Convergence and stability of modified multi-step Noor iterative procedure with errors for strictly hemicontractive-type mappings in Banach spaces

Author:

Asaduzzaman Md.ORCID

Abstract

AbstractIn this paper, we introduce and study a modified multi-step Noor iterative procedure with errors for two Lipschitz strictly hemicontractive-type mappings in arbitrary Banach spaces and constitute its convergence and stability. The obtained results in this paper generalize and extend the corresponding result of Hussain et al. (Fixed Point Theory Appl. 2012:160, 2012) and some analogous results of several authors in the literature. Finally, a numerical example is included to illustrate our analytical results and to display the efficiency of our proposed novel iterative procedure with errors.

Publisher

Springer Science and Business Media LLC

Reference40 articles.

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3. Meche, T.H., Sangago, M.G., Zegeye, H.: Iterative methods for a fixed point of hemicontractive-type mapping and a solution of a variational inequality problem. Creative Math. Inform. 25(2), 175–188 (2016)

4. Chidume, C.E., Osilike, M.O.: Fixed point iterations for strictly hemicontractive maps in uniformly smooth Banach spaces. Numer. Funct. Anal. Optim. 15, 779–790 (1994)

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