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Items from 1 to 15 out of 15 results

article

Strong convergence of Browder’s and Halpern’s type iterations in Hilbert spaces

Kanokwan Wongchan, Satit Saejung

Positivity > 2018 > 22 > 4 > 969-982

We use results from theory of nonexpansive mappings to unify and deduce the recent results of Lin and Takahashi (Positivity 16:429–453, 2012) and of Takahashi (J Optim Theory Appl 157:781–802, 2013).

article

Construction of a common element for the set of solutions of fixed point problems and generalized equilibrium problems in Hilbert spaces

Muhammad Aqeel Ahmad Khan

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica > 2016 > 15

In this paper, we propose and analyse an iterative algorithm for the approximation of a common solution for a finite family of k-strict pseudocontractions and two finite families of generalized equilibrium problems in the setting of Hilbert spaces. Strong convergence results of the proposed iterative algorithm together with some applications to solve the variational inequality problems are established...

article

A new approximation method for finding common elements of equilibrium problems, variational inequality problems and fixed point problems of nonspreading mappings

Kanyarat Cheawchan, Withun Phuengrattana, Atid Kangtunyakarn

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales.... > 2017 > 111 > 4 > 1105-1115

In this paper, we introduce an iterative scheme for finding a common element of the set of solutions of the equilibrium problem, the set of solutions of the variational inequality problem and the set of fixed points of a nonspreading mapping in Hilbert spaces. Under suitable assumptions, weak convergence theorems have been proved in the framework of a Hilbert space. Our results improve and extend...

article

Composite viscosity methods for common solutions of general mixed equilibrium problem, variational inequalities and common fixed points

Lu-Chuan Ceng, Abdul Latif, Abdullah E Al-Mazrooei

Journal of Inequalities and Applications > 2015 > 2015 > 1 > 1-34

In this paper, we introduce a new composite viscosity iterative algorithm and prove the strong convergence of the proposed algorithm to a common fixed point of one finite family of nonexpansive mappings and another infinite family of nonexpansive mappings, which also solves a general mixed equilibrium problem and a finite family of variational inequalities. An example is also provided in support of...

article

Implicit and explicit iterative methods for mixed equilibria with constraints of system of generalized equilibria and hierarchical fixed point problem

Lu-Chuan Ceng, Chin-Tzong Pang, Ching-Feng Wen

Journal of Inequalities and Applications > 2015 > 2015 > 1 > 1-44

In this paper, we introduce one composite implicit relaxed extragradient-like scheme and another composite explicit relaxed extragradient-like scheme for finding a common solution of a finite family of generalized mixed equilibrium problems (GMEPs) with the constraints of a system of generalized equilibrium problems (SGEP) and the hierarchical fixed point problem (HFPP) for a strictly pseudocontractive...

article

General iterative algorithms for mixed equilibrium problems, variational inequalities and fixed point problems

Xiao-Jie Wang, Lu-Chuan Ceng, Hui-Ying Hu, Shi-Xiu Li

Fixed Point Theory and Applications > 2014 > 2014 > 1 > 1-25

In this paper, we introduce and analyze a general iterative algorithm for finding a common solution of a mixed equilibrium problem, a general system of variational inequalities and a fixed point problem of infinitely many nonexpansive mappings in a real Hilbert space. Under some mild conditions, we derive the strong convergence of the sequence generated by the proposed algorithm to a common solution,...

article

Fixed point solutions of generalized mixed equilibrium problems and variational inclusion problems for nonexpansive semigroups

Jae Ug Jeong

Fixed Point Theory and Applications > 2014 > 2014 > 1 > 1-25

In this paper, we introduce a composite iterative method for solving a common element of the set of solutions of fixed points for nonexpansive semigroups, the set of solutions of generalized mixed equilibrium problems and the set of solutions of the variational inclusion for a β-inverse strongly monotone mapping in a real Hilbert space. We prove that the sequence converges strongly to a common element...

article

Strong convergence theorems for a generalized mixed equilibrium problem and variational inequality problems

Jae Ug Jeong

Fixed Point Theory and Applications > 2013 > 2013 > 1 > 1-21

In this paper, a new iterative scheme based on the extragradient-like method for finding a common element of the set of common fixed points of a finite family of nonexpansive mappings, the set of solutions of variational inequalities for a strongly positive linear bounded operator and the set of solutions of a mixed equilibrium problem is proposed. A strong convergence theorem for this iterative scheme...

article

A general iterative method for two maximal monotone operators and 2-generalized hybrid mappings in Hilbert spaces

Rabian Wangkeeree, Uraiwan Boonkong

Fixed Point Theory and Applications > 2013 > 2013 > 1 > 1-23

Let C be a closed and convex subset of a real Hilbert space H. Let T be a 2-generalized hybrid mapping of C into itself, let A be an α-inverse strongly-monotone mapping of C into H, and let B and F be maximal monotone operators on and respectively. The purpose of this paper is to introduce a general iterative scheme for finding a point of which is a unique solution of a hierarchical...

article

A new relaxed extragradient-like algorithm for approaching common solutions of generalized mixed equilibrium problems, a more general system of variational inequalities and a fixed point problem

Yifen Ke, Changfeng Ma

Fixed Point Theory and Applications > 2013 > 2013 > 1 > 1-21

In this paper, we introduce a new iterative algorithm by the relaxed extragradient-like method for finding a common element of the set of solutions of generalized mixed equilibrium problems, the set of solutions of a more general system of variational inequalities for finite inverse strongly monotone mappings and the set of solutions of a fixed point problem of a strictly pseudocontractive mapping...

