Fixed point of ϱ — ℨ - contraction type mapping in b-metric like spaces

2021 ◽  
Author(s):  
Habes Alsamir ◽  
Haitham Qawaqneh ◽  
Hassen Aydi ◽  
Wasfi Shatanawi
Keyword(s):  
Fixed Point ◽  
Type Mapping ◽  
Contraction Type

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.

scholarly journals A New Approach of Some Contractive Mappings on Metric Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1433
Author(s):  
Ion Marian Olaru ◽  
Nicolae Adrian Secelean
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Metric Spaces ◽  
New Approach ◽  
Type Mapping ◽  
Contractive Mappings ◽  
Contraction Type

In this paper, we introduce a new contraction-type mapping and provide a fixed-point theorem which generalizes and improves some existing results in the literature. Thus, we prove that the Boyd and Wong theorem (1969) and, more recently, the fixed-point results due to Wardowski (2012), Turinici (2012), Piri and Kumam (2016), Secelean (2016), Proinov (2020), and others are consequences of our main result. An application in integral equations and some illustrative examples are indicated.

scholarly journals On Recent Results Concerning F-Contraction in Generalized Metric Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 767 ◽  
Author(s):  
Jelena Vujaković ◽  
Slobodanka Mitrović ◽  
Mirjana Pavlović ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Weak Contraction ◽  
New Approach ◽  
Generalized Metric Spaces ◽  
Complete Metric Spaces ◽  
Type Mapping ◽  
Contraction Type ◽  
Picard Sequence ◽  
Open Question

In this manuscript we discuss, consider, generalize, improve and unify several recent results for so-called F-contraction-type mappings in the framework of complete metric spaces. We also introduce ( φ , F ) -weak contraction and establish the corresponding fixed point result. Using our new approach for the proof that a Picard sequence is a Cauchy in metric space, our obtained results complement and enrich several methods in the existing literature. At the end we give one open question for F-contraction of Ćirić-type mapping.

scholarly journals SOME FIXED POINT THEOREMS FOR GENERALIZED $\alpha$-GERAGHTY CONTRACTION TYPE MAPPINGS IN $B$-METRIC~SPACES AND SOME APPLICATIONS TO THE NONLINEAR INTEGRAL EQUATION

2017 ◽  
pp. 231
Author(s):  
Nguyen Trung Hieu ◽  
Le Thi Chac
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorems ◽  
Nonlinear Integral Equation ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Generalized Metric Spaces ◽  
Type Mapping ◽  
Contraction Type

The purpose of this paper is to introduce the notion of a generalized $\alpha$-Geraghty contraction type mapping in $b$-metric~spaces and state the existence and uniqueness of a fixed point for this mapping. These results are generalizations of certain the main results in [D.~\DJ uki\'{c}, Z.~Kadelburg, and S.~Radenovi\'{c}, \emph{Fixed points of Geraghty-type mappings in various generalized metric spaces}, Abstr. Appl. Anal. \textbf{2011} (2011), 13 pages] and [O.~Popescu, \emph{ Some new fixed point theorems for $\alpha$-Geraghty contraction type maps in metric spaces}, Fixed Point Theory Appl. \textbf{2014:190} (2014), 1 -- 12]. Some examples are given to illustrate the obtained results and to show that these results are proper extensions of the existing ones. Then we apply the obtained theorem to study the existence of solutions to the nonlinear integral equation.

scholarly journals Unified multivalued interpolative Reich–Rus–Ćirić-type contractions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Monairah Alansari ◽  
Muhammad Usman Ali
Keyword(s):  
Fixed Point ◽  
Type Condition ◽  
Multivalued Maps ◽  
Contraction Type ◽  
Type Contraction

AbstractThis article examines new multivalued interpolative Reich–Rus–Ćirić-type contraction conditions and fixed point results for multivalued maps that fulfill these conditions. Earlier defined interpolative contraction type conditions cannot be particularized to any contraction type condition. This slackness of the interpolative contraction type condition is addressed through new multivalued interpolative Reich–Rus–Ćirić-type contraction conditions.

scholarly journals Common fixed point theorem on Proinov type mappings via simulation function

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Badr Alqahtani ◽  
Sara Salem Alzaid ◽  
Andreea Fulga ◽  
Seher Sultan Yeşilkaya
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Simulation Function ◽  
Type Mapping ◽  
The Common ◽  
Common Fixed Point Theorem

AbstractIn this paper, we aim to discuss the common fixed point of Proinov type mapping via simulation function. The presented results not only generalize, but also unify the corresponding results in this direction. We also consider an example to indicate the validity of the obtained results.

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 Multiple fixed point theorems for contractive and Meir-Keeler type mappings defined on partially ordered spaces with a distance

2017 ◽  
Vol 18 (2) ◽  
pp. 317 ◽  
Author(s):  
Mitrofan M Choban ◽  
Vasile Berinde
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
General Concept ◽  
Type Condition ◽  
Partially Ordered ◽  
Monotonicity Properties ◽  
Contraction Type ◽  
Partially Ordered Spaces

<p>We introduce and study a general concept of multiple fixed point for mappings defined on partially ordered distance spaces in the presence of a contraction type condition and appropriate monotonicity properties. This notion and the obtained results complement the corresponding ones from [M. Choban, V. Berinde, A general concept of multiple fixed point for mappings defined on  spaces with a distance, Carpathian J. Math. 33 (2017), no. 3, 275--286] and also simplifies some concepts of multiple fixed point considered by various authors in the last decade or so.</p>

scholarly journals TEOREMA TITIK TETAP UNTUK PEMETAAN KANNAN PADA RUANG METRIK MODULAR TERITLAK

1970 ◽  
Vol 11 (2) ◽  
pp. 11
Author(s):  
Lusi Harini
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Modular Metric Space ◽  
Type Mapping ◽  
Kannan Mapping ◽  
Finite Set

In this paper, we will discuss about fixed point theorems in generalized modular metric space for Kannan-  type mapping. The existence of the fixed point of this mapping is guaranteed by providing that the mapping domain is a -finite set and the Kannan-  mapping constant  satisfied  where K is a constant from the axiom of generalized modular metric space.

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