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2007•Journal of Mathematical Research and ExpositionRequires access

A Theorem of Iterative Approximation of Zero Point for Maximal Monotone Operator in Banach Space

Zhou Hai-yun

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Abstract

Let E be a real smooth and uniformly convex Banach space, and E its duality space. Let A ■ E×E be a maximal monotone operator with A-10≠■ . A new iterative scheme is introduced which is proved to be weakly convergent to zero point of maximal monotone operator A by using the techniques of Lyapunov functional, Qr operator and generalized projection operator, etc.

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What this paper is about

Let E be a real smooth and uniformly convex Banach space, and E its duality space. Let A ■ E×E be a maximal monotone operator with A-10≠■ . A new iterative scheme is introduced which is proved to be weakly convergent to zero point of maximal monotone operator A by using the techniques of Lyapunov functional, Qr operator and generalized projection operator, etc.

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Available abstract

Let E be a real smooth and uniformly convex Banach space, and E its duality space. Let A ■ E×E be a maximal monotone operator with A-10≠■ . A new iterative scheme is introduced which is proved to be weakly convergent to zero point of maximal monotone operator A by using the techniques of Lyapunov functional, Qr operator and generalized projection operator, etc.

Key concepts: Mathematics, Pseudo-monotone operator, Banach space, Monotone polygon, Finite-rank operator, Strongly monotone, Approximation property, Compact operator

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