scholarly journals A Best Proximity Point Theorem for Generalized Non-Self-Kannan-Type and Chatterjea-Type Mappings and Lipschitzian Mappings in Complete Metric Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-11
Author(s):  
Kasamsuk Ungchittrakool
Keyword(s):  
Point Theorem ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Complete Metric Spaces ◽  
Contractive Mappings ◽  
Lipschitzian Mappings

The purpose of this paper is to provide and study a best proximity point theorem for generalized non-self-Kannan-type and Chatterjea-type mappings and Lipschitzian mappings in complete metric spaces. The significant mapping in a unified form which related to contractive mappings, Kannan-type mappings, and Chatterjea-type mappings is established. We also provide some examples to illustrate the situation corresponding to the main theorem. The main result of this paper can be viewed as a general and unified form of several previously existing results.

scholarly journals Some New Results on Coincidence Points for Multivalued Suzuki-Type Mappings in Fairly Complete Spaces

Computation ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 17 ◽  
Author(s):  
Naeem Saleem ◽  
Iqra Habib ◽  
Manuel De la Sen
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Coincidence Points ◽  
Ordered Metric Spaces ◽  
Partially Ordered Metric Spaces ◽  
Complete Metric Spaces ◽  
Partially Ordered ◽  
Contractive Mappings

In this paper, we introduce Suzuki-type ( α , β , γ g ) - generalized and modified proximal contractive mappings. We establish some coincidence and best proximity point results in fairly complete spaces. Also, we provide coincidence and best proximity point results in partially ordered complete metric spaces for Suzuki-type ( α , β , γ g ) - generalized and modified proximal contractive mappings. Furthermore, some examples are presented in each section to elaborate and explain the usability of the obtained results. As an application, we obtain fixed-point results in metric spaces and in partially ordered metric spaces. The results obtained in this article further extend, modify and generalize the various results in the literature.

scholarly journals Fixed point results for F-contractive mappings of Hardy-Rogers-type

Filomat ◽  
2014 ◽  
Vol 28 (4) ◽  
pp. 715-722 ◽  
Author(s):  
Monica Cosentino ◽  
Pasquale Vetroa
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Ordered Metric Spaces ◽  
Complete Metric Spaces ◽  
Contractive Mappings ◽  
Banach Contraction

Recently, Wardowski introduced a new concept of contraction and proved a fixed point theorem which generalizes Banach contraction principle. Following this direction of research, in this paper, we will present some fixed point results of Hardy-Rogers-type for self-mappings on complete metric spaces or complete ordered metric spaces. Moreover, an example is given to illustrate the usability of the obtained results.

A generalization of Reich’s fixed point theorem for multi-valued mappings

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3295-3305 ◽  
Author(s):  
Antonella Nastasi ◽  
Pasquale Vetro
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Complete Metric Spaces ◽  
New Class ◽  
Banach Contraction ◽  
The Banach Contraction Principle

Motivated by a problem concerning multi-valued mappings posed by Reich [S. Reich, Some fixed point problems, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 57 (1974) 194-198] and a paper of Jleli and Samet [M. Jleli, B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl. 2014:38 (2014) 1-8], we consider a new class of multi-valued mappings that satisfy a ?-contractive condition in complete metric spaces and prove some fixed point theorems. These results generalize Reich?s and Mizoguchi-Takahashi?s fixed point theorems. Some examples are given to show the usability of the obtained results.

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.

Fixed point of contractive mappings in generalized metric spaces

2009 ◽  
Vol 59 (4) ◽  
Author(s):  
Pratulananda Das ◽  
Lakshmi Dey
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Generalized Metric Spaces ◽  
Contractive Mappings ◽  
Generalized Metric

AbstractWe prove a fixed point theorem for contractive mappings of Boyd and Wong type in generalized metric spaces, a concept recently introduced in [BRANCIARI, A.: A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen 57 (2000), 31–37].

scholarly journals Best Proximity Point Results for Generalized Θ-Contractions and Application to Matrix Equations

Symmetry ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 93
Author(s):  
Zhenhua Ma ◽  
Azhar Hussain ◽  
Muhammad Adeel ◽  
Nawab Hussain ◽  
Ekrem Savas
Keyword(s):  
Metric Spaces ◽  
Best Proximity Point ◽  
Positive Definite ◽  
Matrix Equations ◽  
Nonlinear Matrix Equation ◽  
Complete Metric Spaces ◽  
Partially Ordered ◽  
Positive Definite Solution ◽  
Nonlinear Matrix ◽  
Definite Solution

In this paper, we introduce the notion of C ´ iri c ´ type α - ψ - Θ -contraction and prove best proximity point results in the context of complete metric spaces. Moreover, we prove some best proximity point results in partially ordered complete metric spaces through our main results. As a consequence, we obtain some fixed point results for such contraction in complete metric and partially ordered complete metric spaces. Examples are given to illustrate the results obtained. Moreover, we present the existence of a positive definite solution of nonlinear matrix equation X = Q + ∑ i = 1 m A i * γ ( X ) A i and give a numerical example.

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