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2010•Lobachevskii Journal of MathematicsRequires access

Weak and strong convergence theorems for a finite family of non-lipschitzian mappings in Banach spaces

S. Imnang, Suthep Suantai

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Abstract

The purpose of this paper is to study a new iterative scheme for a finite family of asymptotically nonexpansive mappings in the intermediate sense. Weak and strong convergence theorems for the iterative scheme in a uniformly convex Banach space are established under some conditions which are weaker than demicompactness or completely continuous. Our results improve and generalize the recent known results in the literature.

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What this paper is about

The purpose of this paper is to study a new iterative scheme for a finite family of asymptotically nonexpansive mappings in the intermediate sense. Weak and strong convergence theorems for the iterative scheme in a uniformly convex Banach space are established under some conditions which are weaker than demicompactness or completely continuous. Our results improve and generalize the recent known results in the literature.

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Available abstract

The purpose of this paper is to study a new iterative scheme for a finite family of asymptotically nonexpansive mappings in the intermediate sense. Weak and strong convergence theorems for the iterative scheme in a uniformly convex Banach space are established under some conditions which are weaker than demicompactness or completely continuous. Our results improve and generalize the recent known results in the literature.

Key concepts: Mathematics, Banach space, Scheme (mathematics), Regular polygon, Convergence (economics), Uniformly convex space, Pure mathematics, Weak convergence

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