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

作者：Takahashi, Wataru^*; Wong, Ngai Ching; Yao, Jen Chih

来源：Journal of Fixed Point Theory and Applications, 2014, 16(1-2): 203-227.

DOI：10.1007/s11784-014-0208-x

• Attractive point
• Banach limit
• Banach space
• fixed point
• generalized nonspreading mapping
• invariant mean
• mean convergence
• nonexpansive semigroup

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.

• 出版日期2014-12
• 单位中山大学