scholarly journals On Some Recent Results Concerning F-Suzuki-Contractions in b-Metric Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 940
Author(s):  
Ersin Gilić ◽  
Diana Dolićanin-Đekić ◽  
Zoran D. Mitrović ◽  
Dženis Pučić ◽  
Hassen Aydi
Keyword(s):  
Metric Spaces ◽  
New Approach ◽  
Contraction Mappings ◽  
Picard Sequence ◽  
Theoretical Results

The purpose of this manuscript is to provide much simpler and shorter proofs of some recent significant results in the context of generalized F-Suzuki-contraction mappings in b-complete b-metric spaces. By using our new approach for the proof that a Picard sequence is b-Cauchy, our results generalize, complement and improve many known results in the existing literature. Further, some new contractive conditions are provided here to illustrate the usability of the obtained theoretical results.

scholarly journals Some Results on (s − q)-Graphic Contraction Mappings in b-Metric-Like Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1190 ◽  
Author(s):  
Manuel De la Sen ◽  
Nebojša Nikolić ◽  
Tatjana Došenović ◽  
Mirjana Pavlović ◽  
Stojan Radenović
Keyword(s):  
Contraction Mapping ◽  
New Approach ◽  
Contraction Mappings ◽  
Graphic Contraction ◽  
Picard Sequence ◽  
Theoretical Results

In this paper we consider ( s − q ) -graphic contraction mapping in b-metric like spaces. By using our new approach for the proof that a Picard sequence is Cauchy in the context of b-metric-like space, our results generalize, improve and complement several approaches in the existing literature. Moreover, some examples are presented here to illustrate the usability of the obtained theoretical results.

scholarly journals On some F-contraction of Piri-Kumam-Dung-type mappings in metric spaces

2020 ◽  
Vol 68 (4) ◽  
pp. 697-714 ◽  
Author(s):  
Jelena Vujaković ◽  
Stojan Radenović
Keyword(s):  
Metric Space ◽  
Cauchy Sequence ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Contraction Mappings ◽  
Picard Sequence ◽  
Increasing Function

Introduction/purpose: This paper establishes some new results of Piri-Kumam-Dung-type mappings in a complete metric space.The goal was to improve the already published results. Methods: Using the property of a strictly increasing function as well as the known Lemma formulated in (Radenović et al, 2017), the authors have proved that a Picard sequence is a Cauchy sequence. Results: New results were obtained concerning the F-contraction mappings of S in a complete metric space. To prove it, the authors used only property (W1). Conclusion:The authors believe that the obtained results represent a significant improvement of many known results in the existing literature.

Solving a Fractional-Order Differential Equation Using Rational Symmetric Contraction Mappings

2021 ◽  
Vol 5 (4) ◽  
pp. 159
Author(s):  
Hasanen A. Hammad ◽  
Praveen Agarwal ◽  
Shaher Momani ◽  
Fahad Alsharari
Keyword(s):  
Differential Equation ◽  
Fixed Points ◽  
Fractional Order ◽  
Metric Spaces ◽  
Order Differential Equation ◽  
Fractional Order Differential Equation ◽  
Contraction Mappings ◽  
Continuous Mappings ◽  
Theoretical Results

The intent of this manuscript is to present new rational symmetric ϖ−ξ-contractions and infer some fixed-points for such contractions in the setting of Θ-metric spaces. Furthermore, some related results such as Suzuki-type rational symmetric contractions, orbitally Υ-complete, and orbitally continuous mappings in Θ-metric spaces are introduced. Ultimately, the theoretical results are shared to study the existence of the solution to a fractional-order differential equation with one boundary stipulation.

scholarly journals Coincidence point theorems for KC-contraction mappings in JS-metric spaces endowed with a directed graph

2019 ◽  
Vol 35 (3) ◽  
pp. 263-272
Author(s):  
WATCHAREEPAN ATIPONRAT ◽  
◽  
SUPREEDEE DANGSKUL ◽  
ANCHALEE KHEMPHET ◽  
◽  
...  
Keyword(s):  
Integral Equations ◽  
Directed Graph ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Contraction Mappings ◽  
Theoretical Results

We introduce the class of KC-contraction mappings and prove some coincidence point theorems for these contractions in JS-metric spaces endowed with a directed graph. An illustrative example as well as an application to integral equations are also given in order to support our main theoretical results.

scholarly journals SOME FIXED POINT RESULTS FOR CONVEX CONTRACTION MAPPINGS ON F-METRIC SPACES

2021 ◽  
pp. 939
Author(s):  
Hamid Faraji ◽  
Stojan Radenovic
Keyword(s):  
Fixed Point ◽  
Contraction Mapping ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contraction Mappings ◽  
Alpha Beta ◽  
Theoretical Results

In this paper, we establish some fixed point theorems for convex contraction mappings in F-metric spaces. Also, we introduce the concept of (\alpha,\beta)-convex contraction mapping in F-metric spaces and give some fixed point results for such contractions. Moreover, some examples are given to support our theoretical results.

