scholarly journals Double controlled quasi metric-like spaces and some topological properties of this space

2021 ◽  
Vol 6 (10) ◽  
pp. 11584-11594
Author(s):  
A. M. Zidan ◽  
◽  
Z. Mostefaoui ◽  
◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
The Self ◽  
Topological Properties ◽  
New Type

<abstract><p>In present paper, we introduce a new extension of the double controlled metric-like spaces, so called double controlled quasi metric-like spaces "assuming that the self-distance may not be zero". Also, if the value of the metric is zero, then it has to be "a self-distance". After that, by using this new type of quasi metric spaces, we generalize many results in the literature and we prove fixed point theorems along with some examples illustrating.</p></abstract>

Fixed Point Theorems for Maps With Local and Pointwise Contraction Properties

2018 ◽  
Vol 70 (3) ◽  
pp. 538-594 ◽  
Author(s):  
Krzysztof Chris Ciesielski ◽  
Jakub Jasinski
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Topological Properties ◽  
Open Problems ◽  
Local Contraction ◽  
Path Connectedness ◽  
Perfect Subset ◽  
Minimal Dynamical System ◽  
Comprehensive Study

AbstractThis paper constitutes a comprehensive study of ten classes of self-maps on metric spaces ⟨X, d⟩ with the pointwise (i.e., local radial) and local contraction properties. Each of these classes appeared previously in the literature in the context of fixed point theorems.We begin with an overview of these fixed point results, including concise self contained sketches of their proofs. Then we proceed with a discussion of the relations among the ten classes of self-maps with domains ⟨X, d⟩ having various topological properties that often appear in the theory of fixed point theorems: completeness, compactness, (path) connectedness, rectifiable-path connectedness, and d-convexity. The bulk of the results presented in this part consists of examples of maps that show non-reversibility of the previously established inclusions between these classes. Among these examples, the most striking is a differentiable auto-homeomorphism f of a compact perfect subset X of ℝ with f′ ≡ 0, which constitutes also a minimal dynamical system. We finish by discussing a few remaining open problems on whether the maps with specific pointwise contraction properties must have the fixed points.

scholarly journals Suzuki-Type of Common Fixed Point Theorems in S-Fuzzy Metric Spaces

2021 ◽  
Vol 2 (3) ◽  
pp. 86-91
Author(s):  
M. Jeyaraman ◽  
S. Sowndrarajan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Banach Contraction ◽  
New Type ◽  
Common Fixed Point Theorems

In this paper, by using of Suzuki-type approach [Suzuki, T., A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc., 136, 1861–1869, 2008.] we prove new type of Suzuki- type fixed point theorem for non-Archimedean S - fuzzy metric spaces which is generalization of Suzuki-Type fixed point results in S - metric spaces.

scholarly journals Theta Cone Metric Spaces and Some Fixed Point Theorems

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Sahar Mohamed Ali Abou Bakr
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Topological Properties ◽  
Cone Metric Spaces ◽  
Cone Metric

This paper introduces the concept of the theta cone metric, studies its various topological properties, and gives some examples of it. Furthermore, it proves some lemmas and then uses them to give further generalizations of some well-known fixed point theorems. Specifically, Theorem 2 of the paper is a generalization of Reich’s fixed point theorem.

scholarly journals Fixed Point Theorems for Generalized Kannan-Type Mappings in a New Type of Fuzzy Metric Space

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Mi Zhou ◽  
Xiao-lan Liu ◽  
Nicolae Adrian Secelean
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fuzzy Metric Space ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Weak Compatibility ◽  
New Type ◽  
Common Fixed Point Theorems

In this paper, first, we introduce a new type of S∗−fuzzy metric space which is a generalization of fuzzy metric spaces. Second, we study the topological properties of S∗−fuzzy metric spaces. Finally, we extend Kannan-type mappings to generalized Kannan-type mappings under ϕ−gauge functions introduced by Fang in S∗−fuzzy metric spaces and prove the existence and uniqueness of fixed point for this kind of mappings. Furthermore, we also obtain the common fixed point theorems for weak compatibility along with E.A. property or CLRg property. Our results extend and improve very recent theorems in the related literature.

