Strong convergence theorems for nonexpansive semigroup in Banach spaces

By Yisheng Song, Sumei Xu. 2008

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Abstract Let K be a nonempty closed convex subset of a reflexive and strictly convex Banach space E with a uniformly Gâteaux differentiable norm, and F = { T ( t ) : t > 0 } a nonexpansive self-mappings semigroup of K, and f : K → K a fixed contractive mapping. The strongly convergent theorems of the following implicit and explicit viscosity iterative schemes { x n } are proved. x n = α n f ( x n ) + ( 1 − α n ) T ( t n ) x n , x n + 1 = α n f ( x n ) + ( 1 − α n ) T ( t n ) x n . And the cluster point of { x n } is the unique solution to some co-variational inequality.

Subfields: Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/f137d57d651c20b59d6f469a2274a1392625d750

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In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

Minimum-norm solution of variational inequality and fixed point problem in banach spaces (2015, background): “[6], Reich [20], Song-Xu [22], Takahashi-Ueda [26], Suzuki [23], Yao and Shahzad [32], Yao et al.”