Delta-convergence and sequential delta-compactness on Banach spheres

Authors

Yasunori Kimura Department of Information Science, Faculty of Science, Toho University, Miyama, Funabashi, Chiba 274-8510, Japan
Shuta Shuta Department of Information Science, Graduate School of Science, Toho University, Miyama, Funabashi, Chiba 274-8510, Japan

Keywords:

Banach sphere, delta-convergence, fixed point approximation

Abstract

In this paper, we consider notions of convergence weaker than one with a norm. We call them delta-convergence and dual-delta-convergence, and we investigate the sequential closedness and sequential compactness. As an application, we prove a fixed point approximation theorem with the Krasnosel'skii type iterative scheme.

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