• Korean Journal of Mathematics
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• 제27권3호
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• pp.581-594
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• 2019

In this study a new generalization for operators of two parameters type of fractional in the unit disk is proposed. The fractional operators in this generalization are in the Srivastava-Owa sense. Concerning with the related applications, the generalized Gauss hypergeometric function is introduced. Further, some boundedness properties on Bloch space are also discussed.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제8권1호
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• pp.37-41
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• 2008

In this paper, we investigate the properties of implicative closure operators on the stsc-quantale L. We find implicative closure operators induced by a function.

• Kyungpook Mathematical Journal
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• 제49권1호
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• pp.31-39
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• 2009

Let $T_{\rho}$ be the generalized fractional integral operator associated to a function ${\rho}:(0,{\infty}){\rightarrow}(0,{\infty})$, as defined in [16]. For a function W on $\mathbb{R}^n$, we shall be interested in the boundedness of the multiplication operator $f{\mapsto}W{\cdot}T_{\rho}f$ on generalized Morrey spaces. Under some assumptions on ${\rho}$, we obtain an inequality for $W{\cdot}T_{\rho}$, which can be viewed as an extension of Olsen's and Kurata-Nishigaki-Sugano's results.

• Kyungpook Mathematical Journal
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• 제45권1호
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• pp.1-11
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• 2005

Making use of the multidimensional fractional calculus operators introduced in [20], this paper gives the images under these operators of the celebrated Fox's H-function. Special cases are briefly point out, and some of the results are also studied on general spaces of functions $M_{\lambda}(R_{+}^n)$.

• 대한수학회보
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• 제44권4호
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• pp.701-708
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• 2007

In this paper we characterize the boundedness, compactness and closedness of the range of the weighted composition operators on Lorentz spaces L(p,q), $1.

• 대한수학회논문집
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• 제35권1호
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• pp.217-227
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• 2020

Let ψ be an analytic function on 𝔻, the unit disc in the complex plane, and φ be an analytic self-map of 𝔻. Let 𝓑 be a Banach space of functions analytic on 𝔻. The weighted composition operator W_φ,ψ on 𝓑 is defined as W_φ,ψf = ψf ◦ φ, and the composition operator C_φ defined by C_φf = f ◦ φ for f ∈ 𝓑. Consider α > -1 and 1 ≤ p < ∞. In this paper, we prove that if φ ∈ H^∞(𝔻), then C_φ has closed range on any weighted Dirichlet space 𝒟_α if and only if φ(𝔻) satisfies the reverse Carleson condition. Also, we investigate the closed rangeness of weighted composition operators on the weighted Bergman space A^p_α.

• 대한수학회보
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• 제55권2호
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• pp.659-672
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• 2018

In this note we prove that several classes of Littlewood-Paley square operators defined by the kernels without any regularity are bounded on Triebel-Lizorkin spaces $F^{p,q}_{\alpha}({\mathbb{R}}^n)$ and Besov spaces $B^{p,q}_{\alpha}({\mathbb{R}}^n)$ for 0 < ${\alpha}$ < 1 and 1 < p, q < ${\infty}$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제15권3호
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• pp.221-227
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• 2008

We introduce and study the new concepts of interior and closure operators on strong generalized neighborhood spaces. Also we introduce and investigate the concept of sgn-continuity on SGNS.

• 전자공학회논문지S
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• 제34S권5호
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• pp.52-65
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• 1997

For the degradation of severe noise and ill-conditioned blur the optimization function has the solution spaces which have many local optima around global solution. General restoration methods such as inverse filtering or gradient methods are mainly dependent on the properties of degradation model and tend to be isolated into a local optima because their convergences are determined in the convex space. Hence we introduce genetic algorithm as a searching method which will search solutions beyond the convex spaces including local solutins. In this paper we introudce improved evaluation square error) and fitness value for gray scaled images. Finally we also proposed the local fine tunign of window size and visit number for delicate searching mechanism in the vicinity of th global solution. Through the experiental results we verified the effectiveness of the proposed genetic operators and evaluation function on noise reduction over the conventional ones, as well as the improved performance of local fine tuning.

• 대한수학회보
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• 제58권2호
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• pp.277-303
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• 2021

Under the rough kernels Ω belonging to the block spaces B0,qr (Sn-1) or the radial Grafakos-Stefanov kernels W����(Sn-1) for some r, �� > 1 and q ≤ 0, the boundedness and continuity were proved for two classes of rough maximal singular integrals and maximal operators associated to polynomial mappings on the Triebel-Lizorkin spaces and Besov spaces, complementing some recent boundedness and continuity results in [27, 28], in which the authors established the corresponding results under the conditions that the rough kernels belong to the function class L(log L)α(Sn-1) or the Grafakos-Stefanov class ����(Sn-1) for some α ∈ [0, 1] and �� ∈ (2, ∞).