<abstract xmlns="http://www.w3.org/1999/xhtml"><p> In this paper, the problem of modifying Halpern iteration for approximating a common fixed point of a family of asymptotically quasi- ∅-nonexpansive mappings is considered. Strong convergence theorems are established in a uniformly smooth and strictly convex Banach space which also enjoys the Kadec-Klee property. The results presented in this paper mainly improve the corresponding results announced in [Y.J. Cho, X. Qin, S.M. Kang, Strong convergence of the modified Halpern- type iterative algorithms in Banach spaces, An. Stiint. Univ. Ovidius Constanta Ser. Mat. 17 (2009) 51-68]. </p></abstract>

In this paper, the problem of modifying Halpern iteration for approximating a common fixed point of a family of asymptotically quasi- ∅-nonexpansive mappings is considered. Strong convergence theorems are established in a uniformly smooth and strictly convex Banach space which also enjoys the Kadec-Klee property. The results presented in this paper mainly improve the corresponding results announced in [Y.J. Cho, X. Qin, S.M. Kang, Strong convergence of the modified Halpern- type iterative algorithms in Banach spaces, An. Stiint. Univ. Ovidius Constanta Ser. Mat. 17 (2009) 51-68].

Strong convergence of a modified Halpern-type iteration for asymptotically quasi-∅-nonexpansive mappings

School of Business and Administration, Henan University, Kaifeng 475000, China

School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan 316004, China

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

In this paper, the problem of modifying Halpern iteration for approximating a common fixed point of a family of asymptotically quasi- ∅-nonexpansive mappings...

Strong convergence of a modified Halpern-type iteration for asymptotically quasi-∅-nonexpansive mappings

Published Online: Jul 30, 2013

Page range: 261 - 276

DOI: https://doi.org/10.2478/auom-2013-0017

This content is open access.