Existence and uniqueness of solution for quasi-equilibrium problems and fixed point problems on complete metric spaces with applications

2012 ◽  
Vol 57 (3) ◽  
pp. 829-841 ◽  
Author(s):  
Chih-Sheng Chuang ◽  
Lai-Jiu Lin
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Equilibrium Problems ◽  
Fixed Point Problems ◽  
Uniqueness Of Solution ◽  
Quasi Equilibrium ◽  
Complete Metric Spaces

scholarly journals Metric Characterizations ofα-Well-Posedness for a System of Mixed Quasivariational-Like Inequalities in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
L. C. Ceng ◽  
Y. C. Lin
Keyword(s):  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Equilibrium Problems ◽  
Uniqueness Of Solution ◽  
Quasi Equilibrium ◽  
Well Posedness ◽  
Special Case

The purpose of this paper is to investigate the problems of the well-posedness for a system of mixed quasivariational-like inequalities in Banach spaces. First, we generalize the concept ofα-well-posedness to the system of mixed quasivariational-like inequalities, which includes symmetric quasi-equilibrium problems as a special case. Second, we establish some metric characterizations ofα-well-posedness for the system of mixed quasivariational-like inequalities. Under some suitable conditions, we prove that theα-well-posedness is equivalent to the existence and uniqueness of solution for the system of mixed quasivariational-like inequalities. The corresponding concept ofα-well-posedness in the generalized sense is also considered for the system of mixed quasivariational-like inequalities having more than one solution. The results presented in this paper generalize and improve some known results in the literature.

scholarly journals BANACH FIXED POINT THEOREM ON ORTHOGONAL CONE METRIC SPACES

2021 ◽  
pp. 1239
Author(s):  
Zeinab Eivazi Damirchi Darsi Olia ◽  
Madjid Eshaghi Gordji ◽  
Davood Ebrahimi Bagha
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Uniqueness Of Solution ◽  
Banach Fixed Point Theorem ◽  
Cone Metric Spaces ◽  
Cone Metric

In this paper, we introduce new concept of orthogonal cone metric spaces. We stablish new versions of fixed point theorems in incomplete orthogonal cone metric spaces. As an application, we show the existence and uniqueness of solution of the periodic boundry value problem.

scholarly journals Fixed Point Theorems for a Class ofα-Admissible Contractions and Applications to Boundary Value Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Hamed H. Alsulami ◽  
Selma Gülyaz ◽  
Erdal Karapınar ◽  
İncı M. Erhan
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Boundary Value ◽  
Periodic Boundary Conditions ◽  
Distance Functions ◽  
Ordered Metric Spaces ◽  
Complete Metric Spaces ◽  
Altering Distance

A class ofα-admissible contractions defined via altering distance functions is introduced. The existence and uniqueness conditions for fixed points of such maps on complete metric spaces are investigated and related fixed point theorems are presented. The results are reconsidered in the context of partially ordered metric spaces and applied to boundary value problems for differential equations with periodic boundary conditions.

scholarly journals The Study of Fixed Point Theory for Various Multivalued Non-Self-Maps

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Wei-Shih Du ◽  
Erdal Karapınar ◽  
Naseer Shahzad
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Coincidence Points ◽  
Complete Metric Spaces

The basic motivation of this paper is to extend, generalize, and improve several fundamental results on the existence (and uniqueness) of coincidence points and fixed points for well-known maps in the literature such as Kannan type, Chatterjea type, Mizoguchi-Takahashi type, Berinde-Berinde type, Du type, and other types from the class of self-maps to the class of non-self-maps in the framework of the metric fixed point theory. We establish some fixed/coincidence point theorems for multivalued non-self-maps in the context of complete metric spaces.

scholarly journals Modified F-contractions via α-admissible mappings and application to integral equations

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1141-1148 ◽  
Author(s):  
Hassen Aydi ◽  
Erdal Karapinar ◽  
Habib Yazidi
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Complete Metric Spaces

In this paper, we introduce the concept of a modified F-contraction via ?-admissible mappings and propose some theorems that guarantee the existence and uniqueness of fixed point for such mappings in the frame of complete metric spaces. We also provide some illustrative examples. Moreover, we consider an application solving an integral equation.

Fixed points of set-valued F-contractions and its application to non-linear integral equations

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3377-3390 ◽  
Author(s):  
Satish Shukla ◽  
Dhananjay Gopal ◽  
Juan Martínez-Moreno
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Uniqueness Of Solutions ◽  
Complete Metric Spaces ◽  
Non Linear ◽  
Linear Integral ◽  
Linear Integral Equations

We observe that the assumption of set-valued F-contractions (Sgroi and Vetro [13]) is actually very strong for the existence of fixed point and can be weakened. In this connection, we introduce the notion of set-valued ?-F-contractions and prove a corresponding fixed point theorem in complete metric spaces. Consequently, we derive several fixed point theorems in metric spaces. Some examples are given to illustrate the new theory. Then we apply our results to establishing the existence and uniqueness of solutions for a certain type of non-linear integral equations.

scholarly journals A Fixed Point Theorem for Contraction Type Maps in Partially Ordered Metric Spaces and Application to Ordinary Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
M. Eshaghi Gordji ◽  
H. Baghani ◽  
G. H. Kim
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Generalized Contraction ◽  
Ordered Metric Spaces ◽  
Complete Metric Spaces ◽  
Partially Ordered ◽  
Contraction Type

We present a fixed point theorem for generalized contraction in partially ordered complete metric spaces. As an application, we give an existence and uniqueness for the solution of a periodic boundary value problem.

scholarly journals Fixed point results in $M_{\nu }$-metric spaces with an application

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Mohammad Asim ◽  
Izhar Uddin ◽  
Mohammad Imdad
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Metric Space ◽  
Fredholm Integral Equation ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Banach Contraction Principle ◽  
Uniqueness Of Solution ◽  
Contraction Principle ◽  
Banach Contraction

Abstract In this paper, we introduce the concept of $M_{\nu}$ M ν -metric as a generalization of M-metric and ν-generalized metric and also prove an analogue of Banach contraction principle in an $M_{\nu}$ M ν -metric space. Also, we adopt an example to highlight the utility of our main result which extends and improves the corresponding relevant results of the existing literature. Finally, we use our main result to examine the existence and uniqueness of solution for a Fredholm integral equation.

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