Geodesic
Weak Convergence Theorems for Semigroups of Not Necessarily Continuous Mappings in Banach Spaces
Journal of convex analysis, Tome 22 (2015) no. 1, pp. 81-1
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We first introduce a broad semigroup of not necessarily continuous mappings in a Banach space which contains discrete semigroups generated by generalized nonspreading mappings and semigroups of ϕ-nonexpansive mappings. Then we establish a weak convergence theorem of Mann's type iteration for the semigroups of mappings in a Banach space. Using the result, we obtain well-known and new theorems which are connected with weak convergence results in Banach spaces.
Classification : 47H05, 47H09, 47H20
Mots-clés : Attractive point, Banach space, fixed point, generalized nonspreading mapping, invariant mean, weak converegence, nonexpansive semigroup, strongly asymptotically invariant net 
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     author = {S. M. Alsulami and N. Hussain and W. Takahashi},
     title = {Weak {Convergence} {Theorems} for {Semigroups} of {Not} {Necessarily} {Continuous} {Mappings} in {Banach} {Spaces}},
     journal = {Journal of convex analysis},
     pages = {81--1},
     year = {2015},
     volume = {22},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2015_22_1_JCA_2015_22_1_a4/}
}
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S. M. Alsulami; N. Hussain; W. Takahashi. Weak Convergence Theorems for Semigroups of Not Necessarily Continuous Mappings in Banach Spaces. Journal of convex analysis, Tome 22 (2015) no. 1, pp. 81-1. http://geodesic.mathdoc.fr/item/JCA_2015_22_1_JCA_2015_22_1_a4/