scholarly journals Simulations functions and Geraghty type results

2021 ◽  
Vol 39 (1) ◽  
pp. 35-50
Author(s):  
Sumit Chandok ◽  
Ankush Chanda ◽  
Lakshmi Kanta Dey ◽  
Mirjana Pavlovic ◽  
Stojan Radenovic
Keyword(s):  
Open Problem ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Contraction Mappings ◽  
Point Of Coincidence ◽  
Interesting Open Problem ◽  
Simulation Functions ◽  
Type Contraction

We concern this manuscript with Geraghty type contraction mappings via simulation functions and pull down some sufficient conditions for the existence and uniqueness of point of coincidence for several classes of mappings involving Geraghty functions in the setting of metric spaces. These findings touch up many of the existing results in the literature. Additionally, we elicit one of our main result by a non-trivial example and pose an interesting open problem for the enthusiastic readers.

scholarly journals Simulation type functions and coincidence points

Filomat ◽  
2018 ◽  
Vol 32 (1) ◽  
pp. 141-147 ◽  
Author(s):  
Stojan Radenovic ◽  
Sumit Chandok
Keyword(s):  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Coincidence Points ◽  
Point Of Coincidence ◽  
Simulation Functions ◽  
Proper Generalization ◽  
Appl Math ◽  
American Math

In this paper, we obtain some sufficient conditions for the existence and uniqueness of point of coincidence by using simulation functions in the context of metric spaces and prove some interesting results. Our results generalize the corresponding results of [5, 8, 13, 14, 16] in several directions. Also, we provide an example which shows that our main result is a proper generalization of the result of Jungck [American Math. Monthly 83(1976) 261-263], L-de-Hierro et al. [J. Comput. Appl. Math 275(2015) 345-355] and of Olgun et al. [Turk. J. Math. (2016) 40:832-837].

scholarly journals Fixed point results concerning α-F-contraction mappings in metric spaces

2019 ◽  
Vol 20 (1) ◽  
pp. 81 ◽  
Author(s):  
Lakshmi Kanta Dey ◽  
Poom Kumam ◽  
Tanusri Senapati
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Contraction Mappings

<p>In this paper, we introduce the notions of generalized α-F-contraction and modified generalized α-F-contraction. Then, we present sufficient conditions for existence and uniqueness of fixed points for the above kind of contractions. Necessarily, our results generalize and unify several results of the existing literature. Some examples are presented to substantiate the usability of our obtained results.</p>

scholarly journals Quantum Mean-Field Games with the Observations of Counting Type

Games ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 7
Author(s):  
Vassili N. Kolokoltsov
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Open Problem ◽  
Existence And Uniqueness ◽  
Existence Of Solutions ◽  
Mean Field ◽  
Mean Field Games ◽  
Quantum Game ◽  
Quantum Games ◽  
Interesting Open Problem

Quantum games and mean-field games (MFG) represent two important new branches of game theory. In a recent paper the author developed quantum MFGs merging these two branches. These quantum MFGs were based on the theory of continuous quantum observations and filtering of diffusive type. In the present paper we develop the analogous quantum MFG theory based on continuous quantum observations and filtering of counting type. However, proving existence and uniqueness of the solutions for resulting limiting forward-backward system based on jump-type processes on manifolds seems to be more complicated than for diffusions. In this paper we only prove that if a solution exists, then it gives an ϵ-Nash equilibrium for the corresponding N-player quantum game. The existence of solutions is suggested as an interesting open problem.

scholarly journals Common Fixed-Point Results in Ordered Left (Right) Quasi- b -Metric Spaces and Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-21
Author(s):  
Hemant Kumar Nashine ◽  
Sourav Shil ◽  
Hiranmoy Garai ◽  
Lakshmi Kanta Dey ◽  
Vahid Parvaneh
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Matrix Equations ◽  
Ordered Sets ◽  
Nonlinear Matrix ◽  
Fractional Differential ◽  
Left And Right

