scholarly journals Some Fixed Point Results in Function Weighted Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Awais Asif ◽  
Nawab Hussain ◽  
Hamed Al-Sulami ◽  
Muahammad Arshad
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Closed Ball ◽  
Contractive Condition ◽  
Banach Contraction ◽  
The Banach Contraction Principle ◽  
Type Contraction ◽  
Unique Common Fixed Point

After the establishment of the Banach contraction principle, the notion of metric space has been expanded to more concise and applicable versions. One of them is the conception of ℱ -metric, presented by Jleli and Samet. Following the work of Jleli and Samet, in this article, we establish common fixed points results of Reich-type contraction in the setting of ℱ -metric spaces. Also, it is proved that a unique common fixed point can be obtained if the contractive condition is restricted only to a subset closed ball of the whole ℱ -metric space. Furthermore, some important corollaries are extracted from the main results that describe fixed point results for a single mapping. The corollaries also discuss the iteration of fixed point for Kannan-type contraction in the closed ball as well as in the whole ℱ -metric space. To show the usability of our results, we present two examples in the paper. At last, we render application of our results.

A generalization of Reich’s fixed point theorem for multi-valued mappings

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3295-3305 ◽  
Author(s):  
Antonella Nastasi ◽  
Pasquale Vetro
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Complete Metric Spaces ◽  
New Class ◽  
Banach Contraction ◽  
The Banach Contraction Principle

Motivated by a problem concerning multi-valued mappings posed by Reich [S. Reich, Some fixed point problems, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 57 (1974) 194-198] and a paper of Jleli and Samet [M. Jleli, B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl. 2014:38 (2014) 1-8], we consider a new class of multi-valued mappings that satisfy a ?-contractive condition in complete metric spaces and prove some fixed point theorems. These results generalize Reich?s and Mizoguchi-Takahashi?s fixed point theorems. Some examples are given to show the usability of the obtained results.

scholarly journals Geraghty Type Generalized F-Contractions and Related Applications in Partial b-Metric Spaces

2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Deepak Singh ◽  
Varsha Chauhan ◽  
R. Wangkeeree
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Partial Metric Space ◽  
Partial Metric ◽  
First Order ◽  
New Concepts ◽  
Banach Contraction ◽  
Uniqueness Of A Solution ◽  
The Banach Contraction Principle

The purpose of this paper is to introduce new concepts of (α,β)-admissible Geraghty type generalized F-contraction and to prove that some fixed point results for such mappings are in the perspective of partial b-metric space. As an application, we inaugurate new fixed point results for Geraghty type generalized graphic F-contraction defined on partial metric space endowed with a directed graph. On the other hand, one more application to the existence and uniqueness of a solution for the first-order periodic boundary value problem is also provided. Our findings encompass various generalizations of the Banach contraction principle on metric space, partial metric space, and partial b-metric space. Moreover, some examples are presented to illustrate the usability of the new theory.

scholarly journals Common Fixed Points of a Pair of Hardy Rogers Type Mappings on a Closed Ball in Ordered Dislocated Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Muhammad Arshad ◽  
Abdullah Shoaib ◽  
Pasquale Vetro
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Functional Equations ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Closed Ball ◽  
Nonlinear Functional ◽  
Dislocated Metric Space ◽  
Complete Dislocated Metric Space ◽  
Dislocated Metric

Common fixed point results for mappings satisfying locally contractive conditions on a closed ball in an ordered complete dislocated metric space have been established. The notion of dominated mappings is applied to approximate the unique solution of nonlinear functional equations. Our results improve several well-known conventional results.

scholarly journals Results on common fixed points on complete metric spaces

1980 ◽  
Vol 21 (1) ◽  
pp. 165-167 ◽  
Author(s):  
Brian Fisher
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Unique Fixed Point ◽  
Common Fixed Points ◽  
Complete Metric Spaces ◽  
Image Position ◽  
Commuting Mappings ◽  
Unique Common Fixed Point

The following theorem was proved in [1].Theorem 1. Let S and T be continuous, commuting mappings of a complete, bounded metric space (X, d) into itself satisfying the inequalityfor all x, y in X, where 0≤c<1 and p, p′, q, q′≥0 are fixed integers with p+p′, q+q′≥1. Then S and T have a unique common fixed point z. Further, if p′ or q′ = 0, then z is the unique fixed point of S and if p or q = 0, then z is the unique fixed point of T.

scholarly journals Common Fixed Point Theorems for a Class of Twice Power Type Contraction Maps inG-Metric Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Hongqing Ye ◽  
Feng Gu
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Power Type ◽  
Common Fixed Point Theorems ◽  
Type Contraction ◽  
Contraction Maps

