System of variational inclusions with ${(\emph{\textbf{H}},{\bm\phi})}$-$\bm\eta$-monotone operators in Banach spaces

Abstract

Abstract: This paper introduced a new system of variational inclusions with $(H,\phi)$-$\eta$-monotone operators in real uniformly smooth Banach spaces. By using the proximal mapping technique associated with $(H,\phi)$-$\eta$-monotone operators, we proved the existence and uniqueness of solution for this new system and construct a new iterative algorithm for approximating the solution of this system. The convergence of the iterative sequence generated by the iterative algorithm was also discussed. The results extend and improve some known results in the literature.

Key words: $(H,\phi)$-$\eta$-monotone operator, proximal mapping, system of variational inclusions, iterative algorithm, convergence

CLC Number:

ZHANG Chao. System of variational inclusions with ${(\emph{\textbf{H}},{\bm\phi})}$-$\bm\eta$-monotone operators in Banach spaces[J]. Journal of East China Normal University(Natural Sc, 2012, 2012(1): 74-83.

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