scholarly journals Unique Fixed-Point Results for β-Admissible Mapping under (β-ψˇ)-Contraction in Complete Dislocated Gd-Metric Space

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1584
Author(s):  
Abdullah Al-Mazrooei ◽  
Abdullah Shoaib ◽  
Jamshaid Ahmad
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Unique Fixed Point ◽  
Admissible Mapping ◽  
Shed Light

This paper is designed to display some results which generalize the recent results that cannot be established from the corresponding results in other spaces and do not satisfy the remarks of Jleli et al. (Fixed Point Theor Appl. 210, 2012) and Samet et al. (Int. J. Anal. Article ID 917158, 2013). We obtain unique fixed-point for mapping satisfying β-ψˇ contraction only on a closed Gd ball in complete dislocated Gd-metric space. An example is also discussed to shed light on the main result.

scholarly journals Common Fixed Point Theorems for Generalized Geraghty (α,ψ,ϕ)-Quasi Contraction Type Mapping in Partially Ordered Metric-Like Spaces

Axioms ◽  
2018 ◽  
Vol 7 (4) ◽  
pp. 74 ◽  
Author(s):  
Haitham Qawaqneh ◽  
Mohd Noorani ◽  
Wasfi Shatanawi ◽  
Habes Alsamir
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Partially Ordered ◽  
Type Mapping ◽  
Admissible Mapping ◽  
Contraction Type ◽  
Common Fixed Point Theorems

The aim of this paper is to establish the existence of some common fixed point results for generalized Geraghty ( α , ψ , ϕ ) -quasi contraction self-mapping in partially ordered metric-like spaces. We display an example and an application to show the superiority of our results. The obtained results progress some well-known fixed (common fixed) point results in the literature. Our main results cannot be specifically attained from the corresponding metric space versions. This paper is scientifically novel because we take Geraghty contraction self-mapping in partially ordered metric-like spaces via α − admissible mapping. This opens the door to other possible fixed (common fixed) point results for non-self-mapping and in other generalizing metric spaces.

Extension of fixed point results in intuitionistic fuzzy b metric space

2020 ◽  
Vol 39 (5) ◽  
pp. 7831-7841
Author(s):  
Nabanita Konwar
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Cauchy Sequence ◽  
Fixed Point Theorems ◽  
Unique Fixed Point ◽  
Intuitionistic Fuzzy ◽  
Contraction Theorem

The aim of this paper is to define the notion of intuitionistic fuzzy b metric space (in short, IFbMS) along with some useful results. We establish some important Lemmas in order to study the Cauchy sequence in IFbMS. To further develop the work, we establish some fixed point theorems and study the existence of unique fixed point of some self mappings in IFbMS. We also develop the concept of Ćirić quasi-Contraction theorem in IFbMS. Examples are provided to validate the non-triviality of the results.

scholarly journals Non-Unique Fixed Point Results in Extended B-Metric Space

Mathematics ◽  
2018 ◽  
Vol 6 (5) ◽  
pp. 68 ◽  
Author(s):  
Badr Alqahtani ◽  
Andreea Fulga ◽  
Erdal Karapınar
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Unique Fixed Point

scholarly journals Saturated contraction principles for non self operators, generalizations and applications

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3391-3406 ◽  
Author(s):  
Vasile Berinde ◽  
Ştefan Măruşter ◽  
Ioan Rus
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Closed Subset ◽  
Unique Fixed Point ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Nonempty Closed Subset ◽  
Open Problems ◽  
Displacement Condition ◽  
Well Posed

Let (X; d) be a metric space, Y ? X a nonempty closed subset of X and let f : Y ? X be a non self operator. In this paper we study the following problem: under which conditions on f we have all of the following assertions: 1. The operator f has a unique fixed point; 2. The operator f satisfies a retraction-displacement condition; 3. The fixed point problem for f is well posed; 4. The operator f has the Ostrowski property. Some applications and open problems related to these questions are also presented.

scholarly journals Generalizations of the Converse of the Contraction Mapping Principle

1966 ◽  
Vol 18 ◽  
pp. 1095-1104 ◽  
Author(s):  
James S. W. Wong
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Contraction Mapping ◽  
Unique Fixed Point ◽  
Complete Metric Space ◽  
Contraction Mapping Principle ◽  
Converse Statement ◽  
Natural Formulation

This paper is an outgrowth of studies related to the converse of the contraction mapping principle. A natural formulation of the converse statement may be stated as follows: “Let X be a complete metric space, and T be a mapping of X into itself such that for each x ∈ X, the sequence of iterates ﹛Tnx﹜ converges to a unique fixed point ω ∈ X. Then there exists a complete metric in X in which T is a contraction.” This is in fact true, even in a stronger sense, as may be seen from the following result of Bessaga (1).

scholarly journals On Pata–Suzuki-Type Contractions

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 720
Author(s):  
Obaid Alqahtani ◽  
Venigalla Madhulatha Himabindu ◽  
Erdal Karapınar
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Metric Space ◽  
Complete Metric Space ◽  
Admissible Mapping

In this paper, we aim to obtain fixed-point results by merging the interesting fixed-point theorem of Pata and Suzuki in the framework of complete metric space and to extend these results by involving admissible mapping. After introducing two new contractions, we investigate the existence of a (common) fixed point in these new settings. In addition, we shall consider an integral equation as an application of obtained results.

scholarly journals An application of combinatorial techniques to a topological problem

1973 ◽  
Vol 9 (3) ◽  
pp. 439-443 ◽  
Author(s):  
Ludvik Janos
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Unique Fixed Point ◽  
Lipschitz Constant

The following statement is proved: Let X be a set having at most continuously many elements and f: X → X a mapping such that each iteration fn (n = 1, 2, …) has a unique fixed point. Then for every number c ∈ (0, 1) there exists a metric p on X such that the metric space (X, p) is separable and the mapping f is a.contraction with the Lipschitz constant c.

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.

Extensions of Contractive Mappings and Edelstein's Iterative Test

1973 ◽  
Vol 16 (2) ◽  
pp. 185-192 ◽  
Author(s):  
Jack Bryant ◽  
L. F. Guseman
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Unique Fixed Point ◽  
Convergent Subsequence ◽  
Point Of View ◽  
Contractive Mappings

A mapping f from a metric space (X,d) into itself is said to be contractive if x≠y implies d(f(x),f(y))<d(x,y). Theorems of Edelstein [2] state that a contractive selfmapfofa metric space X has a fixed point if, for some x0, the sequence {fn(x0)} of iterates at x0 has a convergent subsequence; moreover, the sequence {fn(x0)} converges to the unique fixed point of f. Nadler [3] observes that, from the point of view of applications, it is usually as difficult to verify the condition (for some x0 …) as it is to find the fixed point directly.

Sign in / Sign up

Export Citation Format

Share Document