A New Iterative Algorithm for the Set of Fixed-Point Problems of Nonexpansive Mappings and the Set of Equilibrium Problem and Variational Inequality Problem | Zendy

Atid Kangtunyakarn | Zendy

Open Access

A New Iterative Algorithm for the Set of Fixed-Point Problems of Nonexpansive Mappings and the Set of Equilibrium Problem and Variational Inequality Problem

Author(s) -

Atid Kangtunyakarn

Publication year - 2011

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2011/562689

Subject(s) - variational inequality , mathematics , convergence (economics) , fixed point , set (abstract data type) , element (criminal law) , solution set , scheme (mathematics) , point (geometry) , iterative method , maximal element , discrete mathematics , mathematical optimization , mathematical analysis , geometry , computer science , political science , law , economics , programming language , economic growth

We introduce a new iterative scheme and a new mapping generated by infinite family of nonexpansive mappings and infinite real number. By using both of these ideas, we obtain strong convergence theorem for finding a common element of the set of solution of equilibrium problem and the set of variational inequality and the set of fixed-point problems of infinite family of nonexpansive mappings. Moreover, we apply our main result to obtain strong convergence theorems for finding a common element of the set of solution of equilibrium problem and the set of variational inequality and the set of common fixed point of pseudocontractive mappings

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