scholarly journals Best Proximity Point for Generalized and S -Geraphty Contractions

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Abdelhafid Bassou ◽  
Taoufik Sabar ◽  
Mohamed Aamri
Keyword(s):  
Existence And Uniqueness ◽  
Best Proximity Point ◽  
Sufficient Conditions ◽  
New Class

This paper introduces a new class of mappings called S -Geraphty-contractions and provides sufficient conditions for the existence and uniqueness of a best proximity point for such mappings. It also presents the best proximity point result for generalized contractions as well. Our results extend and generalize some theorems in the literature.

scholarly journals Best Proximity Point for Generalized Proximal Weak Contractions in Complete Metric Space

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Erdal Karapınar ◽  
V. Pragadeeswarar ◽  
M. Marudai
Keyword(s):  
Approximate Solution ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Complete Metric Space ◽  
Optimal Approximate Solution ◽  
Weak Contraction ◽  
Complete Metric Spaces ◽  
New Class

We introduce a new class of nonself-mappings, generalized proximal weak contraction mappings, and prove the existence and uniqueness of best proximity point for such mappings in the context of complete metric spaces. Moreover, we state an algorithm to determine such an optimal approximate solution designed as a best proximity point. We establish also an example to illustrate our main results. Our result provides an extension of the related results in the literature.

scholarly journals A Best Proximity Point Result in Modular Spaces with the Fatou Property

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Mohamed Jleli ◽  
Erdal Karapınar ◽  
Bessem Samet
Keyword(s):  
Existence And Uniqueness ◽  
Best Proximity Point ◽  
Sufficient Conditions ◽  
Modular Space ◽  
Fatou Property ◽  
Best Proximity Points ◽  
Modular Spaces

Consider a nonself-mapping , where is a pair of nonempty subsets of a modular space . A best proximity point of is a point satisfying the condition: . In this paper, we introduce the class of proximal quasicontraction nonself-mappings in modular spaces with the Fatou property. For such mappings, we provide sufficient conditions assuring the existence and uniqueness of best proximity points.

scholarly journals Existence of Coupled Best Proximity Points of p-Cyclic Contractions

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 39
Author(s):  
Miroslav Hristov ◽  
Atanas Ilchev ◽  
Diana Nedelcheva ◽  
Boyan Zlatanov
Keyword(s):  
Wide Class ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Best Proximity Points ◽  
Cyclic Contractions ◽  
Ordered Pairs

We generalize the notion of coupled fixed (or best proximity) points for cyclic ordered pairs of maps to p-cyclic ordered pairs of maps. We find sufficient conditions for the existence and uniqueness of the coupled fixed (or best proximity) points. We illustrate the results with an example that covers a wide class of maps.

scholarly journals Correctness conditions for high-order differential equations with unbounded coefficients

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Kordan N. Ospanov
Keyword(s):  
Differential Equation ◽  
Hilbert Space ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Integral Operators ◽  
Order Linear Differential Equation ◽  
Unbounded Coefficients ◽  
Weighted Norms ◽  
Uniqueness Of The Solution ◽  
Linear Differential

AbstractWe give some sufficient conditions for the existence and uniqueness of the solution of a higher-order linear differential equation with unbounded coefficients in the Hilbert space. We obtain some estimates for the weighted norms of the solution and its derivatives. Using these estimates, we show the conditions for the compactness of some integral operators associated with the resolvent.

scholarly journals Horosphere slab separation theorems in manifolds without conjugate points

2019 ◽  
Vol 27 (1) ◽  
Author(s):  
Sameh Shenawy
Keyword(s):  
Euclidean Space ◽  
Hyperbolic Space ◽  
Existence And Uniqueness ◽  
Convex Set ◽  
Sufficient Conditions ◽  
Conjugate Points ◽  
Separation Theorems ◽  
Farthest Points ◽  
Simply Connected ◽  
Convex Subsets

Abstract Let $\mathcal {W}^{n}$ W n be the set of smooth complete simply connected n-dimensional manifolds without conjugate points. The Euclidean space and the hyperbolic space are examples of these manifolds. Let $W\in \mathcal {W}^{n}$ W ∈ W n and let A and B be two convex subsets of W. This note aims to investigate separation and slab horosphere separation of A and B. For example,sufficient conditions on A and B to be separated by a slab of horospheres are obtained. Existence and uniqueness of foot points and farthest points of a convex set A in $W\in \mathcal {W}$ W ∈ W are considered.

Analysis of a New Class of Impulsive Implicit Sequential Fractional Differential Equations

2020 ◽  
Vol 21 (6) ◽  
pp. 571-587 ◽  
Author(s):  
Akbar Zada ◽  
Sartaj Ali ◽  
Tongxing Li
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Sufficient Conditions ◽  
Uniqueness Of Solutions ◽  
Integer Order ◽  
New Class ◽  
Proposed Model ◽  
Fractional Differential ◽  
Sequential Fractional Differential Equations

AbstractIn this paper, we study an implicit sequential fractional order differential equation with non-instantaneous impulses and multi-point boundary conditions. The article comprehensively elaborate four different types of Ulam’s stability in the lights of generalized Diaz Margolis’s fixed point theorem. Moreover, some sufficient conditions are constructed to observe the existence and uniqueness of solutions for the proposed model. The proposed model contains both the integer order and fractional order derivatives. Thus, the exponential function appearers in the solution of the proposed model which will lead researchers to study fractional differential equations with well known methods of integer order differential equations. In the last, few examples are provided to show the applicability of our main results.

scholarly journals Existence of Solutions of Nonlinear Stochastic Volterra Fredholm Integral Equations of Mixed Type

2010 ◽  
Vol 2010 ◽  
pp. 1-16 ◽  
Author(s):  
K. Balachandran ◽  
J.-H. Kim
Keyword(s):  
Integral Equations ◽  
Existence And Uniqueness ◽  
Mixed Type ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Stochastic Integral ◽  
Sufficient Conditions ◽  
Fredholm Integral Equations ◽  
Equations Of Mixed Type ◽  
Stochastic Integral Equations

We establish sufficient conditions for the existence and uniqueness of random solutions of nonlinear Volterra-Fredholm stochastic integral equations of mixed type by using admissibility theory and fixed point theorems. The results obtained in this paper generalize the results of several papers.

scholarly journals Existence and Uniqueness of Solutions to the Wage Equation of Dixit-Stiglitz-Krugman Model with No Restriction on Transport Costs

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Minoru Tabata ◽  
Nobuoki Eshima
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Nonlinear Operator ◽  
Sufficient Conditions ◽  
Wage Equation ◽  
Discrete Equation ◽  
Transport Costs ◽  
Economic Activities ◽  
Uniqueness Of Solutions ◽  
Double Nonlinear

In spatial economics, the distribution of wages is described by a solution to the wage equation of Dixit-Stiglitz-Krugman model. The wage equation is a discrete equation that has a double nonlinear singular structure in the sense that the equation contains a discrete nonlinear operator whose kernel itself is expressed by another discrete nonlinear operator with a singularity. In this article, no restrictions are imposed on the maximum of transport costs of the model and on the number of regions where economic activities are conducted. Applying Brouwer fixed point theorem to this discrete double nonlinear singular operator, we prove sufficient conditions for the wage equation to have a solution and a unique one.

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