Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010, Article ID 914702, 12 pages doi:10.1155/2010/914702 Research Article Convergence Theorems of Modified Ishikawa Iterative Scheme for Two Nonexpansive Semigroups Kriengsak Wattanawitoon and Poom Kumam Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangmod, Thrungkru, Bangkok 10140, Thailand Correspondence should be addressed to Poom Kumam, poom.kum@kmutt.ac.th Received 26 September 2009; Accepted 24 November 2009 Academic Editor: Tomonari Suzuki Copyright q 2010 K. Wattanawitoon and P. Kumam. 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. We prove convergence theorems of modified Ishikawa iterative sequence for two nonexpansive semigroups in Hilbert spaces by the two hybrid methods. Our results improve and extend the corresponding results announced by Saejung 2008 and some others. 1. Introduction Let C be a subset of real Hilbert spaces H with the inner product 〈·, ·〉 and the norm ‖·‖. T : C → C is called a nonexpansive mapping if   Tx - Ty   ≤   x - y   ∀x, y ∈ C. 1.1 We denote by FT  the set of fixed points of T , that is, FT  {x ∈ C : x  Tx}. Let {T t : t ≥ 0} be a family of mappings from a subset C of H into itself. We call it a nonexpansive semigroup on C if the following conditions are satisfied: i T 0x  x for all x ∈ C; ii T s  t T sT t for all s, t ≥ 0; iii for each x ∈ C the mapping t → T tx is continuous; iv ‖T tx - T ty‖≤‖x - y‖ for all x, y ∈ C and t ≥ 0.