A new class of variational-like inclusion problems: algorithmic and analytical approach. (English) Zbl 1516.47098
Summary: The main contribution of this work is the construction of a new iterative algorithm with the help of the notion of resolvent operator associated with an \(\widehat{A}\)-maximal \(m\)-relaxed \(\eta\)-accretive mapping for solving a new class of set-valued variational-like inclusion problems in the setting of Banach spaces. The convergence analysis of the iterative sequences generated by our proposed iterative algorithm is studied under some appropriate conditions. The main attention of the final section is paid to the investigating and analysis of the notion of \((H(., .), \eta)\)-accretive operator introduced and studied by Z. B. Wang and X. P. Ding [Comput. Math. Appl. 59, No. 4, 1559–1567 (2010; Zbl 1189.49027)]. In the light of the considered conditions for an \((H(., .), \eta)\)-accretive operator, we point out that every \((H(., .), \eta)\)-accretive operator is actually an \(\widehat{A}\)-maximal \(m\)-relaxed \(\eta\)-accretive mapping and is not a new one. Finally, our paper is closed with some important comments regarding \((H(., .), \eta)\)-accretive operator and the derived results related to it in the literature.
MSC:
| 47J22 | Variational and other types of inclusions |
| 47J25 | Iterative procedures involving nonlinear operators |
| 47H05 | Monotone operators and generalizations |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
Keywords:
set-valued variational-like inclusion problem; \(\widehat{A}\)-maximal \(m\)-relaxed \(\eta\)-accretive mapping; resolvent operator; \((H(., .), \eta)\)-accretive operator; iterative algorithm; convergence analysisCitations:
Zbl 1189.49027References:
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