Attractive Point Theorems for Generalized Nonspreading Mappings in Banach Spaces

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.