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Convergence analysis and approximation of fixed point of multivalued generalized $\alpha$-nonexpansive mapping in uniformly convex Banach space | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 5، دوره 14، شماره 2، اردیبهشت 2023، صفحه 45-74 اصل مقاله (680.42 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.27791.3715 | ||
| نویسندگان | ||
| Unwana Udofia* ؛ Donatus Ikechi Igbokwe | ||
| Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Abia State, Nigeria | ||
| تاریخ دریافت: 22 تیر 1401، تاریخ بازنگری: 27 مرداد 1401، تاریخ پذیرش: 02 شهریور 1401 | ||
| چکیده | ||
| Recently, the authors introduce a four-step iterative algorithm called the UD-iteration scheme (Udofia and Igbokwe [35]). Here we introduce the multivalued version of the UD-iteration scheme and show that it can be used to approximate the fixed points of multivalued contraction and multivalued generalized $\alpha$-nonexpansive mappings. we prove strong and weak convergence of the iteration scheme to the fixed point of multivalued generalized $\alpha$-nonexpansive mapping. We also prove that the scheme is $\varUpsilon$-stable and Data dependent. Convergence analysis shows that the multivalued UD-iteration scheme has a faster rate of convergence for multivalued contraction and multivalued generalized $\alpha$-nonexpansive mappings than some well-known existing iteration schemes in the literature. | ||
| کلیدواژهها | ||
| Uniformly convex Banach space؛ Multivalued generalized $\alpha$-nonexpansive Mapping؛ Convergence؛ Data dependence؛ Stability | ||
| مراجع | ||
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