Existence and approximation of fixed points of nonlinear mappings in spaces with weak uniform normal structure

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• 作者：D.R. Sahu ; Zeqing Liu ; Shin Min Kang
• 关键词：Asymptotically pseudocontractive mapping ; Asymptotically nonexpansive mapping ; Nearly nonexpansive mapping ; Sunny nonexpansive retraction ; Weak uniform normal structure
• 刊名：Computers and Mathematics with Applications
• 出版年：2012
• 出版时间：August, 2012
• 年：2012
• 卷：64
• 期：4
• 页码：672-685
• 全文大小：272 K

文摘

It is shown that in a Banach space with weak uniform normal structure, every demicontinuous asymptotically regular nearly Lipschitzian self-mapping with defined on a weakly compact convex subset of satisfies the -fixed point property. We show that if has a uniformly Gateaux differentiable norm, then the set of fixed points of every asymptotically pseudocontractive nearly nonexpansive mapping is nonempty and a sunny nonexpansive retract of . Further, we study the approximation of fixed points of by Halpern type iteration process: , where and is a sequence in (0,1) satisfying appropriate conditions. Our results improve several known existence and convergence fixed point theorems in general Banach spaces for a wider class of nonlinear mappings which are not necessarily Lipschitzian.