ON GENERALIZED NONLINEAR QUASI-VARIATIONAL-LIKE INCLUSIONS DEALING WITH (h,η)-PROXIMAL MAPPING

• Liu, Zeqing ;
• Chen, Zhengsheng ;
• Shim, Soo-Hak ;
• Kang, Shin-Min
• Published : 2008.09.30
• 106 6

Abstract

In this paper, a new class of $(h,{\eta})$-proximal for proper functionals in Hilbert spaces is introduced. The existence and Lip-schitz continuity of the $(h,{\eta})$-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$(h,{\eta})$-proximalmapping;perturbed three-step iterative algorithm with errors;strongly monotone mapping;generalized pseudocontractive mapping;mixed Lipschitz mapping;relaxed coercive mapping

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