Geodesic
Attractive Point Theorems for Generalized Nonspreading Mappings in Banach Spaces
Journal of convex analysis, Tome 20 (2013) no. 1, pp. 265-284.

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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.
Classification : 47H05, 47H09, 47H20
Mots-clés : Attractive point, Banach space, fixed point, generalized nonspreading mapping, skew-generalized nonspreading mapping 
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     author = {L.-J. Lin and W. Takahashi},
     title = {Attractive {Point} {Theorems} for {Generalized} {Nonspreading} {Mappings} in {Banach} {Spaces}},
     journal = {Journal of convex analysis},
     pages = {265--284},
     publisher = {mathdoc},
     volume = {20},
     number = {1},
     year = {2013},
     url = {http://geodesic.mathdoc.fr/item/JCA_2013_20_1_JCA_2013_20_1_a16/}
}
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L.-J. Lin; W. Takahashi. Attractive Point Theorems for Generalized Nonspreading Mappings in Banach Spaces. Journal of convex analysis, Tome 20 (2013) no. 1, pp. 265-284. http://geodesic.mathdoc.fr/item/JCA_2013_20_1_JCA_2013_20_1_a16/