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ON GENERALIZED NONLINEAR QUASI-VARIATIONAL-LIKE INCLUSIONS DEALING WITH (h,η)-PROXIMAL MAPPING
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 Title & Authors
ON GENERALIZED NONLINEAR QUASI-VARIATIONAL-LIKE INCLUSIONS DEALING WITH (h,η)-PROXIMAL MAPPING
Liu, Zeqing; Chen, Zhengsheng; Shim, Soo-Hak; Kang, Shin-Min;
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 Abstract
In this paper, a new class of -proximal for proper functionals in Hilbert spaces is introduced. The existence and Lip-schitz continuity of the -proximal mappings for proper functionals are proved. A class of generalized nonlinear quasi-variational-like inclusions in Hilbert spaces is introduced. A perturbed three-step iterative algorithm with errors for the generalized nonlinear quasi-variational-like inclusion is suggested. The existence and uniqueness theorems of solution for the generalized nonlinear quasi-variational-like inclusion are established. The convergence and stability results of iterative sequence generated by the perturbed three-step iterative algorithm with errors are discussed.
 Keywords
generalized nonlinear quasi-variational-like inclusion-proximalmapping;perturbed three-step iterative algorithm with errors;strongly monotone mapping;generalized pseudocontractive mapping;mixed Lipschitz mapping;relaxed coercive mapping;
 Language
English
 Cited by
1.
Perturbed Mann iterative method with errors for a new system of generalized nonlinear variational-like inclusions, Mathematical and Computer Modelling, 2010, 51, 1-2, 63  crossref(new windwow)
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