• 대한수학회지
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• 제54권3호
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• pp.713-732
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• 2017

Let ${\Omega}{\in}L^s(S^{n-1})$ for s > 1 be a homogeneous function of degree zero and b be BMO functions or Lipschitz functions. In this paper, we obtain some boundedness of the $Calder{\acute{o}}n$-Zygmund singular integral operator $T_{\Omega}$ and its commutator [b, $T_{\Omega}$] on Herz-type Hardy spaces with variable exponent.

• Journal of applied mathematics & informatics
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• 제27권3_4호
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• pp.693-702
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• 2009

In this paper, we introduce and study a system of mixed variational inequalities in Banach spaces. By using J-proximal mapping and its Lipschitz continuity for a nonconvex, lower semicontinuous, subdifferentiable, proper functional, an iterative algorithm for computing the approximate solutions of system of mixed variational inequalities is suggested and analyzed. The convergence criteria of the iterative sequences generated by iterative algorithm is also discussed.

• Kyungpook Mathematical Journal
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• 제59권2호
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• pp.241-258
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• 2019

In this paper, we deal with the null controllability of semilinear functional integrodifferential control systems under the Lipschitz continuity of nonlinear terms. Moreover, we establish the regularity and a variation of constant formula for solutions of the given control systems in Hilbert spaces.

• 충청수학회지
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• 제34권4호
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• pp.355-368
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• 2021

In this paper, we investigate necessary and sufficient conditions for the approximate controllability for semilinear stochastic functional differential equations with delays in Hilbert spaces without the strict range condition on the controller even though the equations contain unbounded principal operators, delay terms and local Lipschitz continuity of the nonlinear term.

• 대한수학회지
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• 제32권1호
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• pp.103-108
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• 1995

It is a well-known classical result of Mazur and Ulam that an isometry T from a real Banach space X onto a real Banach space Y with T(0) = 0 is automatically linear[5].

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제13권3호
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• pp.197-206
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• 2006

This paper introduces a class of multivalued mixed quasi-variational-like ineqcalities and shows the existence of solutions to the class of quasi-variational-like inequalities in reflexive Banach spaces.

• 대한수학회보
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• 제56권4호
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• pp.929-937
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• 2019

The main purpose of this paper is to establish $H{\ddot{o}}lder$ estimates for the Cauchy transform in a class of finite/infinite type convex domains in $\mathbb{C}^2$.

• 대한수학회지
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• 제61권3호
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• pp.461-494
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• 2024

We prove the Sobolev continuity of maximal commutator and its fractional variant with Lipschitz symbols, both in the global and local cases. The main result in global case answers a question originally posed by Liu and Wang in [29].

• 대한수학회논문집
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• 제33권2호
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• pp.677-693
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• 2018

In this work, we generalize a family of optimal eighth order weighted-Newton methods to Banach spaces and study its local convergence to approximate a locally-unique solution of a system of nonlinear equations. The convergence in this study is shown under hypotheses only on the first derivative. Our analysis avoids the usual Taylor expansions requiring higher order derivatives but uses generalized Lipschitz-type conditions only on the first derivative. Moreover, our new approach provides computable radius of convergence as well as error bounds on the distances involved and estimates on the uniqueness of the solution based on some functions appearing in these generalized conditions. Such estimates are not provided in the approaches using Taylor expansions of higher order derivatives which may not exist or may be very expensive or impossible to compute. The convergence order is computed using computational order of convergence or approximate computational order of convergence which do not require usage of higher derivatives. This technique can be applied to any iterative method using Taylor expansions involving high order derivatives. The study of the local convergence based on Lipschitz constants is important because it provides the degree of difficulty for choosing initial points. In this sense the applicability of the method is expanded. Finally, numerical examples are provided to verify the theoretical results and to show the convergence behavior.

• Korean Journal of Mathematics
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• 제24권4호
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• pp.647-662
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• 2016

In this paper, we study Lipschitz continuous, the boundedness and compactness of the composition operator $C_{\phi}$ acting between the general hyperbolic Bloch type-classes ${\mathcal{B}}^{\ast}_{p,{\log},{\alpha}}$ and general hyperbolic Besov-type classes $F^{\ast}_{p,{\log}}(p,q,s)$. Moreover, these classes are shown to be complete metric spaces with respect to the corresponding metrics.