• Honam Mathematical Journal
• /
• v.45 no.1
• /
• pp.123-129
• /
• 2023

In this paper, we introduce the reverse of the operator Davis-Choi-Jensen's inequality. Our results are employed to establish a new bound for the Furuta inequality. More precisely, we prove that, if $A,\;B{\in}{\mathcal{B}}({\mathcal{H}})$ are self-adjoint operators with the spectra contained in the interval [m, M] with m < M and A ≤ B, then for any $r{\geq}{\frac{1}{t}}>1,\,t{\in}(0,\,1)$ $A^r{\leq}({\frac{M1_{\mathcal{H}}-A}{M-m}}m^{rt}+{\frac{A-m1_{\mathcal{H}}}{M-m}}M^{rt}){^{\frac{1}{t}}}{\leq}K(m,\;M,\;r)B^r,$ where K (m, M, r) is the generalized Kantorovich constant.

• Kyungpook Mathematical Journal
• /
• v.48 no.3
• /
• pp.359-366
• /
• 2008

Let A(p) be the class of functions $f\;:\;z^p\;+\;\sum\limits_{j=1}^{\infty}a_jz^{p+j}$ analytic in the open unit disc E. Let, for any integer n > -p, $f_{n+p-1}(z)\;=\;z^p+\sum\limits_{j=1}^{\infty}(p+j)^{n+p-1}z^{p+j}$. We define $f_{n+p-1}^{(-1)}(z)$ by using convolution * as $f_{n+p-1}\;*\;f_{n+p-1}^{-1}=\frac{z^p}{(1-z)^{n+p}$. A function p, analytic in E with p(0) = 1, is in the class $P_k(\rho)$ if ${\int}_0^{2\pi}\|\frac{Re\;p(z)-\rho}{p-\rho}\|\;d\theta\;\leq\;k{\pi}$, where $z=re^{i\theta}$, $k\;\geq\;2$ and $0\;{\leq}\;\rho\;{\leq}\;p$. We use the class $P_k(\rho)$ to introduce a new class of multivalent analytic functions and define an integral operator $L_{n+p-1}(f)\;\;=\;f_{n+p-1}^{-1}\;*\;f$ for f(z) belonging to this class. We derive some interesting properties of this generalized integral operator which include inclusion results and radius problems.

• Journal of the Korean Institute of Telematics and Electronics C
• /
• v.34C no.7
• /
• pp.82-91
• /
• 1997

In this paper, we analyze the dynamics of langevine competitive learning neural network based on its fokker-plank equation. From the viewpont of the stochastic differential equation (SDE), langevine competitive learning equation is one of langevine stochastic differential equation and has the diffusin equation on the topological space (.ohm., F, P) with probability measure. We derive the fokker-plank equation from the proposed algorithm and prove by introducing a infinitestimal operator for markov semigroups, that the weight vector in the particular simplex can converge to the globally optimal point under the condition of some convex or pseudo-convex performance measure function. Experimental resutls for pattern recognition of the remote sensing data indicate the superiority of langevine competitive learning neural network in comparison to the conventional competitive learning neural network.

• Communications for Statistical Applications and Methods
• /
• v.24 no.6
• /
• pp.673-683
• /
• 2017

The least absolute shrinkage and selection operator (LASSO) has been a popular regression estimator with simultaneous variable selection. However, LASSO does not have the oracle property and its robust version is needed in the case of heavy-tailed errors or serious outliers. We propose a robust penalized regression estimator which provide a simultaneous variable selection and estimator. It is based on the rank regression and the non-convex penalty function, the smoothly clipped absolute deviation (SCAD) function which has the oracle property. The proposed method combines the robustness of the rank regression and the oracle property of the SCAD penalty. We develop an efficient algorithm to compute the proposed estimator that includes a SCAD estimate based on the local linear approximation and the tuning parameter of the penalty function. Our estimate can be obtained by the least absolute deviation method. We used an optimal tuning parameter based on the Bayesian information criterion and the cross validation method. Numerical simulation shows that the proposed estimator is robust and effective to analyze contaminated data.

