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In this paper, we first introduce a class of nonlinear mappings called generalized nonspreading which contains the class of nonspreading mappings in a Banach space and then prove a fixed point theorem, a nonlinear mean convergence theorem of Baillon’s type and a weak convergence theorem of Mann’s type for such nonlinear mappings in a Banach space. Using these theorems, we obtain some fixed point theorems,...
In this paper, we first introduce a broad semigroup of mappings without continuity in a Banach space which contains discrete semigroups generated by generalized nonspreading mappings and semigroups of nonexpansive mappings. Then we prove an attractive point and fixed point theorem for the semigroups of mappings without continuity. Furthermore, we establish a mean convergence theorem for the semigroups...
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