Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 21, No. 2, pp. 185-197 (2005)

Stable iteration schemes for local strongly pseudocontractions and nonlinear equations involving local strongly accretive operators

Z. Liu and J.S. Ume

Liaoning Normal University, Changwon National University

Abstract: Let T be a local strongly pseudocontractive and uniformly continuous operator from an arbitrary Banach space X into itself. Under certain conditions, we establish that the Noor iteration scheme with errors both converges strongly to a unique fixed point of T and is almost T-stable. The related results deal with the convergence and almost stability of the Noor iteration scheme with errors of solutions of nonlinear equations of the local strongly accretive type.

Keywords: Local strongly pseudocontractive operator, local strongly accretive operator, the Noor iteration scheme with errors, fixed point, convergence, almost stability, nonempty bounded closed convex subset, Banach space.

Classification (MSC2000): 47H06; 47H10, 47H15, 47H17

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