
Journal of Convex Analysis 20 (2013), No. 1, 265284 Copyright Heldermann Verlag 2013 Attractive Point Theorems for Generalized Nonspreading Mappings in Banach Spaces LaiJiu Lin Dept. of Mathematics, National University of Education, Changhua, Taiwan maljlin@cc.ncu.edu.tw Wataru Takahashi Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo 1528552, Japan and: Dept. of Mathematics, National University of Education, Changhua, Taiwan wataru@is.titech.ac.jp We introduce the concept of attractive points of a nonlinear mapping in a Banach space and obtain some fundamental properties for the points. Using these results, we prove attractive point theorems for generalized nonspreading mappings in a Banach space. Using these results, we also obtain some results for skewgeneralized nonspreading mappings in a Banach space. Finally, we prove nonlinear ergodic theorems without convexity for generalized nonspreading mappings in a Banach space. These results extend attractive point theorems which were proved by W. Takahashi and Y. Takeuchi ["Nonlinear ergodic theorem without convexity for generalized hybrid mappings in a Hilbert space", J. Nonlinear Convex Anal. 12 (2011) 399406] in Hilbert spaces to Banach spaces. Keywords: Attractive point, Banach space, fixed point, generalized nonspreading mapping, skewgeneralized nonspreading mapping. MSC: 47H05, 47H09, 47H20 [ Fulltextpdf (154 KB)] for subscribers only. 