Convergence theorems for finite family of a general class of multi-valued strictly pseudo-contractive mappings

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• 作者：Charles E Chidume ; Mmaduabuchi E Okpala…
• 关键词：generalized k ; strictly pseudo ; contractive multi ; valued mappings ; multi ; valued maps
• 刊名：Fixed Point Theory and Applications
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：2015
• 期：1
• 全文大小：1,414 KB
• 刊物主题：Analysis; Mathematics, general; Applications of Mathematics; Differential Geometry; Topology; Mathematical and Computational Biology;
• 出版者：Springer International Publishing
• ISSN：1687-1812

文摘

Let H be a real Hilbert space, K a nonempty subset of H, and \(T:K\rightarrow \mathit{CB}(K)\) a multi-valued mapping. Then T is called a generalized k-strictly pseudo-contractive multi-valued mapping if there exists \(k\in[0,1)\) such that, for all \(x,y\in D(T)\), we have \(D^{2}(Tx,Ty)\leq\|x-y\|^{2}+kD^{2}(Ax,Ay)\), where \(A:=I-T\), and I is the identity operator on K. A Krasnoselskii-type algorithm is constructed and proved to be an approximate fixed point sequence for a common fixed point of a finite family of this class of maps. Furthermore, assuming existence, strong convergence to a common fixed point of the family is proved under appropriate additional assumptions.