Lee, C.-H.; Ansari, Q. H.; Yao, J.-C. A perturbed algorithm for strongly nonlinear variational-like inclusions. (English) Zbl 0979.49008 Bull. Aust. Math. Soc. 62, No. 3, 417-426 (2000). A generalized \(\eta\)-subdifferential is defined, and applied to solvability of a strongly nonlinear variational-like inclusion with a nonlinear operator \(T\): \[ (\forall y\in H)\quad \langle T(x)- A(x), \eta(y,x)\rangle\geq \varphi(x)- \varphi(y). \] Conditions are found for convergence of a perturbed iterative algorithm to a solution, assuming monotone and other properties of \(T\) and \(\eta\), and inequalities on Lipschitz constants. Reviewer: Bruce D.Craven (Parkville) Cited in 3 ReviewsCited in 45 Documents MSC: 49J40 Variational inequalities 47J20 Variational and other types of inequalities involving nonlinear operators (general) Keywords:monotone operator; \(\eta\)-subdifferential; variational-like inclusion; convergence; perturbed iterative algorithm PDFBibTeX XMLCite \textit{C. H. Lee} et al., Bull. Aust. Math. Soc. 62, No. 3, 417--426 (2000; Zbl 0979.49008) Full Text: DOI References: [1] DOI: 10.1006/jmaa.1994.1277 · Zbl 0809.49008 · doi:10.1006/jmaa.1994.1277 [2] DOI: 10.1080/02331939408843995 · Zbl 0816.49005 · doi:10.1080/02331939408843995 [3] Ansari, Optimization: Techniques and Applications pp 1165– (1998) [4] DOI: 10.1006/jmaa.1996.0277 · Zbl 0856.65077 · doi:10.1006/jmaa.1996.0277 [5] Zhang, Top. Meth. Nonlinear Anal. 12 pp 169– (1998) [6] DOI: 10.1016/0167-6377(94)90011-6 · Zbl 0874.49012 · doi:10.1016/0167-6377(94)90011-6 [7] DOI: 10.1006/jmaa.1993.1139 · Zbl 0792.49009 · doi:10.1006/jmaa.1993.1139 [8] DOI: 10.1080/02331939108843677 · Zbl 0777.49018 · doi:10.1080/02331939108843677 [9] DOI: 10.1016/0022-247X(92)90084-Q · Zbl 0779.90067 · doi:10.1016/0022-247X(92)90084-Q [10] Siddiqi, Ann. Sci. Math. Quebec 18 pp 39– (1994) [11] DOI: 10.1016/0022-247X(92)90305-W · Zbl 0770.49006 · doi:10.1016/0022-247X(92)90305-W [12] Siddiqi, Indian J. Pure Appl. Math. 25 pp 969– (1994) [13] Parida, Bull. Austral. Math. Soc. 39 pp 225– (1989) [14] Ortega, Iterative solution of nonlinear equations in several variables (1970) · Zbl 0241.65046 [15] DOI: 10.1007/BF02192137 · Zbl 0840.90107 · doi:10.1007/BF02192137 [16] Dien”, Bull. Austral. Math. Soc. 46 pp 335– (1992) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.