scholarly journals Construction of ball spaces and the notion of continuity

10.53733/157 ◽  
2021 ◽  
Vol 51 ◽  
pp. 49-64
Author(s):  
René Bartsch ◽  
Katarzyna Kuhlmann ◽  
Franz-Viktor Kuhlmann
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Topological Category ◽  
Ordered Structures ◽  
Quotient Spaces ◽  
Definition Of

Spherically complete ball spaces provide a simple framework for the encoding of completeness properties of various spaces and ordered structures. This allows to prove generic versions of theorems that work with these completeness properties, such as fixed point theorems and related results. For the purpose of applying the generic theorems, it is important to have methods for the construction of new spherically complete ball spaces from existing ones. Given various ball spaces on the same underlying set, we discuss the construction of new ball spaces through set theoretic operations on the balls. A definition of continuity for functions on ball spaces leads to the notion of quotient spaces. Further, we show the existence of products and coproducts and use this to derive a topological category associated with ball spaces.

scholarly journals Some related fixed point theorems for multivalued mappings on two metric spaces

2020 ◽  
Vol 12 (2) ◽  
pp. 392-400
Author(s):  
Ö. Biçer ◽  
M. Olgun ◽  
T. Alyildiz ◽  
I. Altun
Keyword(s):  
Fixed Point ◽  
Classical Result ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Multivalued Mappings ◽  
Compact Set ◽  
Complete Metric Spaces ◽  
Bounded Set ◽  
Contraction Type ◽  
Definition Of

The definition of related mappings was introduced by Fisher in 1981. He proved some theorems about the existence of fixed points of single valued mappings defined on two complete metric spaces and relations between these mappings. In this paper, we present some related fixed point results for multivalued mappings on two complete metric spaces. First we give a classical result which is an extension of the main result of Fisher to the multivalued case. Then considering the recent technique of Wardowski, we provide two related fixed point results for both compact set valued and closed bounded set valued mappings via $F$-contraction type conditions.

scholarly journals Some fixed point theorems in n-normed spaces

2020 ◽  
Vol 25 (3) ◽  
pp. 1-15 ◽  
Author(s):  
Hanan Sabah Lazam ◽  
Salwa Salman Abed
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Normed Space ◽  
Fixed Point Theorems ◽  
Normed Spaces ◽  
Weak Contraction ◽  
Contraction Mappings ◽  
Basic Properties ◽  
Definition Of

In this article, we recall the definition of a real n-normed space and some basic properties. fixed point theorems for types of Kannan, Chatterge, Zamfirescu, -Weak contraction and  - (,)-Weak contraction mappings in  Banach spaces.

scholarly journals Coupled Fixed-Point Theorems for Contractions in Partially Ordered Metric Spaces and Applications

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
M. Eshaghi Gordji ◽  
Y. J. Cho ◽  
S. Ghods ◽  
M. Ghods ◽  
M. Hadian Dehkordi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Contractive Condition ◽  
Coincidence Points ◽  
Ordered Metric Spaces ◽  
Coupled Coincidence Points ◽  
Definition Of ◽  
Coupled Coincidence

Bhaskar and Lakshmikantham (2006) showed the existence of coupled coincidence points of a mappingFfromX×XintoXand a mappinggfromXintoXwith some applications. The aim of this paper is to extend the results of Bhaskar and Lakshmikantham and improve the recent fixed-point theorems due to Bessem Samet (2010). Indeed, we introduce the definition of generalizedg-Meir-Keeler type contractions and prove some coupled fixed point theorems under a generalizedg-Meir-Keeler-contractive condition. Also, some applications of the main results in this paper are given.

scholarly journals Remarks on α , β -Admissible Mappings and Fixed Points under Z -Contraction Mappings

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Bulbul Khomdram ◽  
N. Priyobarta ◽  
Yumnam Rohen ◽  
Thounaojam Indubala
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Topological Properties ◽  
Simulation Function ◽  
Contraction Mappings ◽  
Different Types ◽  
Contraction Type ◽  
Definition Of

In this paper, we discuss about different types of α , β -admissible mappings and introduce some new α , β -contraction-type mappings under simulation function. Furthermore, we present the definition of S -metric-like space and its topological properties. Some fixed point theorems in this space are established, proved, and verified with examples.

