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Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011, Article ID 187439, 3

Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011, Article ID 187439, 3 pages doi:10.1155/2011/187439 Erratum Erratum to “Iterative Methods for Variational Inequalities over the Intersection of the Fixed Points Set of a Nonexpansive Semigroup in Banach Spaces” Issa Mohamadi Department of Mathematics, Islamic Azad University, Sanandaj Branch, Sanandaj 418, Kurdistan, Iran Correspondence should be addressed to Issa Mohamadi, imohamadi@iausdj.ac.ir Received 22 February 2011; Accepted 24 February 2011 Copyright q 2011 Issa Mohamadi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly. | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011 Article ID 187439 3 pages doi 10.1155 2011 187439 Erratum Erratum to Iterative Methods for Variational Inequalities over the Intersection of the Fixed Points Set of a Nonexpansive Semigroup in Banach Spaces Issa Mohamadi Department of Mathematics Islamic Azad University Sanandaj Branch Sanandaj 418 Kurdistan Iran Correspondence should be addressed to Issa Mohamadi imohamadi@iausdj.ac.ir Received 22 February 2011 Accepted 24 February 2011 Copyright 2011 Issa Mohamadi. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. In my recent published paper 1 to prove Lemmas 3.1 and 5.1 an inequality involving the single-valued normalized duality mapping J from X into 2X has been used that generally turns out there is no certainty about its accuracy. In this erratum we fix this problem by imposing additional assumptions in a way that the proofs of the main theorems do not change. We recall that a uniformly smooth Banach space X is q-uniformly smooth for q 1 if and only if there exists a constant pq 0 such that for all x y e X x y q xhq q x q 2 y J x 2pq y q 1 for more details see 2 . Therefore if q 2 then there exists a constant ộ 0 such that x yII2 x 2 2 y J x 2 y 2. 2 It is well known that Hilbert spaces Ip and Lp for p 2 are 2-uniformly smooth. 2 Fixed Point Theory and Applications Throughout the paper we suggest to impose one of the following conditions a the Banach space X is 2-uniformly smooth b there exists a constant p e R for which J satisfies the following inequality w x ý py J x p y 2 3 for all x y e X. Remark 1.1. If J is p-Lipschitzian then J satisfies 3 and is norm-to-norm uniformly continues that suffices to guarantee that X is 2-uniformly smooth. For more results concerning P-Lipschitzian normalized duality mapping see 3 . .