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2007•Journal of Mathematical Research and ExpositionRequires access

An Iterative Algorithm of Common Zero Points for Two Maximal Monotone Operators in Banach Space

Wei Li, Zhou Hai-yun

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Abstract

Let E be a real smooth and uniformly convex Banach space with E~* being its duality space. Let A,B■E×E~* be maximal monotone operators with A~(-1)0∩B~(-1)0≠■.A new iterative algorithm is introduced which is proved to be weakly convergent to common zero points of maximal monotone operators A and B by using the techniques of Lyapunov functional and generalized projection operator, etc.

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Let E be a real smooth and uniformly convex Banach space with E~* being its duality space. Let A,B■E×E~* be maximal monotone operators with A~(-1)0∩B~(-1)0≠■.A new iterative algorithm is introduced which is proved to be weakly convergent to common zero points of maximal monotone operators A and B by using the techniques of Lyapunov functional and generalized projection operator, etc.

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Available abstract

Let E be a real smooth and uniformly convex Banach space with E~* being its duality space. Let A,B■E×E~* be maximal monotone operators with A~(-1)0∩B~(-1)0≠■.A new iterative algorithm is introduced which is proved to be weakly convergent to common zero points of maximal monotone operators A and B by using the techniques of Lyapunov functional and generalized projection operator, etc.

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

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