• Kyungpook Mathematical Journal
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• 제33권2호
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• pp.149-161
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• 1993

• 대한수학회보
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• 제47권4호
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• pp.839-857
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• 2010

We give a set of continuous characterizations for the homogeneous Triebel-Lizorkin spaces and use them to study boundedness properties of Fourier multiplier operators whose symbols satisfy a generalization of H$\ddot{o}$rmander's condition. As an application, we give new direct proofs of the imbedding theorems of the Sobolev type.

• Journal of applied mathematics & informatics
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• 제32권3_4호
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• pp.331-341
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• 2014

In this article we introduce the sequence spaces $_2c^I_0(f,p)$, $_2c^I(f,p)$ and $_2l^I_{\infty}(f,p)$ for a modulus function f, where $p=(p_k)$ is a sequence of positive reals and study some of the properties of these spaces.

• Journal of applied mathematics & informatics
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• 제31권3_4호
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• pp.565-575
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• 2013

Let H be a real Hilbert space and let T : H ${\rightarrow}$ H be a Lipschitz pseudocontractive mapping. We introduce a modified Ishikawa iterative algorithm and prove that if $F(T)=\{x{\in}H:Tx=x\}{\neq}{\emptyset}$, then our proposed iterative algorithm converges strongly to a fixed point of T. No compactness assumption is imposed on T and no further requirement is imposed on F(T).

• 대한수학회보
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• 제51권2호
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• pp.303-315
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• 2014

In this work, we construct Kantorovich type generalization of a class of linear positive operators via Riemann type q-integral. We obtain estimations for the rate of convergence by means of modulus of continuity and the elements of Lipschitz class and also investigate weighted approximation properties.

• 대한수학회논문집
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• 제19권2호
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• pp.267-281
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• 2004

In this paper, we establish almost stability of Ishikawa iterative schemes with errors for the classes of Lipschitz $\phi$-strongly quasi-accretive operators and Lipschitz $\phi$-hemicontractive operators in arbitrary Banach spaces. The results of this paper extend a few well-known recent results.

• 대한수학회보
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• 제55권5호
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• pp.1503-1521
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• 2018

The paper introduces a modified subgradient extragradient method for solving equilibrium problems involving pseudomonotone and Lipschitz-type bifunctions in Hilbert spaces. Theorem of weak convergence is established under suitable conditions. Several experiments are implemented to illustrate the numerical behavior of the new algorithm and compare it with a well known extragradient method.

• Nonlinear Functional Analysis and Applications
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• 제28권2호
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• pp.337-363
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• 2023

In this paper, we propose a new subgradient extragradient algorithm for finding a solution of monotone bilevel equilibrium problem in reflexive Banach spaces. The strong convergence of the algorithm is established under monotone assumptions of the cost bifunctions with Bregman Lipschitz-type continuous condition. Finally, a numerical experiments is reported to illustrate the efficiency of the proposed algorithm.

• 대한수학회지
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• 제39권2호
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• pp.277-287
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• 2002

Let B be the open unit ball with center 0 in the complex space $C^n$. For each q>0, B$_{q}$ consists of holomorphic functions f : B longrightarrow C which satisfy sup z $\in$ B $(1-\parallel z \parallel^2)^q\parallel\nabla f(z)\parallel < \infty$ In this paper, we will show that functions in weighted Bloch spaces $B_{q}$ (0 < q < 1) satifies the following Lipschitz type result for Bergman metric $\beta$: ｜f(z)-f($\omega$)｜< $C\beta$(z, $\omega$) for some constant C.

• 대한수학회보
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• 제56권3호
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• pp.745-756
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• 2019

We obtain Lipschitz type characterization and double integral characterization for Fock-type spaces with the norm $${\parallel}f{\parallel}^p_{F^p_{m,{\alpha},t}}\;=\;{\displaystyle\smashmargin{2}{\int\nolimits_{{\mathbb{C}}^n}}\;{\left|{f(z){e^{-{\alpha}}{\mid}z{\mid}^m}}\right|^p}\;{\frac{dV(z)}{(1+{\mid}z{\mid})^t}}$$, where ${\alpha}>0$, $t{\in}{\mathbb{R}}$, and $m{\in}\mathbb{N}$. The results of this paper are the extensions of the classical weighted Fock space $F^p_{2,{\alpha},t}$.