Abstract
We show some stability and convergence theorems of the modified Ishikawa iterative sequence with errors for a strongly successively pseudocontractive and strictly asymptotically pseudocontractive mapping in a real Banach space. Additionally, we prove that if T is a uniformly Lipschitzian strongly accretive mapping, the modified Ishikawa iteration sequence with errors converges strongly to the unique solution of the equation . The main results of this paper improve and extend the known results in the current literature. MSC:47H09, 47H10, 47J25.
Highlights
Developments in fixed point theory reflect that the iterative construction of fixed points is proposed and vigorously analyzed for various classes of maps in different spaces
The class of pseudocontractive mappings in their relation with iteration procedures has been studied by several researchers under suitable conditions; for more details, see [ – ] and the references therein
Stability results established in metric space, normed linear space, and Banach space settings are available in the literature
Summary
Developments in fixed point theory reflect that the iterative construction of fixed points is proposed and vigorously analyzed for various classes of maps in different spaces. The purpose in this paper is to study the modified Ishikawa iteration sequence with errors converging strongly to a fixed point of the uniformly Lipschitzian strongly successively pseudocontractive mapping under the lack of some conditions.
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