• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.15-26
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• 2002

In this paper, we suggest and analyze a class of resolvent dynamical systems associated with mixed variational inequalities. We study the globally asymptotic stability of the solution of the resolvent dynamical systems for the pseudomonotone operators. We also discuss some special cases, which can be obtained from our main results.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1387-1407
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• 2017

In this paper, we introduce a family resolvent cocycle and express the Chern Character of Dai-Zhang higher spectral flow as a pairing of a family resolvent cocycle and the odd Chern character of a unitary matrix, which generalize the odd index formula of Carey et al. to the family case.

• Communications of the Korean Mathematical Society
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• v.31 no.4
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• pp.845-855
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• 2016

We introduce the proximal point algorithm in a p-uniformly convex metric space. We first introduce the notion of p-resolvent map in a p-uniformly convex metric space as a generalization of the Moreau-Yosida resolvent in a CAT(0)-space, and then we secondly prove the convergence of the proximal point algorithm by the p-resolvent map in a p-uniformly convex metric space.

• Journal of applied mathematics & informatics
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• v.4 no.2
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• pp.407-418
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• 1997

In this paper we establish the equivalence between the general resolvent equations and variational inequalities. This equiva-lence is used to suggest and analyze a number of iterative algorithms for solving variational inclusions. We also study the convergence criteria of the iterative algorithms. Our results include several pre-viously known results as special cases.

• Bulletin of the Korean Mathematical Society
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• v.41 no.2
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• pp.241-256
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• 2004

In this paper, we introduce and study a new class of variational inclusions, called the general variational inclusion. We prove the equivalence between the general variational inclusions, the general resolvent equations, and the fixed-point problems, using the resolvent operator technique. This equivalence is used to suggest and analyze a few iterative algorithms for solving the general variational inclusions and the general resolvent equations. Under certain conditions, the convergence analyses are also studied. The results presented in this paper generalize, improve and unify a number of recent results.

• Korean Journal of Mathematics
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• v.24 no.2
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• pp.199-213
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• 2016

The resolvent operator approach of [2] is applied to solve a set-valued variational inclusion problem in ordered Hilbert spaces. The resolvent operator under consideration is called relaxed resolvent operator and we demonstrate some of its properties. To obtain the solution of a set-valued variational inclusion problem, an iterative algorithm is developed and weak-RRD set-valued mapping is used. The problem as well as main result of this paper are more general than many previous problems and results available in the literature.

• Bulletin of the Korean Mathematical Society
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• v.60 no.3
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• pp.785-827
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• 2023

In this paper, under some new appropriate conditions imposed on the parameter and mappings involved in the resolvent operator associated with a P-accretive mapping, its Lipschitz continuity is proved and an estimate of its Lipschitz constant is computed. This paper is also concerned with the construction of a new iterative algorithm using the resolvent operator technique and Nadler's technique for solving a new system of generalized multi-valued resolvent equations in a Banach space setting. The convergence analysis of the sequences generated by our proposed iterative algorithm under some appropriate conditions is studied. The final section deals with the investigation and analysis of the notion of H(·, ·)-co-accretive mapping which has been recently introduced and studied in the literature. We verify that under the conditions considered in the literature, every H(·, ·)-co-accretive mapping is actually P-accretive and is not a new one. In the meanwhile, some important comments on H(·, ·)-co-accretive mappings and the results related to them appeared in the literature are pointed out.

• East Asian mathematical journal
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• v.30 no.1
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• pp.69-77
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• 2014

In this paper, we introduce a new generalized resolvent in a Banach space and discuss its some properties. Using these properties, we obtain an iterative scheme for finding a point which is a fixed point of relatively weak nonexpansive mapping and a zero of monotone mapping. Furthermore, strong convergence of the scheme to a point which is a fixed point of relatively weak nonexpansive mapping and a zero of monotone mapping is proved.

• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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• pp.701-707
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• 2022

In this article, we put forward a new type of variational inclusion problem known as resolvent inclusion. An algorithm is given for approximating its solution. The convergence of the algorithm is explained with the help of an example and plots using Matlab.

• Honam Mathematical Journal
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• v.26 no.4
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• pp.401-409
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• 2004

In this paper, we show that C-resolvent of generator can be represented by Laplace transform and establish an exponential formula for C regularized semigroups whose antiderivatives are exponentially bounded.