scholarly journals Proinov type contractions on dislocated b-metric spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Badr Alqahtani ◽  
Sara S. Alzaid ◽  
Andreea Fulga ◽  
Antonio Francisco Roldán López de Hierro
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Definition Of ◽  
Rational Expressions

AbstractIn this paper, we improve the Proinov theorem by adding certain rational expressions to the definition of the corresponding contractions. After that, we prove fixed point theorems for these modified Proinov contractions in the framework of dislocated b-metric spaces. We show some illustrative examples to indicate the validity of the main results.

scholarly journals A note on the paper "A fixed point theorems in Sb-metric spaces"

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3335-3346 ◽  
Author(s):  
Yumnam Rohen ◽  
Tatjana Dosenovic ◽  
Stojan Radenovic
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Common Fixed Point ◽  
Definition Of ◽  
Common Fixed Point Theorems ◽  
Theoretical Results

Very recently, N. Souayan and N. Mlaiki [Nazir Souayan and Nabil Mlaiki, A fixed point theorem in Sb-metric spaces, J. Math. Comput. Sci. 16 (2016), 131-139] and S. Sedghi et al. [S. Sedghi, A. Gholidahneb, T. Dosenovic, J. Esfahani, S. Radenovic, Common fixed point of four maps in Sb-metric spaces, to appear in J. Linear Topol. Algebra], introduced the concept of Sb-metric space as a generalization of S-metric space. In this paper, we modified the definition of Sb-metric introduced by Souayan and Mlaiki and prove some coupled common fixed point theorems in Sb-metric space. We also present an example to confirm our theoretical results.

scholarly journals Fixed Point Theory Using ψ Contractive Mapping in C ∗ -Algebra Valued B-Metric Space

Mathematics ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 92
Author(s):  
Rahmah Mustafa ◽  
Saleh Omran ◽  
Quang Ngoc Nguyen
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Fixed Point Theory ◽  
Positive Function ◽  
Contractive Mapping ◽  
Point Theory ◽  
C Algebra ◽  
Definition Of ◽  
Multiple Scenarios

In this paper, fixed point theorems using ψ contractive mapping in C∗-algebra valued b-metric space are introduced. By stating multiple scenarios that illustrate the application domains, we demonstrate several applications from the obtained results. In particular, we begin with the definition of the positive function and then recall some properties of the function that lay the fundamental basis for the research. We then study some fixed point theorems in the C∗-algebra valued b-metric space using a positive function.

scholarly journals Some Fixed Point Theorems in intuitionistic fuzzy metric spaces

2011 ◽  
Vol 42 (4) ◽  
pp. 405-414
Author(s):  
Sushil Sharma ◽  
Prashant Tilwankar
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Intuitionistic Fuzzy ◽  
Weakly Commuting Mappings ◽  
Definition Of ◽  
Common Fixed Point Theorems ◽  
Commuting Mappings

The aim of this paper is to prove some common fixed point theorems by using the property ($S$-$B$) and the notion of R-weak commutativity of type $(S_p)$ in intuitionistic fuzzy metric spaces. We first formulate the definition of R-weakly commuting mappings of type $(S_p)$ in intuitionistic fuzzy metric spaces and prove the intuitionistic fuzzy version of Pant's theorem.

scholarly journals Fixed point theorems in uniformly rotund metric spaces

1976 ◽  
Vol 14 (2) ◽  
pp. 181-192 ◽  
Author(s):  
John Staples
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Linear Structure ◽  
Uniform Convexity ◽  
Uniformly Convex ◽  
Underlying Space ◽  
Uniformly Convex Banach Spaces ◽  
Definition Of

In recent years fixed point theorems have been proved for non-expansive and similar mappings on uniformly convex Banach spaces. The only role the linear structure plays in the statement of these results occurs in the definition of uniform convexity. It is therefore natural to ask whether the results depend essentially on the linear structure, or whether an extension of the notion of uniform convexity to metric spaces would allow the hypothesis of linear structure on the underlying space to be removed.

scholarly journals Compatible Mappings of Type (γ) and (δ)

2019 ◽  
Vol 8 (6S4) ◽  
pp. 1062-1065
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Compatible Mappings ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Different Types ◽  
Definition Of ◽  
Common Fixed Point Theorems

In this article, we introduce the definition of two different types of compatible mappings and prove common fixed point theorems in fuzzy metric spaces. Examples are given to support the results proved herein.

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