scholarly journals Global optimal approximate solutions of best proximity points

Filomat ◽  
2021 ◽  
Vol 35 (5) ◽  
pp. 1555-1564
Author(s):  
Mohammad Haddadi ◽  
Vahid Parvaneh ◽  
Mohammad Mursaleen
Keyword(s):  
Fixed Point Theory ◽  
Best Proximity Point ◽  
Sufficient Conditions ◽  
Approximate Solutions ◽  
Point Theory ◽  
Cyclic Contraction ◽  
Best Proximity Points ◽  
Asymptotic Contraction ◽  
Global Optimal ◽  
Necessary And Sufficient

In this paper, we introduce the concept of contractive pair maps and give some necessary and sufficient conditions for existence and uniqueness of best proximity points for such pairs. In our approach, some conditions have been weakened. An application has been presented to demonstrate the usability of our results. Also, we introduce the concept of cyclic ?-contraction and cyclic asymptotic ?-contraction and give some existence and convergence theorems on best proximity point for cyclic ?-contraction and cyclic asymptotic ?-contraction mappings. The presented results extend, generalize and improve some known results from best proximity point theory and fixed-point theory.

scholarly journals Fixed point theory in the setting of $(\alpha,\beta,\psi,\phi)$-interpolative contractions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Erdal Karapınar ◽  
Andreea Fulga ◽  
Antonio Francisco Roldán López de Hierro
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Necessary And Sufficient Conditions ◽  
Alpha Beta ◽  
Necessary And Sufficient

AbstractIn this manuscript we introduce the notion of $(\alpha,\beta,\psi,\phi)$ ( α , β , ψ , ϕ ) -interpolative contraction that unifies and generalizes significant concepts: Proinov type contractions, interpolative contractions, and ample spectrum contraction. We investigate the necessary and sufficient conditions to guarantee existence and uniqueness of the fixed point of such mappings.

scholarly journals Qualitative Analysis of a Mathematical Model in the Time of COVID-19

2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
Kamal Shah ◽  
Thabet Abdeljawad ◽  
Ibrahim Mahariq ◽  
Fahd Jarad
Keyword(s):  
Mathematical Model ◽  
Qualitative Analysis ◽  
Existence And Uniqueness ◽  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Point Theory ◽  
Adomian Decomposition ◽  
The Mathematical Model

In this article, a qualitative analysis of the mathematical model of novel corona virus named COVID-19 under nonsingular derivative of fractional order is considered. The concerned model is composed of two compartments, namely, healthy and infected. Under the new nonsingular derivative, we, first of all, establish some sufficient conditions for existence and uniqueness of solution to the model under consideration. Because of the dynamics of the phenomenon when described by a mathematical model, its existence must be guaranteed. Therefore, via using the classical fixed point theory, we establish the required results. Also, we present the results of stability of Ulam’s type by using the tools of nonlinear analysis. For the semianalytical results, we extend the usual Laplace transform coupled with Adomian decomposition method to obtain the approximate solutions for the corresponding compartments of the considered model. Finally, in order to support our study, graphical interpretations are provided to illustrate the results by using some numerical values for the corresponding parameters of the model.

scholarly journals Stability Conditions of Second Order Integrodifferential Equations with Variable Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Dingheng Pi
Keyword(s):  
Fixed Point Theory ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Point Theory ◽  
Stability Conditions ◽  
Asymptotically Stable ◽  
Variable Delay ◽  
Functional Differential ◽  
Necessary And Sufficient

We investigate integrodifferential functional differential equationsẍ+f(t,x,ẋ)ẋ+∫t-r(t)t‍a(t,s)g(x(s))ds=0with variable delay. By using the fixed point theory, we obtain conditions which ensure that the zero solution of this equation is stable under an exponentially weighted metric. Then we establish necessary and sufficient conditions ensuring that the zero solution is asymptotically stable. We will give an example to apply our results.

scholarly journals A Note on Best Proximity Point Theorems under WeakP-Property

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Angel Almeida ◽  
Erdal Karapınar ◽  
Kishin Sadarangani
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theory ◽  
Best Proximity Point ◽  
Late Results ◽  
Point Theory ◽  
Best Proximity Points

In the very recent paper of Akbar and Gabeleh (2013), by using the notion ofP-property, it was proved that some late results about the existence and uniqueness of best proximity points can be obtained from the versions of associated existing results in the fixed point theory. Along the same line, in this paper, we prove that these results can be obtained under a weaker condition, namely, weakP-property.

