IJPAM: Volume 106, No. 1 (2016)

ON THE CONVERGENCE FOR THE SUM OF
MONOTONE OPERATORS IN HILBERT SPACES

Chahn Yong Jung$^1$, Shin Min Kang$^2$
$^1$Department of Business Administration
Gyeongsang National University
Jinju 52828, KOREA
$^{2}$Department of Mathematics and RINS
Gyeongsang National University
Jinju 52828, KOREA


Abstract. Let $C$ be a nonempty closed convex subset of a Hilbert space $H,$ $A:C\rightarrow C$ be a nonexpansive mapping, $B:C\rightarrow H$ be a $\tau$-inverse strongly monotone mapping and $M$ be a maximal monotone operator on $H$ such that the domain of $M$ is included in $C.$ In this paper, we prove the iterative sequence with errors converges weakly to a common element of $F(A)$ and $(B+M)^{-1}0$ under the suitable conditions.

Received: November 2, 2015

AMS Subject Classification: 47H05, 47H09, 46C05

Key Words and Phrases: nonexpansive mapping, inverse strongly monotone mapping, maximal monotone operator, resolvent

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DOI: 10.12732/ijpam.v106i1.18 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 106
Issue: 1
Pages: 237 - 248


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