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2016•International Journal of Pure and Apllied MathematicsOpen access

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

C.Y. Jung, Seung Mi Kang

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Abstract

Let C be a nonempty closed convex subset of a Hilbert space H, A : C → C be a nonexpansive mapping, B : C → H be a τ -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.

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Let C be a nonempty closed convex subset of a Hilbert space H, A : C → C be a nonexpansive mapping, B : C → H be a τ -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.

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Available abstract

Let C be a nonempty closed convex subset of a Hilbert space H, A : C → C be a nonexpansive mapping, B : C → H be a τ -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.

Key concepts: Monotone polygon, Hilbert space, Mathematics, Strongly monotone, Sequence (biology), Regular polygon, Inverse, Convergence (economics)

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