We use the notions of left- and right-complete quasi- b -metric spaces and partial ordered sets to obtain a couple of common fixed-point results for strictly weakly isotone increasing mappings and relatively weakly increasing mappings, which satisfy a pair of almost generalized contractive conditions. To illustrate our results, throughout the paper, we give several relevant examples. Further, we use our results to establish sufficient conditions for existence and uniqueness of solution of a system of nonlinear matrix equations and a pair of fractional differential equations. Finally, we provide a nontrivial example to validate the sufficient conditions for nonlinear matrix equations with numerical approximations.

scholarly journals A Hybrid Contraction that Involves Jaggi Type

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 715
Author(s):  
Erdal Karapınar ◽  
Andreea Fulga
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Complete Metric Spaces ◽  
Hybrid Type ◽  
Fractional Differential ◽  
The Given ◽  
Type Contraction

In this manuscript, we aim to provide a new hybrid type contraction that is a combination of a Jaggi type contraction and interpolative type contraction in the framework of complete metric spaces. We investigate the existence and uniqueness of such a hybrid contraction in separate theorems. We consider a solution to certain fractional differential equations as an application of the given results. In addition, we provide an example to indicate the genuineness of the given results.

Best approximation and fixed points for rational-type contraction mappings

2019 ◽  
Vol 25 (2) ◽  
pp. 205-209
Author(s):  
Sumit Chandok
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Best Approximation ◽  
Contraction Mapping ◽  
Metric Spaces ◽  
Contraction Mappings ◽  
Invariant Approximation ◽  
Frame Work ◽  
Rational Type ◽  
Type Contraction

AbstractIn this paper, we prove a fixed point theorem for a rational type contraction mapping in the frame work of metric spaces. Also, we extend Brosowski–Meinardus type results on invariant approximation for such class of contraction mappings. The results proved extend some of the known results existing in the literature.

scholarly journals Multivalued Problems, Orthogonal Mappings, and Fractional Integro-Differential Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
R. K. Sharma ◽  
Sumit Chandok
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Fixed Point Problem ◽  
Existence Of Solution ◽  
Point Problem ◽  
Contraction Mappings ◽  
Integro Differential Equation

In this manuscript, we propose some sufficient conditions for the existence of solution for the multivalued orthogonal ℱ -contraction mappings in the framework of orthogonal metric spaces. As a consequence of results, we obtain some interesting results. Also as application of the results obtained, we investigate Ulam’s stability of fixed point problem and present a solution for the Caputo-type nonlinear fractional integro-differential equation. An example is also provided to illustrate the usability of the obtained results.

scholarly journals On Some Fixed Point Results forH+-Type Contraction Mappings in Metric Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Hemant Kumar Pathak ◽  
Rosana Rodríguez-López
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contraction Mappings ◽  
Contractive Mappings ◽  
Type Contraction

We prove some fixed point theorems forH+-type multivalued contractive mappings in the setting of Banach spaces and metric spaces. The results provided allow recovering different well-known results.

scholarly journals Admissible Hybrid Z-Contractions in b-Metric Spaces

Axioms ◽  
2019 ◽  
Vol 9 (1) ◽  
pp. 2 ◽  
Author(s):  
Ioan Cristian Chifu ◽  
Erdal Karapınar
Keyword(s):  
Metric Space ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Fixed Point Problem ◽  
Uniqueness Result ◽  
Point Problem ◽  
Well Posedness ◽  
Simulation Functions ◽  
Set Up ◽  
The Given

In this manuscript, we introduce a new notion, admissible hybrid Z -contraction that unifies several nonlinear and linear contractions in the set-up of a b-metric space. In our main theorem, we discuss the existence and uniqueness result of such mappings in the context of complete b-metric space. The given result not only unifies the several existing results in the literature, but also extends and improves them. We express some consequences of our main theorem by using variant examples of simulation functions. As applications, the well-posedness and the Ulam–Hyers stability of the fixed point problem are also studied.

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