Descent in Buildings (AM-190)

2017 ◽  
Author(s):  
Bernhard Mühlherr ◽  
Holger P. Petersson ◽  
Richard M. Weiss
Keyword(s):  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Algebraic Solution ◽  
Affine Buildings ◽  
The Third ◽  
Final Volume ◽  
Geometric Context ◽  
Necessary And Sufficient ◽  
Open Question

This book begins with the resolution of a major open question about the local structure of Bruhat-Tits buildings. It then puts forward an algebraic solution into a geometric context by developing a general fixed point theory for groups acting on buildings of arbitrary type, giving necessary and sufficient conditions for the residues fixed by a group to form a kind of subbuilding or “form” of the original building. At the center of this theory is the notion of a Tits index, a combinatorial version of the notion of an index in the relative theory of algebraic groups. These results are combined at the end to show that every exceptional Bruhat-Tits building arises as a form of a “residually pseudo-split” building. The book concludes with a display of the Tits indices associated with each of these exceptional forms. This is the third and final volume of a trilogy that began with The Structure of Spherical Buildings and The Structure of Affine Buildings.

scholarly journals A Note on Some Best Proximity Point Theorems Proved underP-Property

2013 ◽  
Vol 2013 ◽  
pp. 1-3 ◽  
Author(s):  
Ali Abkar ◽  
Moosa Gabeleh
Keyword(s):  
Fixed Point ◽  
Fixed Point Theory ◽  
Best Proximity Point ◽  
Point Theory ◽  
Best Proximity Points

We show that some recent results concerning the existence of best proximity points can be obtained from the same results in fixed point theory.

scholarly journals Fixed Point Theory and Positive Solutions for a Ratio-Dependent Elliptic System

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Jingmei Liu ◽  
Aixia Qian
Keyword(s):  
Positive Solutions ◽  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Degree Theory ◽  
Index Theory ◽  
Point Theory ◽  
Energy Estimates ◽  
Predator Prey Model ◽  
Ratio Dependent ◽  
Necessary And Sufficient

We consider a ratio-dependent predator-prey model under zero Dirichlet boundary condition. By using topological degree theory and fixed index theory, we study the necessary and sufficient conditions for the existence of positive solutions. Then we present the asymptotic behavior analysis of positive solutions, by bifurcation theory and energy estimates.

scholarly journals Fixed Points and Stability of a Class of Integrodifferential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Dingheng Pi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theory ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Point Theory ◽  
Asymptotically Stable ◽  
Variable Delay ◽  
Functional Differential ◽  
Necessary And Sufficient

We study a class of integrodifferential functional differential equationsx¨+f(t,x,x˙)x˙+∑j=1N∫t-rj(t)taj(t,s)gj(s,x(s))ds=0with variable delay. By using the fixed point theory, we establish necessary and sufficient conditions ensuring that the zero solution of this equation is asymptotically stable.

scholarly journals Some Random Coupled Best Proximity Points for a Generalized ω-Cyclic Contraction in Polish Spaces

2017 ◽  
Vol 59 (1) ◽  
pp. 91-105 ◽  
Author(s):  
C. Kongban ◽  
P. Kumam
Keyword(s):  
Metric Spaces ◽  
Best Proximity Point ◽  
Cyclic Contraction ◽  
Polish Spaces ◽  
Best Proximity Points ◽  
Coupled Best Proximity Point

AbstractIn this paper, we will introduce the concepts of a random coupled best proximity point and then we prove the existence of random coupled best proximity points in separable metric spaces. Our results extend the previous work of Akbar et al.[1].

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