Some fixed point theorems for multi-valued mappings in graphical metric spaces

2020 ◽  
Vol 70 (3) ◽  
pp. 719-732
Author(s):  
Satish Shukla ◽  
Hans-Peter A. Künzi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Topological Properties ◽  
Nadler’S Fixed Point Theorem

AbstractIn this paper, we discuss some topological properties of graphical metric spaces and introduce the G-set metric with respect to a graphical metric. Some fixed point results are introduced which generalize the famous Nadler’s fixed point theorem.

scholarly journals A constructive approach to coupled fixed point theorems in metric spaces

2015 ◽  
Vol 31 (3) ◽  
pp. 277-287
Author(s):  
VASILE BERINDE ◽  
◽  
MADALINA PACURAR ◽  
◽  
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Iterative Methods ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Contractive Condition ◽  
Constructive Approach ◽  
New Type

In this paper we establish the existence and uniqueness of a coupled fixed point for operators F : X × X → X satisfying a new type of contractive condition, which is weaker than all the corresponding ones studied in literature so far. We also provide constructive features to our coupled fixed point results by proving that the unique coupled fixed point of F can be approximated by means of two distinct iterative methods: a Picard type iterative method of the form xn+1 = F(xn, xn), n ≥ 0, with x0 ∈ X, as well as a two step iterative method of the form yn+1 = F(yn−1, yn), n ≥ 0, with y0, y1 ∈ X. We also give appropriate error estimates for both iterative methods. Essentially we point out that all coupled fixed point theorems existing in literature, that establish the existence and uniqueness of a coupled fixed point with equal components, could be derived in a much more simpler manner.

scholarly journals Some Generalizations of Prešić Type Mappings and Applications

2015 ◽  
Vol 0 (0) ◽  
Author(s):  
Satish Shukla ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Difference Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Iterative Sequence ◽  
Order Difference ◽  
New Type ◽  
The Common ◽  
Common Fixed Point Theorems

Abstract In this paper, we prove some common fixed point theorems for the mappings satisfying Prešić type contractive conditions in metric spaces. Our results generalize and extend the result of Prešić for some new type of contractive conditions. The common fixed point of mappings is approximated by a k-step iterative sequence. Some examples are provided to illustrate the results. An application of Prešić type mappings to second order difference equations is also given.

scholarly journals S ∗ p ‐ b -Partial Metric Spaces with some Results in Common Fixed Point Theorems

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
A. M. Zidan
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Partial Metric Space ◽  
Partial Metric ◽  
Topological Properties ◽  
Partial Metric Spaces ◽  
Common Fixed Point Theorems ◽  
Common Fixed Point Theorem

In this paper, we introduce the notion of S ∗ P ‐ b -partial metric spaces which is a generalization each of S ‐ b -metric spaces and partial-metric space. Also, we study and prove some topological properties, to know the convergence of the sequences and Cauchy sequence. Finally, we study a new common fixed point theorem in these spaces.

scholarly journals Fixed Point Theorems for Two Pairs of Mappings Satisfying a New Type of Common Limit Range Property in Gp Metric Spaces

2018 ◽  
Vol 32 (1) ◽  
pp. 295-312
Author(s):  
Valeriu Popa ◽  
Alina-Mihaela Patriciu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Integral Type ◽  
Contractive Mappings ◽  
Common Limit ◽  
New Type ◽  
Common Limit Range Property

Abstract The purpose of this paper is to prove a general fixed point theorem for mappings involving almost altering distances and satisfying a new type of common limit range property in Gpmetric spaces. In the last part of the paper, some fixed point results for mappings satisfying contractive conditions of integral type and for ⱷ-contractive mappings are obtained.

scholarly journals On Fixed Point Results in Partial b -Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Haitham Qawaqneh ◽  
Mohd Salmi Md Noorani ◽  
Hassen Aydi ◽  
Amjed Zraiqat ◽  
Arslan Hojat Ansari
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
The Self ◽  
Topological Properties ◽  
Triangular Inequality ◽  
Contraction Mappings ◽  
Symmetric Property

Partial b -metric spaces are characterised by a modified triangular inequality and that the self-distance of any point of space may not be zero and the symmetry is preserved. The spaces with a symmetric property have interesting topological properties. This manuscript paper deals with the existence and uniqueness of fixed point points for contraction mappings using triangular weak α -admissibility with regard to η and C -class functions in the class of partial b -metric spaces. We also introduce an example to demonstrate the obtained results.

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