## Taiwanese Journal of Mathematics

### NONLINEAR $(A,\eta)$-MONOTONE OPERATOR INCLUSION SYSTEMS INVOLVING NON-MONOTONE SET-VALUED MAPPINGS

#### Abstract

In this paper, we introduce a new concept of $(A,\eta)$-monotone operators, which generalizes the $(H,\eta)$-monotonicity and $A$-monotonicity in Hilbert spaces and other existing monotone operators as special cases. We study some properties of $(A,\eta)$-monotone operators and define the resolvent operators associated with $(A,\eta)$-monotone operators. Further, by using the new resolvent operator technique, we construct some new iterative algorithms for solving a new class of nonlinear $(A,\eta)$-monotone operator inclusion systems involving non-monotone set-valued mappings in Hilbert spaces. We also prove the existence of solutions for the nonlinear operator inclusion systems and the convergence of iterative sequences generated by the algorithm. Our results improve and generalize the corresponding results of recent works.

#### Article information

Source
Taiwanese J. Math., Volume 11, Number 3 (2007), 683-701.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500404752

Digital Object Identifier
doi:10.11650/twjm/1500404752

Mathematical Reviews number (MathSciNet)
MR2340158

Zentralblatt MATH identifier
1149.47041

#### Citation

Lan, Heng-you; Kang, Jung Im; Cho, Yeol Je. NONLINEAR $(A,\eta)$-MONOTONE OPERATOR INCLUSION SYSTEMS INVOLVING NON-MONOTONE SET-VALUED MAPPINGS. Taiwanese J. Math. 11 (2007), no. 3, 683--701. doi:10.11650/twjm/1500404752. https://projecteuclid.org/euclid.twjm/1500404752