functional equation.

scholarly journals New Generalizations of Set Valued Interpolative Hardy-Rogers Type Contractions in b-Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Muhammad Usman Ali ◽  
Hassen Aydi ◽  
Monairah Alansari
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Contraction Mapping ◽  
Metric Spaces ◽  
Contraction Mappings ◽  
Type Contraction

Debnath and De La Sen introduced the notion of set valued interpolative Hardy-Rogers type contraction mappings on b-metric spaces and proved that on a complete b-metric space, whose all closed and bounded subsets are compact, the set valued interpolative Hardy-Rogers type contraction mapping has a fixed point. This article presents generalizations of above results by omitting the assumption that all closed and bounded subsets are compact.

scholarly journals Common Fixed Point Theorem via Cyclic (α,β)-(ψ,φ)S-Contraction with Applications

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 198
Author(s):  
Mian Zada ◽  
Muhammad Sarwar ◽  
Fahd Jarad ◽  
Thabet Abdeljawad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Functional Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Common Fixed Point Theorems ◽  
Common Fixed Point Theorem ◽  
Rational Type ◽  
Type Contraction

In this paper, we introduce the notion of cyclic ( α , β ) - ( ψ , φ ) s -rational-type contraction in b-metric spaces, and using this contraction, we prove common fixed point theorems. Our work generalizes many existing results in the literature. In order to highlight the usefulness of our results, applications to functional equations are given.

scholarly journals Fixed Point Theorem for Cyclic Weakly Generalized Contraction Mapping of Ciric Type

2020 ◽  
Vol 12 (4) ◽  
pp. 463-471
Author(s):  
S. Goyal ◽  
M. Garg
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Contraction Mapping ◽  
Metric Spaces ◽  
Generalized Contraction ◽  
Contraction Mappings ◽  
Complete Metric Spaces

In this article, the concept of cyclic weakly generalized contraction mapping of Ciric type has been introduced and the existence of a fixed point for such mappings in the setup of complete metric spaces has been established. Result obtained extends and improves some fixed point results in the literature. Example is also given to show that class of contraction mappings introduced in the paper is strictly larger class than the class of mappings used in the literature and thus ensures wider applicability of the result by producing the solutions to new problems.

scholarly journals Fixed-Point Study of Generalized Rational Type Multivalued Contractive Mappings on Metric Spaces with a Graph

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 31
Author(s):  
Binayak S. Choudhury ◽  
Nikhilesh Metiya ◽  
Debashis Khatua ◽  
Manuel de la Sen
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Metric Spaces ◽  
Graph Theoretic ◽  
Contractive Mappings ◽  
Control Functions ◽  
Special Cases ◽  
Multivalued Contractions ◽  
Rational Type ◽  
Type Contraction

The main result of this paper is a fixed-point theorem for multivalued contractions obtained through an inequality with rational terms. The contraction is an F-type contraction. The results are obtained in a metric space endowed with a graph. The main theorem is supported by illustrative examples. Several results as special cases are obtained by specific choices of the control functions involved in the inequality. The study is broadly in the domain of setvalued analysis. The methodology of the paper is a blending of both graph theoretic and analytic methods.

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