Journal of Convex Analysis 20 (2013), No. 1, 265--284
Copyright Heldermann Verlag 2013
Attractive Point Theorems for Generalized Nonspreading Mappings in Banach Spaces
Dept. of Mathematics, National University of Education, Changhua, Taiwan
Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo 152-8552, Japan
and: Dept. of Mathematics, National University of Education, Changhua, Taiwan
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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