• Nonlinear Functional Analysis and Applications
• /
• v.26 no.5
• /
• pp.887-902
• /
• 2021

In this paper, we have introduced a generalized class Sⁱ_H (m, n, 𝛾, 𝜙, 𝜓; 𝛼), i ∈ {0, 1} of harmonic univalent functions in unit disc 𝕌, a sufficient coefficient condition for the normalized harmonic function in this class is obtained. It is also shown that this coefficient condition is necessary for its subclass 𝒯 Sⁱ_H (m, n, 𝛾, 𝜙, 𝜓; 𝛼). We further obtained extreme points, bounds and a covering result for the class 𝒯 Sⁱ_H (m, n, 𝛾, 𝜙, 𝜓; 𝛼). Also, show that this class is closed under convolution and convex combination. While proving our results, certain conditions related to the coefficients of 𝜙 and 𝜓 are considered, which lead to various well-known results.

• East Asian mathematical journal
• /
• v.32 no.1
• /
• pp.47-59
• /
• 2016

The purpose of the present paper is to introduce and investigate two new subclasses of bi-univalent functions of complex order defined in the open unit disk, which are associated with Hurwitz-Lerch zeta function and satisfying subordinate conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients ${\mid}a_2{\mid}$ and ${\mid}a_3{\mid}$ for functions in the new subclasses. Several (known or new) consequences of the results are also pointed out.

• The Pure and Applied Mathematics
• /
• v.30 no.2
• /
• pp.109-129
• /
• 2023

In this paper, we introduce a second order linear differential operator ^T□: C^∞ (M) → C^∞ (M) as a natural generalization of Cheng-Yau operator, [8], where T is a (1, 1)-tensor on Riemannian manifold (M, h), and then we show on compact Riemannian manifolds, divT = divT^t, and if divT = 0, and f be a smooth function on M, the condition ^T□ f = 0 implies that f is constant. Hereafter, we introduce T-energy functionals and by deriving variations of these functionals, we define T-harmonic maps between Riemannian manifolds, which is a generalization of L_k-harmonic maps introduced in [3]. Also we have studied fT-harmonic maps for conformal immersions and as application of it, we consider fL_k-harmonic hypersurfaces in space forms, and after that we classify complete fL₁-harmonic surfaces, some fL_k-harmonic isoparametric hypersurfaces, fL_k-harmonic weakly convex hypersurfaces, and we show that there exists no compact fL_k-harmonic hypersurface either in the Euclidean space or in the hyperbolic space or in the Euclidean hemisphere. As well, some properties and examples of these definitions are given.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
• /
• v.33 no.3
• /
• pp.155-161
• /
• 2015

Dike lines are important features for describing the detailed shapes of dikes and for detecting topographic changes on dike surfaces. Historically, dike lines have been generated using only the LiDAR data. This paper proposes a new methodology for selecting an appropriate dike line on various dike surfaces using the topographic LiDAR data and multispectral orthoimages taken in the Nakdong River basins. The fi rst baselines were generated from the given LiDAR data using the modified convex hull algorithm and smoothing spline function, and the second baselines were generated from the given orthoimages by the Canny operator. Next, one baseline was selected among the two baselines at 10m intervals by comparing their elevations, and the selected baseline at 10m interval was defined as the dike line segment. Finally, the selected dike line segments were connected to construct the 3D dike lines. The statistical results show that the dike lines generated using both the LiDAR data and multispectral orthoimages had the improved horizontal and vertical accuracies than the dike lines generated only using the LiDAR data on the various dike surfaces.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.6
• /
• pp.1805-1818
• /
• 2015

In this article, we first consider a linear multiplier fractional q-differintegral operator and then use it to define new subclasses of p-valent analytic functions in the open unit disk U. An attempt has also been made to obtain two new q-integral operators and study their sufficient conditions on some classes of analytic functions. We also point out that the operators and classes presented here, being of general character, are easily reducible to yield many diverse new and known operators and function classes.

• Communications of the Korean Mathematical Society
• /
• v.36 no.4
• /
• pp.671-684
• /
• 2021

The tenacity of the current paper is to find connections between various subclasses of analytic univalent functions by applying certain convolution operator involving generalized hypergeometric distribution series. To be more specific, we examine such connections with the classes of analytic univalent functions k - 𝓤𝓒𝓥^* (𝛽), k - 𝓢^*_p (𝛽), 𝓡 (𝛽), 𝓡^𝜏 (A, B), k - 𝓟𝓤𝓒𝓥^* (𝛽) and k - 𝓟𝓢^*_p (𝛽) in the open unit disc 𝕌.