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 α − ϕ -Fuzzy Cone Contraction Results with Integral Type Application

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Saif Ur Rehman ◽  
Shamoona Jabeen ◽  
Sami Ullah Khan ◽  
Mohammed M. M. Jaradat
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Nonlinear Integral Equation ◽  
Metric Spaces ◽  
Integral Type ◽  
Contraction Mappings ◽  
Theoretical Results ◽  
Cone Metric

In this paper, we define α -admissible and α - ϕ -fuzzy cone contraction in fuzzy cone metric space to prove some fixed point theorems. Some related sequences with contraction mappings have been discussed. Ultimately, our theoretical results have been utilized to show the existence of the solution to a nonlinear integral equation. This application is also illustrative of how fuzzy metric spaces can be used in other integral type operators.

scholarly journals Meir-Keeler type contractions on modular metric spaces

Filomat ◽  
2018 ◽  
Vol 32 (10) ◽  
pp. 3697-3707 ◽  
Author(s):  
Ümit Aksoy ◽  
Erdal Karapınar ◽  
İnci Erhan ◽  
Vladimir Rakocevic
Keyword(s):  
Fixed Points ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Contraction Mappings ◽  
Modular Metric Spaces ◽  
Theoretical Results

In this paper we introduce contraction mappings of Meir-Keeler types on modular metric spaces and investigate the existence and uniqueness of their fixed points. We give an example which demonstrates our theoretical results.

scholarly journals Some new observations on fixed point results in rectangular metric spaces with applications to chemical sciences

2021 ◽  
Vol 69 (1) ◽  
pp. 8-30
Author(s):  
Mudasir Younis ◽  
Nicola Fabiano ◽  
Zaid Fadail ◽  
Zoran Mitrović ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Nonlinear Problems ◽  
Point Theory ◽  
New Approach ◽  
Generalized Metric Spaces ◽  
Picard Sequence ◽  
Open Question

Introduction/purpose: This paper considers, generalizes and improves recent results on fixed points in rectangular metric spaces. The aim of this paper is to provide much simpler and shorter proofs of some new results in rectangular metric spaces. Methods: Some standard methods from the fixed point theory in generalized metric spaces are used. Results: The obtained results improve the well-known results in the literature. The new approach has proved that the Picard sequence is Cauchy in rectangular metric spaces. The obtained results are used to prove the existence of solutions to some nonlinear problems related to chemical sciences. Finally, an open question is given for generalized contractile mappings in rectangular metric spaces. Conclusions: New results are given for fixed points in rectangular metric spaces with application to some problems in chemical sciences.

scholarly journals An Intrinsic Characterization of Five Points in a CAT(0) Space

2020 ◽  
Vol 8 (1) ◽  
pp. 114-165
Author(s):  
Tetsu Toyoda
Keyword(s):  
Metric Space ◽  
Isometric Embedding ◽  
Metric Spaces ◽  
Necessary Conditions ◽  
New Approach ◽  
Intrinsic Characterization ◽  
New Family

AbstractGromov (2001) and Sturm (2003) proved that any four points in a CAT(0) space satisfy a certain family of inequalities. We call those inequalities the ⊠-inequalities, following the notation used by Gromov. In this paper, we prove that a metric space X containing at most five points admits an isometric embedding into a CAT(0) space if and only if any four points in X satisfy the ⊠-inequalities. To prove this, we introduce a new family of necessary conditions for a metric space to admit an isometric embedding into a CAT(0) space by modifying and generalizing Gromov’s cycle conditions. Furthermore, we prove that if a metric space satisfies all those necessary conditions, then it admits an isometric embedding into a CAT(0) space. This work presents a new approach to characterizing those metric spaces that admit an isometric embedding into a CAT(0) space.

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