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JOURNALS // Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika // Archive

Izv. Vyssh. Uchebn. Zaved. Mat., 2013 Number 7, Pages 52–61 (Mi ivm8810)

This article is cited in 1 paper

Iterative processes of the second order monotone inclusions in a Hilbert space

I. P. Ryazantseva

Chair of Applied Mathematics, Nizhny Novgorod Technical University, 24 Minina str., Nizhny Novgorod, 603155 Russia

Abstract: We study equations with multiple-valued operators in a Hilbert space. We understand their solutions in the sense of inclusion. We reduce such equations to mixed variational inequalities or to equations with single-valued operators. For constructed problems we propose implicit iterative processes of the second order and establish sufficient conditions for their strong convergence.

Keywords: monotone operator, convex functional, inversely strongly monotone operator, resolvent, mixed variational inequality, iterative method.

UDC: 519.624

Received: 13.04.2012


 English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2013, 57:7, 45–52

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