scholarly journals A New Modified Hybrid Steepest-Descent by Using a Viscosity Approximation Method with a Weakly Contractive Mapping for a System of Equilibrium Problems and Fixed Point Problems with Minimization Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-29 ◽  
Author(s):  
Uamporn Witthayarat ◽  
Thanyarat Jitpeera ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Approximation Method ◽  
Contractive Mapping ◽  
Steepest Descent ◽  
Common Element ◽  
Viscosity Approximation Method ◽  
Viscosity Approximation ◽  
Weakly Contractive Mapping ◽  
Minimization Problems ◽  
Weakly Contractive

The purpose of this paper is to consider a modified hybrid steepest-descent method by using a viscosity approximation method with a weakly contractive mapping for finding the common element of the set of a common fixed point for an infinite family of nonexpansive mappings and the set of solutions of a system of an equilibrium problem. The sequence is generated from an arbitrary initial point which converges in norm to the unique solution of the variational inequality under some suitable conditions in a real Hilbert space. The results presented in this paper generalize and improve the results of Moudafi (2000), Marino and Xu (2006), Tian (2010), Saeidi (2010), and some others. Finally, we give an application to minimization problems and a numerical example which support our main theorem in the last part.

scholarly journals A Viscosity Approximation Method with a Weakly Contractive Mapping of General Iterative Processes for Nonexpansive Semigroups in Banach Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-17
Author(s):  
Pongsakorn Sunthrayuth ◽  
Chanan Sudsukh ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Approximation Method ◽  
Contractive Mapping ◽  
Viscosity Approximation Method ◽  
Viscosity Approximation ◽  
Iterative Processes ◽  
Weakly Contractive Mapping ◽  
Weakly Contractive

We introduce a new viscosity approximation method with a weakly contractive mapping of general iterative processes for finding common fixed point of nonexpansive semigroups {T(t):t∈ℝ+} in the framework of Banach spaces. We proved that under some mild conditions these iterative processes converge strongly to the common fixed point of {T(t):t∈ℝ+}, which is the unique solution of some variational inequality. The results obtained in this paper extend and improve on the recent results of Li et al. (2009), Chen and He (2007), and many others as special cases.

scholarly journals Relaxed Viscosity Approximation Methods with Regularization for Constrained Minimization Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-19 ◽  
Author(s):  
Lu-Chuan Ceng ◽  
Hong-Kun Xu ◽  
Ching-Feng Wen
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mappings ◽  
Approximation Methods ◽  
Viscosity Approximation Method ◽  
Convex Minimization Problem ◽  
Viscosity Approximation ◽  
Minimization Problems ◽  
Strict Pseudocontraction ◽  
Constrained Minimization Problems ◽  
Viscosity Approximation Methods

We introduce a new relaxed viscosity approximation method with regularization and prove the strong convergence of the method to a common fixed point of finitely many nonexpansive mappings and a strict pseudocontraction that also solves a convex minimization problem and a suitable equilibrium problem.

scholarly journals Some weakly contractive mapping theorems in partially ordered spaces and applications

2012 ◽  
Vol 45 (3) ◽  
Author(s):  
B. E. Rhoades ◽  
H. K. Pathak ◽  
S. N. Mishra
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Contractive Mapping ◽  
Partially Ordered ◽  
Weakly Contractive Mapping ◽  
Contractive Mappings ◽  
Weakly Contractive ◽  
Partially Ordered Spaces

AbstractThe purpose of this paper is to present some fixed point theorems for certain weakly contractive mappings, known as weakly (

WEAKLY CONTRACTIVE MAPPING IN PARTIAL METRIC SPACE

2017 ◽  
Vol 5 (3) ◽  
pp. 377
Author(s):  
Sagita Charolina Sihombing
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Partial Metric Space ◽  
Contractive Mapping ◽  
Partial Metric ◽  
Weakly Contractive Mapping ◽  
Kannan Mapping ◽  
Weakly Contractive

Contractive mapping is one kind of mapping that guarantees a fixed point in a metric space  Many experts has developed this kind of mapping to show the existence of a fixed point such as Kannan mapping and Chatterjea Contractive mapping. In this study, we will show the weakly contractive mapping to show the existence of fixed point in the partial metric space

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