We introduce a new twice power type contractive condition for three mappings inG-metric spaces, and several new common fixed point theorems are established in completeG-metric space. An example is provided to support our result. The results obtained in this paper differ from other comparable results already known.

scholarly journals Fixed Point Theorems for Mizoguchi-Takahashi Type Contraction in Bicomplex-Valued Metric Spaces and Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Fuli He ◽  
Z. Mostefaoui ◽  
M. Abdalla
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Nonlinear Integral Equation ◽  
Metric Spaces ◽  
Banach Contraction ◽  
Uniqueness Of The Solution ◽  
Contractive Maps ◽  
The Banach Contraction Principle ◽  
Type Contraction

The main aim of this paper is to study and establish some new fixed point theorems for contractive maps that satisfied Mizoguchi-Takahashi’s condition in the setting of bicomplex-valued metric spaces. These new results improve and generalize the Banach contraction principle and some well-known results in the literature. Finally, as applications of our results, we give the existence and uniqueness of the solution of a nonlinear integral equation.

Analysis of F-contractions in function weighted metric spaces with an application

2020 ◽  
Vol 18 (1) ◽  
pp. 582-594 ◽  
Author(s):  
Zhenhua Ma ◽  
Awais Asif ◽  
Hassen Aydi ◽  
Sami Ullah Khan ◽  
Muhammad Arshad
Keyword(s):  
Fixed Points ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Closed Ball ◽  
Contractive Condition ◽  
Whole Space ◽  
Empirical Perspective ◽  
Rational Type

Abstract In this work, we show that the existence of fixed points of F-contraction mappings in function weighted metric spaces can be ensured without third condition (F3) imposed on Wardowski function F\mathrm{:(0,\hspace{0.33em}}\infty )\to \Re . The present article investigates (common) fixed points of rational type F-contractions for single-valued mappings. The article employs Jleli and Samet’s perspective of a new generalization of a metric space, known as a function weighted metric space. The article imposes the contractive condition locally on the closed ball, as well as, globally on the whole space. The study provides two examples in support of the results. The presented theorems reveal some important corollaries. Moreover, the findings further show the usefulness of fixed point theorems in dynamic programming, which is widely used in optimization and computer programming. Thus, the present study extends and generalizes related previous results in the literature in an empirical perspective.

scholarly journals Common fixed points using (ψ,ϕ ) - type contractive maps in fuzzy metric spaces

2020 ◽  
Vol 18 (1) ◽  
Author(s):  
Vishal Gupta ◽  
Manu Verma
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Fuzzy Metric Space ◽  
Contractive Condition ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Control Functions ◽  
Contractive Maps

This In this paper, we define new control functions to give unique fixed point in fuzzy metric space. A fruitful contractive condition of (ψ, ϕ)- type is used to obtain common fixed point theorem for two maps in fuzzy metric spaces. We extend the existing results in metric space to fuzzy metric space using these control functions. The first theorem is the extension of the result of Zhang and Song (2009) under the required contractive conditions. Second result is analogous to the result of Doric (2009) in metric spaces.

scholarly journals A generalization of Nadler fixed point theorem

2015 ◽  
Vol 31 (3) ◽  
pp. 403-410
Author(s):  
FRANCESCA VETRO ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Metric Spaces ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Multivalued Mappings ◽  
Contractive Condition ◽  
Complete Metric Spaces ◽  
Banach Contraction ◽  
The Banach Contraction Principle

Jleli and Samet gave a new generalization of the Banach contraction principle in the setting of Branciari metric spaces [Jleli, M. and Samet, B., A new generalization of the Banach contraction principle, J. Inequal. Appl., 2014:38 (2014)]. The purpose of this paper is to study the existence of fixed points for multivalued mappings, under a similar contractive condition, in the setting of complete metric spaces. Some examples are provided to illustrate the new theory.

scholarly journals On Some New Results in Graphical Rectangular b-Metric Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 488
Author(s):  
Pravin Baradol ◽  
Jelena Vujaković ◽  
Dhananjay Gopal ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Banach Contraction ◽  
The Banach Contraction Principle

In this paper, we provide an approach to establish the Banach contraction principle ( for the case λ ∈ [ 0 , 1 ) ) , Edelstein, Reich, and Meir–Keeler type contractions in the context of graphical rectangular b-metric space. The obtained results not only enrich and improve recent fixed point theorems of this new metric spaces but also provide positive answers to the questions raised by Mudasir Younis et al. (J. Fixed Point Theory Appl., doi:10.1007/s11784-019-0673-3, 2019).

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