Journal of Convex Analysis 20 (2013), No. 1, 265--284
Copyright Heldermann Verlag 2013
Attractive Point Theorems for Generalized Nonspreading Mappings in Banach Spaces
Lai-Jiu 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 152-8552, 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 skew-generalized 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) 399--406] in Hilbert spaces to Banach spaces.
Keywords: Attractive point, Banach space, fixed point, generalized nonspreading mapping, skew-generalized nonspreading mapping.
MSC: 47H05, 47H09, 47H20
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