Taiwanese Journal of Mathematics

ALGORITHM OF SOLUTIONS FOR A SYSTEM OF GENERALIZED MIXED IMPLICIT QUASI-VARIATIONAL INCLUSIONS INVOLVING $h$-$\eta$-MAXIMAL MONOTONE MAPPINGS

Xie-Ping Ding, Chinsan Lee, and Su-Jane Yu

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Abstract

In this paper, we introduce a new class of $h$-$\eta$-maximal monotone mappings and a new system of generalized mixed implicit quasi-variational inclusions involving set-valued mappings and $h$-$\eta$-maximal monotone mappings. By using resolvent operator technique of $h$-$\eta$-maximal monotone mappings, A new iterative algorithm to compute approximate solutions of the system is suggested and analyzed. The convergence of the iterative sequence generated by the new algorithm is also proved. These results generalize many known results in literature.

Article information

Source
Taiwanese J. Math., Volume 11, Number 3 (2007), 577-593.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500404745

Digital Object Identifier
doi:10.11650/twjm/1500404745

Mathematical Reviews number (MathSciNet)
MR2340151

Zentralblatt MATH identifier
1138.49011

Subjects
Primary: 49J40: Variational methods including variational inequalities [See also 47J20] 49J53: Set-valued and variational analysis [See also 28B20, 47H04, 54C60, 58C06] 47J20: Variational and other types of inequalities involving nonlinear operators (general) [See also 49J40]

Keywords
system of generalized mixed implicit quasi-variational inclusions $h$-$\eta$-maximal monotone resolvent operator iterative algorithm Hilbert space

Citation

Ding, Xie-Ping; Lee, Chinsan; Yu, Su-Jane. ALGORITHM OF SOLUTIONS FOR A SYSTEM OF GENERALIZED MIXED IMPLICIT QUASI-VARIATIONAL INCLUSIONS INVOLVING $h$-$\eta$-MAXIMAL MONOTONE MAPPINGS. Taiwanese J. Math. 11 (2007), no. 3, 577--593. doi:10.11650/twjm/1500404745. https://projecteuclid.org/euclid.twjm/1500404745


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