article

Regularization method for Noor’s variational inequality problem induced by a hemicontinuous monotone operator

Yeol Je Cho, Narin Petrot

Fixed Point Theory and Applications > 2012 > 2012 > 1 > 1-13

In this paper, we provide a regularization method for finding a solution of Noor’s variational inequality problem induced by a hemicontinuous monotone operator. Moreover, such a solution is related to the set of zero of inverse strongly monotone mappings. Consequently, since we do not assume the strong monotonicity of the considered operator, our results are general and extend some well-known results...

article

Strong convergence theorems for variational inequalities and fixed points of a countable family of nonexpansive mappings

Aunyarat Bunyawat, Suthep Suantai

Fixed Point Theory and Applications > 2011 > 2011 > 1 > 1-13

A new general iterative method for finding a common element of the set of solutions of variational inequality and the set of common fixed points of a countable family of nonexpansive mappings is introduced and studied. A strong convergence theorem of the proposed iterative scheme to a common fixed point of a countable family of nonexpansive mappings and a solution of variational inequality of an inverse...

article

Hybrid projection method for generalized mixed equilibrium problems, variational inequality problems, and fixed point problems in Banach spaces

Ya-qin Wang, Liu-chuan Zeng

Applied Mathematics and Mechanics > 2011 > 32 > 2 > 251-264

A new hybrid projection iterative scheme is introduced to approximate a common element of the solution set of a generalized mixed equilibrium problem, the solution set of a variational inequality problem, and the set of fixed points of a relatively weak nonexpansive mapping in the Banach spaces. The obtained results generalize and improve the recent results announced by many other authors.

article

Regularization and iterative method for general variational inequality problem in hilbert spaces

Yeol Je Cho, Narin Petrot

Journal of Inequalities and Applications > 2011 > 2011 > 1 > 1-11

Without the strong monotonicity assumption of the mapping, we provide a regularization method for general variational inequality problem, when its solution set is related to a solution set of an inverse strongly monotone mapping. Consequently, an iterative algorithm for finding such a solution is constructed, and convergent theorem of the such algorithm is proved. It is worth pointing out that, since...

chapter

A Strong Convergence Theorem for Nonexpansive Mappings and Monotone Mappings

Junhong Wang, Yongfu Su

2009 International Joint Conference on Computational Sciences and Optimization > 2 > 797 - 801

2009 International Joint Conference on Computational Sciences and Optimization, CSO

The purpose of this paper is to propose a hybrid method for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a variational inequality problem for an inverse strongly monotone mapping. We obtain a strong convergence theorem. The results of this paper improved and extended the results of W. Takahashi and Toyoda [W. Takahashi, Toyoda W, Weak convergence...

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Keywords

INVERSE STRONGLY MONOTONE MAPPING (15)
FIXED POINT (6)
VARIATIONAL INEQUALITY (4)
VARIATIONAL INEQUALITY PROBLEM (4)
EQUILIBRIUM PROBLEM (3)
GENERALIZED MIXED EQUILIBRIUM PROBLEM (3)
MONOTONE MAPPING (3)
NONEXPANSIVE MAPPING (3)
STRICTLY PSEUDOCONTRACTIVE MAPPING (3)
GENERAL VARIATIONAL INEQUALITY PROBLEM (2)
REGULARIZATION (2)
2-GENERALIZED HYBRID MAPPING (1)
APPROXIMATION THEORY (1)
COMMON FIXED POINT (1)
COMPOSITE RELAXED EXTRAGRADIENT-LIKE METHOD (1)
COMPOSITE VISCOSITY ITERATIVE ALGORITHM (1)
CONVERGENCE (1)
CONVERGENCE OF NUMERICAL METHODS (1)
CONVERGENCE THEOREM (1)
COUNTABLE FAMILY OF NONEXPANSIVE MAPPINGS (1)
COUNTABLE FAMILY OF UNIFORMLY K-STRICTLY PSEUDOCONTRACTIVE MAPPINGS (1)
DATA MINING (1)
GENERAL MIXED EQUILIBRIUM (1)
GENERALIZED MIXED EQUILIBRIUM PROBLEMS (1)
GOLD (1)
HEMICONTINUOUS MAPPING (1)
HIERARCHICAL VARIATIONAL INEQUALITY (1)
HILBERT SPACE (1)
HYBRID METHOD (1)
INERTIAL PROXIMAL POINT ALGORITHM (1)
INVERSE STRONGLY-MONOTONE MAPPING (1)
MAXIMAL MONOTONE MAPPING (1)
MAXIMAL MONOTONE OPERATOR (1)
MIXED EQUILIBRIUM PROBLEM (1)
MORE GENERAL SYSTEM OF VARIATIONAL INEQUALITIES (1)
NONEXPANSIVE SEMIGROUP (1)
NONSPREADING MAPPING (1)
OPTIMIZATION (1)
RELATIVELY WEAK NONEXPANSIVE MAPPING (1)
RESOLVENT (1)
SET THEORY (1)
SHRINKING PROJECTION METHOD (1)
STRICT PSEUDO-CONTRACTION (1)
STRONG CONVERGENCE (1)
STRONGLY POSITIVE BOUNDED LINEAR OPERATOR (1)
SYSTEM OF GENERALIZED EQUILIBRIUM PROBLEMS (1)
TV (1)
VARIATIONAL INEQUALITIES (1)
VARIATIONAL TECHNIQUES (1)
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