tailieunhanh - Báo cáo hóa học: " COMPARISON OF FASTNESS OF THE CONVERGENCE AMONG KRASNOSELSKIJ, MANN, AND ISHIKAWA ITERATIONS IN ARBITRARY REAL BANACH SPACES"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: COMPARISON OF FASTNESS OF THE CONVERGENCE AMONG KRASNOSELSKIJ, MANN, AND ISHIKAWA ITERATIONS IN ARBITRARY REAL BANACH SPACES | COMPARISON OF FASTNESS OF THE CONVERGENCE AMONG KRASNOSELSKIJ MANN AND ISHIKAWA ITERATIONS IN ARBITRARY REAL BANACH SPACES G. V. R. BABU AND K. N. V. V. VARA PRASAD Received 25 April 2006 Accepted 4 September 2006 Let E be an arbitrary real Banach space and K a nonempty closed convex not necessarily bounded subset of E. If T is a member of the class of Lipschitz strongly pseudocontrac-tive maps with Lipschitz constant L 1 then it is shown that to each Mann iteration there is a Krasnosleskij iteration which converges faster than the Mann iteration. It is also shown that the Mann iteration converges faster than the Ishikawa iteration to the fixed point of T. Copyright 2006 G. V. R. Babu and K. N. V. V. Vara Prasad. 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. 1. Introduction By approximation of fixed points of certain classes of operators which satisfy weak contractive-type conditions that do not guarantee the convergence of Picard iteration 2 Example page 76 certain mean value fixed point iterations namely Krasnoselskij Mann and Ishikawa iteration methods are useful to approximate fixed points. For more details on these iterations and further literature see Berinde 3 . When for a certain class of mappings two or more fixed point iteration procedures can be used to approximate their fixed points it is of theoretical and practical importance to compare the rate of convergence of these iterations and to find out if possible which one of them converges faster. Recent works in this direction are 1 4 5 . Verma 9 approximated fixed points of Lipschitzian and generalized pseudocontrac-tive operators in Hilbert spaces by both Krasnoselskij and Mann iteration and Berinde 4 established that for any Mann iteration there is a Krasnoselskij iteration which converges faster to the fixed point of such an operator.

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