Convergence theorems for asymptotically quasi-nonexpansive sequences with applications

Abstract

In this paper, $\mathrm{△}$-convergence and strong convergence theorems for asymptotically quasi-nonexpansive sequences in Hadamard spaces are derived. The results extend and improve recent results in the literature and some of them seem new even in Hilbert spaces. Applications to convex minimization and common fixed point problems are discussed.

Keywords:

• Asymptotically quasi-nonexpansive sequence
• convex minimization
• fixed point
• Hadamard space
• Halpern type iteration
• proximal point method
• strong convergence
• $\mathrm{△}$-convergence

2010 Mathematics Subject Classifications:

• 47H09
• 47H10
• 90C25
• 90C30

Acknowledgments

The authors thank the referee for comments and suggestions on the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research of the first author is supported by the Thailand Research Fund and Khon Kaen University under Grant RSA6280002. The research of the second author is supported by the Thailand Research Fund under Grant MRG6080243.