Convergence theorems of fixed points for <textbox>κtextbox>-strict pseudo-contractions in Hilbert spaces

详细信息	查看全文 | 推荐本文 |

• 作者：Haiyun Zhou
• 关键词：style="text-decoration ; none ; color ; black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V0Y-4NWCGSN-7&_mathId=mml24&_user=1067359&_cdi=5659&_rdoc=7&_acct=C000050221&_version=1&_userid=10&md5=813d75916ab9f2d0b089282eed7b871f" ti
• 刊名：Nonlinear Analysis
• 出版年：2008
• 期刊代码：43_0362546x
• 类别：mt
• 出版时间：15 July 2008
• 卷：69
• 期：2
• 页码：456-462
• 文件大小：228 K

摘要

Let style="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V0Y-4NWCGSN-7&_mathId=mml2&_user=1067359&_cdi=5659&_rdoc=7&_acct=C000050221&_version=1&_userid=10&md5=9073b60498c38b2a3bb029dc094eefad" title="Click to view the MathML source" alt="Click to view the MathML source">C be a closed convex subset of a real Hilbert space style="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V0Y-4NWCGSN-7&_mathId=mml3&_user=1067359&_cdi=5659&_rdoc=7&_acct=C000050221&_version=1&_userid=10&md5=767eb2bf328bb32f6a1d69d9aca87d16" title="Click to view the MathML source" alt="Click to view the MathML source">H and assume that style="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V0Y-4NWCGSN-7&_mathId=mml4&_user=1067359&_cdi=5659&_rdoc=7&_acct=C000050221&_version=1&_userid=10&md5=53b311f0e5c0f51198c0e564ea594bf5" title="Click to view the MathML source" alt="Click to view the MathML source">T:C→H is a style="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V0Y-4NWCGSN-7&_mathId=mml5&_user=1067359&_cdi=5659&_rdoc=7&_acct=C000050221&_version=1&_userid=10&md5=45993647185f393d02ff9c1ed318e067" title="Click to view the MathML source" alt="Click to view the MathML source">κ-strict pseudo-contraction such that style="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V0Y-4NWCGSN-7&_mathId=mml6&_user=1067359&_cdi=5659&_rdoc=7&_acct=C000050221&_version=1&_userid=10&md5=a5d1ef0836242dc6417dc68bb65d5f9c" title="Click to view the MathML source" alt="Click to view the MathML source">F(T)={xC:x=Tx}≠0/. Consider the normal Mann’s iterative algorithm given by

where style="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V0Y-4NWCGSN-7&_mathId=mml8&_user=1067359&_cdi=5659&_rdoc=7&_acct=C000050221&_version=1&_userid=10&md5=acf77e3b116431cce31b1174fc47ccfa" title="Click to view the MathML source" alt="Click to view the MathML source">S:C→H is defined by style="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V0Y-4NWCGSN-7&_mathId=mml9&_user=1067359&_cdi=5659&_rdoc=7&_acct=C000050221&_version=1&_userid=10&md5=e915dfa5791d42f53892ec47b3af0c72" title="Click to view the MathML source" alt="Click to view the MathML source">Sx=κx+(1−κ)Tx, style="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V0Y-4NWCGSN-7&_mathId=mml10&_user=1067359&_cdi=5659&_rdoc=7&_acct=C000050221&_version=1&_userid=10&md5=bccfb0172f29f13ec4050cbc852ab446" title="Click to view the MathML source" alt="Click to view the MathML source">P_C is the metric projection of style="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V0Y-4NWCGSN-7&_mathId=mml11&_user=1067359&_cdi=5659&_rdoc=7&_acct=C000050221&_version=1&_userid=10&md5=4a4526d8c57b7c47621ae1e530ba4b46" title="Click to view the MathML source" alt="Click to view the MathML source">H onto style="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V0Y-4NWCGSN-7&_mathId=mml12&_user=1067359&_cdi=5659&_rdoc=7&_acct=C000050221&_version=1&_userid=10&md5=7f27e9075e2f48fe618c843a971ef299" title="Click to view the MathML source" alt="Click to view the MathML source">C and for all style="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V0Y-4NWCGSN-7&_mathId=mml14&_user=1067359&_cdi=5659&_rdoc=7&_acct=C000050221&_version=1&_userid=10&md5=e0f71ca2a6351c837e8fc3bca7e4b8fc" title="Click to view the MathML source" alt="Click to view the MathML source">n≥1. It is proved that if the control parameter sequence style="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V0Y-4NWCGSN-7&_mathId=mml15&_user=1067359&_cdi=5659&_rdoc=7&_acct=C000050221&_version=1&_userid=10&md5=9f74ffc6e13c88a4b68b1cac5d26127e" title="Click to view the MathML source" alt="Click to view the MathML source">{_n} is chosen so that style="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V0Y-4NWCGSN-7&_mathId=mml16&_user=1067359&_cdi=5659&_rdoc=7&_acct=C000050221&_version=1&_userid=10&md5=d5f38117b7fa713c3d0adbf297760d42" title="Click to view the MathML source" alt="Click to view the MathML source">κ≤_n≤1 and , then style="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V0Y-4NWCGSN-7&_mathId=mml18&_user=1067359&_cdi=5659&_rdoc=7&_acct=C000050221&_version=1&_userid=10&md5=0dc881e2197766fe117677e89633a39a" title="Click to view the MathML source" alt="Click to view the MathML source">{x_n} converges weakly to a fixed point of style="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V0Y-4NWCGSN-7&_mathId=mml19&_user=1067359&_cdi=5659&_rdoc=7&_acct=C000050221&_version=1&_userid=10&md5=15c6411e9baa35ac005d402ae4a9fa56" title="Click to view the MathML source" alt="Click to view the MathML source">T. In order to get a strong convergence theorem, we modify the normal Mann’s iterative algorithm by using a suitable convex combination of a fixed vector and a sequence in style="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V0Y-4NWCGSN-7&_mathId=mml20&_user=1067359&_cdi=5659&_rdoc=7&_acct=C000050221&_version=1&_userid=10&md5=5a0be91dce5cf767ba6bac73ec5f44f0" title="Click to view the MathML source" alt="Click to view the MathML source">C. The results presented in this article respectively improve and extend the recent results of Marino and Xu [G. Marino, H.K. Xu, Weak and strong convergence theorems for style="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V0Y-4NWCGSN-7&_mathId=mml21&_user=1067359&_cdi=5659&_rdoc=7&_acct=C000050221&_version=1&_userid=10&md5=ca3eb30ff74834d8a410b843ad47f2d6" title="Click to view the MathML source" alt="Click to view the MathML source">κ-strict pseudo-contractions in Hilbert spaces, J. Math. Anal. Appl. 329 (2007) 336–349] from style="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V0Y-4NWCGSN-7&_mathId=mml22&_user=1067359&_cdi=5659&_rdoc=7&_acct=C000050221&_version=1&_userid=10&md5=dcaabfd3ad2195dbf460f9655d9b4fa8" title="Click to view the MathML source" alt="Click to view the MathML source">κ-strictly pseudo-contractive self-mappings to nonself-mappings and of Kim and Xu [T.H. Kim, H.K. Xu, Strong convergence of modified Mann iterations, Nonlinear Anal. 61 (2005) 51–60] from nonexpansive mappings to style="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V0Y-4NWCGSN-7&_mathId=mml23&_user=1067359&_cdi=5659&_rdoc=7&_acct=C000050221&_version=1&_userid=10&md5=6ce11a3ac06100dcad3d2aa1df6dc87a" title="Click to view the MathML source" alt="Click to view the MathML source">κ-strict pseudo-contractions.