• East Asian mathematical journal
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• 제28권1호
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• pp.73-79
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• 2012

It is well-known that the BMO norm is equivalent to the Garsia norm. In this paper, we characterize mean-Lipschitz spaces by using Garsia-type norms on the upper half space $\mathbb{R}_+^{n+1}$.

• Kyungpook Mathematical Journal
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• 제47권2호
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• pp.253-265
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• 2007

In this paper, the boundedness for some multilinear operators generated by singular integralv operators and Lipschitz functions on Hardy and Herz-type spaces are obtained.

• 대한수학회보
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• 제59권6호
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• pp.1371-1385
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• 2022

For setting a general weight function on n dimensional complex space ℂⁿ, we expand the classical Fock space. We define Fock type space $F^{p,q}_{{\phi},t}({\mathbb{C}}^n)$ of entire functions with a mixed norm, where 0 < p, q < ∞ and t ∈ ℝ and prove that the mixed norm of an entire function is equivalent to the mixed norm of its radial derivative on $F^{p,q}_{{\phi},t}({\mathbb{C}}^n)$. As a result of this application, the space $F^{p,q}_{{\phi},t}({\mathbb{C}}^n)$ is especially characterized by a Lipschitz type condition.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제13권3호
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• pp.207-215
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• 2006

Using more precise majorizing sequences than before [6], [10], [11], [14] we provide a finer semilocal convergence analysis for a certain class of Euler-Halley type methods for approximating a solution of an equation in a Banach space setting.

• 대한수학회보
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• 제50권4호
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• pp.1277-1288
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• 2013

Wulan and Zhu [16] have characterized the weighted Bergman space in the setting of the unit ball of $C^n$ in terms of Lipschitz type conditions in three different metrics. In this paper, we study characterizations of the harmonic Bergman space on the upper half-space in $R^n$. Furthermore, we extend harmonic analogues in the setting of the unit ball to the full range 0 < p < ${\infty}$. In addition, we provide the application of characterizations to showing the boundedness of a mapping defined by a difference quotient of harmonic function.

• 대한수학회보
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• 제58권2호
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• pp.481-495
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• 2021

In this paper, we investigate the properties of Bergman spaces, Bloch spaces and integral means of p-harmonic functions on the unit ball in ℝn. Firstly, we offer some Lipschitz-type and double integral characterizations for Bergman space ��kγ. Secondly, we characterize Bloch space ��αω in terms of weighted Lipschitz conditions and BMO functions. Finally, a Hardy-Littlewood type theorem for integral means of p-harmonic functions is established.

• Korean Journal of Mathematics
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• 제24권3호
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• pp.335-344
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• 2016

In this paper, we obtain quantitative estimates for generalized double Baskakov operators. We calculate global results for these operators using Lipschitz-type spaces and estimate the error using modulus of continuity.

• 대한수학회보
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• 제45권3호
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• pp.467-475
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• 2008

The aim of the present paper is three fold. Firstly, we obtain common fixed point theorems for a pair of selfmaps satisfying nonexpansive or Lipschitz type condition by using the notion of pointwise R-weak commutativity but without assuming the completeness of the space or continuity of the mappings involved (Theorem 1, Theorem 2 and Theorem 3). Secondly, we generalize the results obtained in first three theorems for four mappings by replacing the condition of noncompatibility of maps with the property (E.A) and using the R-weak commutativity of type $(A_g)$ (Theorem 4). Thirdly, in Theorem 5, we show that if the aspect of noncompatibility is taken in place of the property (E.A), the maps become discontinuous at their common fixed point. We, thus, provide one more answer to the problem posed by Rhoades [11] regarding the existence of contractive definition which is strong enough to generate fixed point but does not forces the maps to become continuous.

• 대한수학회논문집
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• 제21권3호
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• pp.419-428
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• 2006

The Berezin transform is the analogue of the Poisson transform in the Bergman spaces. Dyakonov characterize the holomorphic weighted Lipschitz function in the unit disk in terms of the Possion integral. In this paper, we characterize the harmonic weighted Lispchitz function in terms of the Berezin transform instead of the Poisson integral.

• Journal of applied mathematics & informatics
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• 제6권3호
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• pp.685-696
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• 1999

We present local and semilocal convergence results for New-ton's method in a Banach space setting. In particular using Lipschitz-type assumptions on the second Frechet-derivative we find results con-cerning the radius of convergence of Newton's method. Such results are useful in the context of predictor-corrector continuation procedures. Finally we provide numerical examples to show that our results can ap-ply where earlier ones using Lipschitz assumption on the first Frechet-derivative fail.