• Communications of the Korean Mathematical Society
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• v.28 no.4
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• pp.723-733
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• 2013

A Bachet equation $Y^2=X^3+k$ will have a rational solution if and only if there is $b{\in}\mathbb{Q}$ for which $X^3-b^2X^2+k$ is reducible. In this paper we show that such cubics arise as a cubic resolvent of a biquadratic polynomial. And we prove various properties of cubic resolvents.

• East Asian mathematical journal
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• v.4
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• pp.129-137
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• 1988

• Journal of the Korean Mathematical Society
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• v.24 no.1
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• pp.73-82
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• 1987

• Journal of the Korean Mathematical Society
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• v.22 no.1
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• pp.75-85
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• 1985

• Communications of the Korean Mathematical Society
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• v.8 no.4
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• pp.629-641
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• 1993

• Korean Journal of Mathematics
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• v.8 no.2
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• pp.139-146
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• 2000

In this paper, we discuss convergence theorem for contraction C-regularized semigroups. We establish the convergence of the sequence of generators of contraction regularized semigroups in some sense implies the convergence of the sequence of the corresponding contraction regularized semigroups. Under the assumption that R(C) is dense, we show the convergence of generators is implied by the convergence of C-resolvents of generators.

• Korean Journal of Mathematics
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• v.22 no.2
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• pp.349-354
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• 2014

In this paper, we establish convergence of contraction $C_0$ semigroups in the weak topology on a general Banach space. We remove the restriction on a Banach space X and weaken the condition on resolvents of generators in the previous results [4, 5].

• Korean Journal of Mathematics
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• v.4 no.2
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• pp.125-133
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• 1996

We show that if X is a reflexive Banach space with a uniformly G$\hat{a}$teaux differentiable norm, then the convergence of semigroups acting on Banach spaces $X_n$ implies the convergence of resolvents of generators of semigroups.

• Journal of applied mathematics & informatics
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• v.4 no.2
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• pp.487-500
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• 1997

In this paper we introduce a multigrid method for solving the nonliear Urysohn integral equation. The algorithm is derived from a discrete resolvent equation which approximates the continuous resolvent equation of the nonlinear Urysohn integral equa-tion. The algorithm is mathematically equivalent to Atkinson's adap-tive twogrid iteration. But the two are different computationally. We show the convergence of the algorithm and its equivalence to Atkinson's adaptive twogrid iteration. in our numerical example we compare our algorithm to other multigrid methods for solving the nonliear Urysohn integral equation including the nonlinear multigrid nethod introduced by hackbush.

• Journal of the Korean Mathematical Society
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• v.54 no.6
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• pp.1905-1926
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• 2017

In this paper we introduce a new iterative method by the combination of the prox-Tikhonov regularization and the alternating resolvents for finding a common zero of two accretive operators in Banach spaces. And we will give some applications and numerical examples. The results of this paper improve and extend the corresponding results announced by many others.