# Hybrid iterative methods for two asymptotically nonexpansive semigroups in Hilbert spaces

Volume 12, Issue 10, pp 621--633
Publication Date: May 30, 2019 Submission Date: July 18, 2018 Revision Date: April 23, 2019 Accteptance Date: May 10, 2019
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### Authors

Issara Inchan - Department of Mathematics, Uttaradit Rajabhat University, Uttaradit, Thailand.

### Abstract

The main objective of this work is to modify two hybrid projection algorithm. First, we prove the strongly convergence to common fixed points of a sequence $\{x_{n}\}$ generated by the hybrid projection algorithm of two asymptotically nonexpansive mappings, second, we prove the strongly convergence of a sequence $\{x_{n}\}$ generated by the hybrid projection algorithm of two asymptotically nonexpansive semigroups. Our main results extend and improve the results of Dong et al. [Q.-L. Dong, S. N. He, Y. J. Cho, Fixed Point Theory Appl., $\textbf{2015}$ (2015), 12 pages].

### Keywords

• Asymptotically nonexpansive mappings
• asymptotically nonexpansive semigroup
• fixed point

•  46C05
•  47D03
•  47H09
•  47H10
•  47H20

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