
Journal of Convex Analysis 22 (2015), No. 1, 081100 Copyright Heldermann Verlag 2015 Weak Convergence Theorems for Semigroups of Not Necessarily Continuous Mappings in Banach Spaces Saud M. Alsulami Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia alsulami@kau.edu.sa Nawab Hussain Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia nhusain@kau.edu.sa Wataru Takahashi Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo 1528552, Japan wataru@is.titech.ac.jp We first introduce a broad semigroup of not necessarily continuous mappings in a Banach space which contains discrete semigroups generated by generalized nonspreading mappings and semigroups of φnonexpansive mappings. Then we establish a weak convergence theorem of Mann's type iteration for the semigroups of mappings in a Banach space. Using the result, we obtain wellknown and new theorems which are connected with weak convergence results in Banach spaces. Keywords: Attractive point, Banach space, fixed point, generalized nonspreading mapping, invariant mean, weak converegence, nonexpansive semigroup, strongly asymptotically invariant net. MSC: 47H05, 47H09, 47H20 [ Fulltextpdf (164 KB)] for subscribers only. 