scholarly journals Global Attractivity Results on Complete Ordered Metric Spaces for Third-Order Difference Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Mujahid Abbas ◽  
Maher Berzig
Keyword(s):  
Metric Spaces ◽  
Global Attractivity ◽  
Iterative Algorithms ◽  
Monotone Mappings ◽  
Contractive Condition ◽  
Third Order ◽  
Ordered Metric Spaces ◽  
All Solutions ◽  
The Difference ◽  
The Given

We establish fixed-point theorems for mixed monotone mappings in the setting of ordered metric spaces which satisfy a contractive condition for all points that are related by a given ordering. We also give a global attractivity result for all solutions of the difference equation where satisfies certain monotonicity conditions with respect to the given ordering. As an application of our obtained results, we present some iterative algorithms to solve a class of matrix equations. A numerical example is also presented to test the validity of the algorithms.

scholarly journals Coupled Fixed Point Theorems for (φ,ψ)-Contractive Mixed Monotone Mappings in Partially Ordered Metric Spaces and Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Manish Jain ◽  
Neetu Gupta ◽  
Sanjay Kumar
Keyword(s):  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Monotone Operators ◽  
Monotone Mappings ◽  
Contractive Condition ◽  
Nonlinear Integral Equations ◽  
Ordered Metric Spaces ◽  
Partially Ordered Metric Spaces ◽  
Partially Ordered

The object of this paper is to establish the existence and uniqueness of coupled fixed points under a (φ, ψ)-contractive condition for mixed monotone operators in the setup of partially ordered metric spaces. Presented work generalizes the recent results of Berinde (2011, 2012) and weakens the contractive conditions involved in the well-known results of Bhaskar and Lakshmikantham (2006), and Luong and Thuan (2011). The effectiveness of our work is validated with the help of a suitable example. As an application, we give a result of existence and uniqueness for the solutions of a class of nonlinear integral equations.

scholarly journals Tripled coincidence theorems for monotone mappings in partially ordered metric spaces

2012 ◽  
Vol 21 (2) ◽  
pp. 135-142
Author(s):  
MARIN BORCUT ◽  
Keyword(s):  
Metric Spaces ◽  
Monotone Mappings ◽  
Contractive Condition ◽  
Ordered Metric Spaces ◽  
Tripled Fixed Point ◽  
Partially Ordered Metric Spaces ◽  
Partially Ordered ◽  
Nonlinear Anal ◽  
Coincidence Theorems ◽  
Contractive Type

In this paper, we establish tripled coincidence point theorems for a pair of mappings F : X × X × X → X and g : X → X satisfying a nonlinear contractive condition ordered metric spaces. Presented theorems extend several existing results in the literature: [Borcut, M. and Berinde, V., Tripled coincidente point theorems for contractive type mappings in partially ordered metric spaces, Aplied Mathematics and Computation, 218 (2012), No. 10, 5929–5936], and Berinde, Borcut in article [Berinde, V., Borcut, M., Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal., 74 (2011), 4889-4897].

scholarly journals A Fixed Point Theorem for Mappings Satisfying a Contractive Condition of Rational Type on a Partially Ordered Metric Space

2010 ◽  
Vol 2010 ◽  
pp. 1-8 ◽  
Author(s):  
J. Harjani ◽  
B. López ◽  
K. Sadarangani
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Ordered Metric Space ◽  
Partially Ordered Metric Space ◽  
Ordered Metric Spaces ◽  
Partially Ordered ◽  
Rational Type

The purpose of this paper is to present a fixed point theorem using a contractive condition of rational type in the context of partially ordered metric spaces.

scholarly journals On the Power of Simulation and Admissible Functions in Metric Fixed Point Theory

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Areej S. S. Alharbi ◽  
Hamed H. Alsulami ◽  
Erdal Karapinar
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Admissible Function ◽  
Point Theory ◽  
Contractive Condition ◽  
Simulation Function ◽  
The Given ◽  
Admissible Functions

We investigate the existence and uniqueness of certain operators which form a new contractive condition via the combining of the notions of admissible function and simulation function contained in the context of completeb-metric spaces. The given results not only unify but also generalize a number of existing results on the topic in the corresponding literature.

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