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2010•Journal of Hebei Normal UniversityRequires access

The Iterative Construction of Common Zero Points for a Family of Maximal Monotone Operators in Banach Space

Li Wei

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Abstract

Let E be a real smooth and uniformly convex Banach space with E* its duality space.Let AiE×E*,i=1,2,…,m be maximal monotone operators and there exists i0∈{1,2,…,m} such that φ≠A-1i0(0)∩mi=1i≠i0 A-1i(0).A new accurate iterative algorithm and a new proximate algorithm are introduced which are proved to be strongly convergent to common zero points of maximal monotone operators{Ai}mi=1 by using the techniques of Lyapunov functional.

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Let E be a real smooth and uniformly convex Banach space with E* its duality space.Let AiE×E*,i=1,2,…,m be maximal monotone operators and there exists i0∈{1,2,…,m} such that φ≠A-1i0(0)∩mi=1i≠i0 A-1i(0).A new accurate iterative algorithm and a new proximate algorithm are introduced which are proved to be strongly convergent to common zero points of maximal monotone operators{Ai}mi=1 by using the techniques of Lyapunov functional.

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Available abstract

Let E be a real smooth and uniformly convex Banach space with E* its duality space.Let AiE×E*,i=1,2,…,m be maximal monotone operators and there exists i0∈{1,2,…,m} such that φ≠A-1i0(0)∩mi=1i≠i0 A-1i(0).A new accurate iterative algorithm and a new proximate algorithm are introduced which are proved to be strongly convergent to common zero points of maximal monotone operators{Ai}mi=1 by using the techniques of Lyapunov functional.

Key concepts: Mathematics, Monotone polygon, Banach space, Zero (linguistics), Pseudo-monotone operator, Regular polygon, Duality (order theory), Approximation property

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