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

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.

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1190 ◽  
Author(s):  
Manuel De la Sen ◽  
Nebojša Nikolić ◽  
Tatjana Došenović ◽  
Mirjana Pavlović ◽  
Stojan Radenović

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.


2020 ◽  
Vol 68 (4) ◽  
pp. 697-714 ◽  
Author(s):  
Jelena Vujaković ◽  
Stojan Radenović

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.


2021 ◽  
Vol 5 (4) ◽  
pp. 159
Author(s):  
Hasanen A. Hammad ◽  
Praveen Agarwal ◽  
Shaher Momani ◽  
Fahad Alsharari

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.


2019 ◽  
Vol 35 (3) ◽  
pp. 263-272
Author(s):  
WATCHAREEPAN ATIPONRAT ◽  
◽  
SUPREEDEE DANGSKUL ◽  
ANCHALEE KHEMPHET ◽  
◽  
...  

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.


Author(s):  
Hamid Faraji ◽  
Stojan Radenovic

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.


Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 767 ◽  
Author(s):  
Jelena Vujaković ◽  
Slobodanka Mitrović ◽  
Mirjana Pavlović ◽  
Stojan Radenović

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.


2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Saif Ur Rehman ◽  
Shamoona Jabeen ◽  
Sami Ullah Khan ◽  
Mohammed M. M. Jaradat

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.


Filomat ◽  
2018 ◽  
Vol 32 (10) ◽  
pp. 3697-3707 ◽  
Author(s):  
Ümit Aksoy ◽  
Erdal Karapınar ◽  
İnci Erhan ◽  
Vladimir Rakocevic

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.


2021 ◽  
Vol 69 (1) ◽  
pp. 8-30
Author(s):  
Mudasir Younis ◽  
Nicola Fabiano ◽  
Zaid Fadail ◽  
Zoran Mitrović ◽  
Stojan Radenović

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.


2020 ◽  
Vol 8 (1) ◽  
pp. 114-165
Author(s):  
Tetsu Toyoda

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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