A note on two recent papers on approximation of fixed points

C. E. Chidume, H. Zegeye

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Recently, Sharma and Sahu (Indian J. pure Appl. Math. 31 (2000), 185-96) claimed to have improved a theorem of Schu (J. Math. Anal. Appl. 158 (1991), 407-13) from Hilbert spaces to Banach spaces satisfying Opial's condition. These spaces include lp spaces, 1 <p < ∞, but exclude L p (1 < p < ∞, p ≠ 2). In a subsequent paper, the two authors, in collaboration with Bounias claimed to have extended this result to Banach spaces with property (U, λ, m+ 1, m), λ ε IR, m ε IN. These spaces include the Lp spaces, p ≥ 2. It is shown in this note that these claims are false. The proofs of all the results in these two papers of Sharma et al. are valid in Hubert spaces. The validity of the theorems in Lp (or lp), p > 2, has not been proved.

Original languageEnglish
Pages (from-to)701-703
Number of pages3
JournalIndian Journal of Pure and Applied Mathematics
Volume34
Issue number5
Publication statusPublished - May 1 2003

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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