### 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 l_{p} 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 L_{p} 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 L_{p} (or l_{p}), p > 2, has not been proved.

Original language | English |
---|---|

Pages (from-to) | 701-703 |

Number of pages | 3 |

Journal | Indian Journal of Pure and Applied Mathematics |

Volume | 34 |

Issue number | 5 |

Publication status | Published - May 1 2003 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

*Indian Journal of Pure and Applied Mathematics*,

*34*(5), 701-703.

}

*Indian Journal of Pure and Applied Mathematics*, vol. 34, no. 5, pp. 701-703.

**A note on two recent papers on approximation of fixed points.** / Chidume, C. E.; Zegeye, H.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A note on two recent papers on approximation of fixed points

AU - Chidume, C. E.

AU - Zegeye, H.

PY - 2003/5/1

Y1 - 2003/5/1

N2 - 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 (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.

AB - 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 (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.

UR - http://www.scopus.com/inward/record.url?scp=26844572943&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=26844572943&partnerID=8YFLogxK

M3 - Article

VL - 34

SP - 701

EP - 703

JO - Indian Journal of Pure and Applied Mathematics

JF - Indian Journal of Pure and Applied Mathematics

SN - 0019-5588

IS - 5

ER -