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 Sudo 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 compactness. As an application, we prove a fixed point approximation theorem with the Krasnosel'skii type iterative scheme.

References

[1] M. Bacak, Convex analysis and optimization in Hadamard spaces, De Gruyter, Berlin, 2014.

[2] R. Esp´ınola and A. Fern´andez-Le´on, CAT(k)-spaces, weak convergence and fixed points, J. Math. Anal. Appl. 353 (2009), 410–427.

[3] T. Ibaraki and Y. Kimura, Approximation of a fixed point of generalized firmly nonexpansive mappings with nonsummable errors, Journal of Nonlinear and Convex Analysis 2 (2016), 301–310.

[4] Y. Kimura and S. Sudo, Fixed point theory on Banach spheres, Topol. Methods Nonlinear Anal. 64 (2024), 655–673.

[5] W. A. Kirk and B. Panyanak, A concept of convergence in geodesic spaces, Nonlinear Anal. 68 (2008), 3689–3696.

[6] F. Kohsaka, Fixed points of metrically nonspreading mappings in Hadamard spaces, Appl. Anal. Optim. 3 (2019), 213–230.

[7] F. Kohsaka and W. Takahashi, Fixed point theorems for a class of nonlinear mappings related to maximal monotone operators in Banach spaces, Arch. Math. (Basel) 91 (2008), 166–177.

[8] M. A. Krasnosel’skii, Two remarks on the method of successive approximations, Uspehi Mat. Nauk 10 (1955), 123–127.

[9] T. C. Lim, Remarks on some fixed point theorems, Proc. Amer. Math. Soc. 60 (1976), 179–182.

[10] W. Takahashi, Nonlinear functional analysis, Yokohama Publishers, Yokohama, 2000.

[11]W. Takahashi, Introduction to nonlinear and convex analysis, Yokohama Publishers, Yokohama, 2009.

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Published

2025-03-30

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Section

Articles