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Jul 27, 2011Download as PPTX, PDF0 likes154 views

This document discusses weak and strong convergence to common fixed points of a countable family of multivalued mappings in Banach spaces. It examines the convergence properties of iterative algorithms that generate sequences with the goal of finding common fixed points for a family of mappings defined on a Banach space. The authors are from Chiang Mai University in Thailand and Gyeongsang National University in Korea.

Weak and strong convergence to common fixed points of a countable family of multivalued mappings in Banach spacesWatctarapornCholamjiak, Chiang Mai University, ThailandSuthepSuantai, Chiang Mai University, ThailandYeol Je Cho, Gyeongsang National University, Korea

This document summarizes a research article that introduces a new iterative scheme for finding a common element of the set of common fixed points of a countable family of nonexpansive multivalued maps, the set of solutions to a variational inequality problem, and the set of solutions to an equilibrium problem in a Hilbert space. The authors provide background on existing methods for related problems and note the need to construct an iteration process that can solve this more general problem. They then introduce their new monotone hybrid iterative scheme and state that they will establish strong convergence theorems for their proposed iteration method.

Puy chosuantai2Watcharaporn Cholamjiak

This document presents a modified Mann iteration method for finding common fixed points of a countable family of multivalued mappings in Banach spaces. It introduces using the best approximation operator PTn to define the iteration (1.2), where xn+1 is defined as a convex combination of the previous iterate xn and an element in PTn xn . The paper aims to establish weak and strong convergence theorems for this iterative method to find a common fixed point for a countable family of nonexpansive multivalued mappings. It provides relevant background on fixed points, nonexpansive mappings, and best approximation operators in Banach and Hilbert spaces.

W.cholamjiak2Watcharaporn Cholamjiak

W.cholamjiakWatcharaporn Cholamjiak

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W.cholamjiakWatcharaporn Cholamjiak

This document defines concepts related to multivalued mappings and fixed point theory in Banach spaces. It defines multivalued nonexpansive mappings, the Hausdorff metric, the best approximation operator, and conditions like the SC-condition. It then presents theorems on the weak and strong convergence of the modified Mann iteration sequence to common fixed points when applied to families of multivalued mappings satisfying certain conditions, like the SC-condition. The document acknowledges support from universities and research centers.

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