Algorithms for Solving System of Extended General Variational Inclusions and Fixed Points Problems | Zendy

Narin Petrot | Zendy; Javad Balooee | Zendy

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Algorithms for Solving System of Extended General Variational Inclusions and Fixed Points Problems

Author(s) -

Narin Petrot,

Javad Balooee

Publication year - 2012

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 - 10.1155/2012/569592

Subject(s) - mathematics , uniqueness , fixed point , equivalence (formal languages) , nonlinear system , fixed point theorem , convergence (economics) , resolvent , iterative method , variational inequality , mathematical analysis , mathematical optimization , pure mathematics , physics , quantum mechanics , economics , economic growth

We introduce a new system of extended general nonlinear variational inclusions with different nonlinear operators and establish the equivalence between the aforesaid system and the fixed point problem. By using this equivalent formulation, we prove the existence and uniqueness theorem for solution of the system of extended general nonlinear variational inclusions. We suggest and analyze a new resolvent iterative algorithm to approximate the unique solution of the system of extended general nonlinear variational inclusions which is a fixed point of a nearly uniformly Lipschitzian mapping. Subsequently, the convergence analysis of the proposed iterative algorithm under some suitable conditions is considered. Furthermore, some related works to our main problem are pointed out and discussed

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