• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제16권1호
• /
• pp.19-30
• /
• 2009

In this paper, we prove some common fixed point theorems for six maps satisfying compatible maps of type(${\alpha}$) on intuitionistic fuzzy metric spaces in sense of Park et al.[7]. Our research are generalization and extension for the results of [1], [2], [3] and [13].

• 호남수학학술지
• /
• 제33권3호
• /
• pp.311-320
• /
• 2011

We in this paper construct Dirichlet's type twisted q-Euler numbers and polynomials with weight ${\alpha}$. We give some interestin identities some relations.

• Kyungpook Mathematical Journal
• /
• 제58권4호
• /
• pp.651-675
• /
• 2018

We present ${\alpha}$-type rational F-contractions in metric-like spaces, and respective fixed and common fixed point results for weakly ${\alpha}$-admissible mappings. Useful examples illustrate the effectiveness of the presented results. As applications, we obtain sufficient conditions for the existence of solutions of a certain type of integral equations followed by examples of nonlinear fractional differential equations that are verified numerically.

• Korean Journal of Mathematics
• /
• 제26권1호
• /
• pp.87-101
• /
• 2018

The purpose of this paper is to define a new class of hyperholomorphic functions spaces, which will be called $F^{\alpha}_{{\omega},G}$(p, q, s) type spaces. For this class, we characterize hyperholomorphic weighted ${\alpha}$-Bloch functions by functions belonging to $F^{\alpha}_{{\omega},G}$(p, q, s) spaces under some mild conditions. Moreover, we give some essential properties for the extended weighted little ${\alpha}$-Bloch spaces. Also, we give the characterization for the hyperholomorphic weighted Bloch space by the integral norms of $F^{\alpha}_{{\omega},G}$(p, q, s) spaces of hyperholomorphic functions. Finally, we will give the relation between the hyperholomorphic ${\mathcal{B}}^{\alpha}_{{\omega},0}$ type spaces and the hyperholomorphic valued-functions space $F^{\alpha}_{{\omega},G}$(p, q, s).

• 대한수학회보
• /
• 제52권2호
• /
• pp.661-677
• /
• 2015

In this paper, we consider the following Kirchhoff-type Schr$\ddot{o}$dinger system $$\{-\(a_1+b_1{\int}_{\mathbb{R^3}}{\mid}{\nabla}u{\mid}^2dx\){\Delta}u+{\gamma}V(x)u=\frac{2{\alpha}}{{\alpha}+{\beta}}{\mid}u{\mid}^{\alpha-2}u{\mid}v{\mid}^{\beta}\;in\;\mathbb{R}^3,\\-\(a_2+b_2{\int}_{\mathbb{R^3}}{\mid}{\nabla}v{\mid}^2dx\){\Delta}v+{\gamma}W(x)v=\frac{2{\beta}}{{\alpha}+{\beta}}{\mid}u{\mid}^{\alpha}{\mid}v{\mid}^{\beta-2}v\;in\;\mathbb{R}^3,\\u,v{\in}H^1(\mathbb{R}^3),$$ where $a_i$ and $b_i$ are positive constants for i = 1, 2, ${\gamma}$ > 0 is a parameter, V (x) and W(x) are nonnegative continuous potential functions. By applying the Nehari manifold method and the concentration-compactness principle, we obtain the existence and concentration of ground state solutions when the parameter ${\gamma}$ is sufficiently large.

• 생약학회지
• /
• 제50권4호
• /
• pp.285-290
• /
• 2019

This study was carried out to identify the skin anti-aging effect of cycloheterophyllin on dermal fibroblasts. To elucidate anti-aging effects of cycloheterophyllin on dermal fibroblasts, I measured cell viability, mRNA expressions, and Collagen, type I/matrix metallopeptidase 1(MMP1)-ELISA assay. In this study, I investigated the effects of cycloheterophyllin on Collagen, type I, alpha 1(COL1A1)/Collagen, type III, alpha 1(COL3A1)/MMP1/Superoxide dismutases/Catalase(CAT) mRNA expressions and Collagen, type I/MMP1 protein production. Quantitative Real-time RT-PCR showed that cycloheterophyllin increased mRNA level of COL1A1/COL3A1/CAT genes and collagen, type I protein by ELISA assay compared to UVA-treated dermal fibroblasts. Furthermore MMP1 mRNA and protein expressions were decreased by cycloheterophyllin treatment. These observations revealed that cycloheterophyllin increased anti-aging effects in dermal fibroblasts. Therefore, I identified the anti-aging effects of cycloheterophyllin, and these results showed that the cycloheterophyllin can be a considerable potent ingredient for skin anti-aging. Based on this, I anticipated further researches about cycloheterophyllin for mechanism to develop not only cosmetics but for healthcare food or medicine.

• 대한수학회보
• /
• 제56권3호
• /
• pp.745-756
• /
• 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 $F^p_{2,{\alpha},t}$.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제28권4호
• /
• pp.355-376
• /
• 2021

In this paper we wish to establish the integral representations of generalized relative order (𝛼, 𝛽) and generalized relative type (𝛼, 𝛽) of entire and meromorphic functions where 𝛼 and 𝛽 are continuous non-negative functions defined on (-∞, +∞). We also investigate their equivalence relation under some certain condition.

• Bulletin of the Korean Chemical Society
• /
• 제20권1호
• /
• pp.101-102
• /
• 1999

• 호남수학학술지
• /
• 제32권4호
• /
• pp.663-673
• /
• 2010

In this paper, we will establish common fixed point for compatible mappings of type(${\alpha}$) for four self mappings defined on intuitionistic fuzzy metric space with implicit relations.