ITERATIVE SOLUTION OF NONLINEAR EQUATIONS INVOLVING SET-VALUED UNIFORMLY ACCRETIVE OPERATORS

By C. Moore, B. Nnoli. 2001

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Abstract Let E be a real normed linear space and let A : E ↦ 2 E be a uniformly continuous and uniformly quasi-accretive multivalued map with nonempty closed values such that the range of ( I – A ) is bounded and the inclusion f ϵ Ax has a solution x * ϵ E . It is proved that Ishikawa and Mann type iteration processes converge strongly to x *. Further, if T : E ↦ 2 E is a uniformly continuous and uniformly hemicontractive set-valued map with bounded range and a fixed point x * ϵ E , it is proved that both the Mann and Ishikawa type iteration processes converge strongly to x *. The strong convergence of these iteration processes with errors is also proved.

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

View Paper: https://www.semanticscholar.org/paper/17e461e4088852c4b488eb11bf45216cd056f259