Strong convergence theorems for infinite families of nonexpansive mappings in general Banach spaces

By Tomonari Suzuki. 2005

241 citations recorded by the source corpus.

In 1979, Ishikawa proved a strong convergence theorem for finite families of nonexpansive mappings in general Banach spaces. Motivated by Ishikawa's result, we prove strong convergence theorems for infinite families of nonexpansive mappings.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/c67ccfc6fa989d8c7a26834921e87d59979a5ed1

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In Computational Theory and Mathematics

In Geometry and Topology

In Numerical Analysis

Citations in the corpus

New Methods with Perturbations for Non-Expansive Mappings in Hilbert Spaces (2011, background): “Recently, iterative methods for finding fixed points of non-expansive mappings have received vast investigations due to its extensive applications in a variety of applied areas of inverse problem, partial differential equations, image recovery, and signal processing; see [1-34] and the references th”
A modified Korpelevich's method convergent to the minimum-norm solution of a variational inequality (2014, background): “3 [21] Let {xn} and {yn} be bounded sequences in a Banach space X and let { n} be a sequence in [0, 1] with 05 lim infn!1 n lim supn!1 n5 1.”
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.”
A sufficient and necessary condition for Halpern-type strong convergence to fixed points of nonexpansive mappings (2006, unknown): “Lemma 1 ([21]).”