Erratum to “Mann and Ishikawa iterative processes for multivalued mappings in Banach spaces” [Comput. Math. Appl. 54 (2007) 872–877]

Fixed points of multivalued quasi-nonexpansive mappings using a faster iterative process

“…Based on the above lemma, Song and Wang [14] modified the iterative process due to Panyanak [8] and improved the results presented there. They used (1.2) but with a n ∈ [0, 1]; b n ∈ [0, 1] with lim n→∞ b n = 0 and…”

“…It is to be noted that Song and Wang [14] needed the condition T p = {p} in order to prove their Theorem 1. Actually, Panyanak [8] proved some results using Ishikawa type iterative process without this condition.…”

“…Actually, Panyanak [8] proved some results using Ishikawa type iterative process without this condition. Song and Wang [14] showed that without this condition his process was not well-defined. They reconstructed the process using the condition T p = {p} which made it well-defined.…”

Strong and weak convergence of an iterative process for a finite family of multivalued mappings satisfying the condition (C)

“…They further revised the gap and also gave the a¢ rmative answer to Panyanak's open question. Shazad and Zegeye [16] extended and improved results already appeared in the papers [12,13,15].…”

“…They also claimed that the …xed point q may be di¤erent from p. Panyanak [12] extended result of Sastry and Babu [13] to uniformly convex Banach spaces. After, Song and Wang [15] noted that there was a gap in the proof of the main result in [12]. They further revised the gap and also gave the a¢ rmative answer to Panyanak's open question.…”