Iterative Solutions of Nonlinear Equations of the Strongly Accretive Type
- 1 January 1998
- journal article
- Published by Wiley in Mathematische Nachrichten
- Vol. 189 (1) , 49-60
- https://doi.org/10.1002/mana.19981890105
Abstract
Let E be a real q‐uniformly smooth Banach space. Suppose T is a strongly pseudo‐contractive map with open domain D(T) in E. Suppose further that T has a fixed point in D(T). Under various continuity assumptions on T it is proved that each of the Mann iteration process or the Ishikawa iteration method converges strongly to the unique fixed point of T. Related results deal with iterative solutions of nonlinear operator equations involving strongly accretive maps. Explicit error estimates are also provided.Keywords
This publication has 28 references indexed in Scilit:
- Fixed Point Iteration for Local Strictly Pseudo-Contractive MappingProceedings of the American Mathematical Society, 1991
- Inequalities in Banach spaces with applicationsNonlinear Analysis, 1991
- On a Theorem of C. E. Chidume Concerning the Iterative Approximation of Fixed PointsMathematische Nachrichten, 1991
- Iterative solution of nonlinear equations of the monotone type in Banach spacesBulletin of the Australian Mathematical Society, 1990
- Iterative Approximation of Fixed Points of Lipschitzian Strictly Pseudo-Contractive MappingsProceedings of the American Mathematical Society, 1987
- A fixed point theorem for local pseudo-contractions in uniformly convex spacesmanuscripta mathematica, 1979
- Zeros of accretive operatorsmanuscripta mathematica, 1974
- The iterative solution of the equation $y \in x + Tx$ for a monotone operator $T$ in Hilbert spaceBulletin of the American Mathematical Society, 1973
- A global existence theorem for autonomous differential equations in a Banach spaceProceedings of the American Mathematical Society, 1970
- Mean Value Methods in IterationProceedings of the American Mathematical Society, 1953