Fixed point theorems and convergence theorems for generalized nonspreading mappings in Banach spaces
The authors deal with the class of \(2\)-generalized nonspreading mappings which is one of the three classes of nonlinear mappings defined in the authors' paper [J. Nonlinear Convex Anal. 13, No.~2, 363--381 (2012; Zbl 1248.47056)] in Banach spaces. They first prove a general fixed point theorem for nonlinear mappings in a Banach space. Using this result, the authors give another proof of their earlier fixed point theorem [loc.\,cit.]\ for 2-generalized nonspreading mappings in Banach spaces. Then they prove a nonlinear mean convergence theorem of \textit{J.-B. Baillon}'s type [C. R. Acad. Sci., Paris, Sér. A 280, 1511--1514 (1975; Zbl 0307.47006)] and a weak convergence theorem of \textit{W. R. Mann}'s type [Proc. Am. Math. Soc. 4, 506--510 (1953; Zbl 0050.11603)] for such nonlinear mappings in a Banach space.
scientific article; zbMATH DE number 6112752
scientific article