Attractive point and mean convergence theorems for semigroups of mappings without continuity in Banach spaces

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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 of mappings without continuity in a Banach space. Using these results, we obtain well-known and new theorems which are connected with attractive point, fixed point and mean convergence results in Banach spaces.

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