• Journal of applied mathematics & informatics
• /
• 제16권1_2호
• /
• pp.195-205
• /
• 2004

To the unconstrained programme of non-convex function, this article give a modified BFGS algorithm. The idea of the algorithm is to modify the approximate Hessian matrix for obtaining the descent direction and guaranteeing the efficacious of the quasi-Newton iteration pattern. We prove the global convergence properties of the algorithm associating with the general form of line search, and prove the quadratic convergence rate of the algorithm under some conditions.

• Journal of applied mathematics & informatics
• /
• 제28권5_6호
• /
• pp.1239-1248
• /
• 2010

In this paper, an implementable BFGS bundle algorithm for solving a nonsmooth convex optimization problem is presented. The typical method minimizes an approximate Moreau-Yosida regularization using a BFGS algorithm with inexact function and the approximate gradient values which are generated by a finite inner bundle algorithm. The approximate subgradient of the objective function is used in the algorithm, which can make the algorithm easier to implement. The convergence property of the algorithm is proved under some additional assumptions.

• Journal of the Korean Statistical Society
• /
• 제16권1호
• /
• pp.21-25
• /
• 1987

The combined estimator of inter- and intra-block estimators in incomplete block designs can be expressed as a weighted average of two location estimators. The weight should be between 0 and 1. However, the negative variance component estimate could result in the weight being negative or larger than 1. In this paper, we show that if two location estimators have symmetric unimodal distributions, truncating the weight to 0 or 1 accordingly improves the combined estimator under an arbitrary convex loss function.

• 대한수학회보
• /
• 제37권1호
• /
• pp.127-134
• /
• 2000

Let $\Omega$ be a bounded pseudoconvex domain in$C^{n}$ with smooth defining function r and let$z_0\; {\in}\; b{\Omega}$ be a point of finite type. We also assume that $\Omega$ is convex in a neighborhood of $z_0$. Then we prove that all the holomorphic sectional curvatures of the Bergman metric of $\Omega$ are bounded below by a negative constant near $z_0$.

• Nonlinear Functional Analysis and Applications
• /
• 제26권1호
• /
• pp.1-11
• /
• 2021

In this paper we study the weak and strong convergence to minimizers of convex function of proximal point algorithm SP-iteration of three multivalued nonexpansive mappings in a Hilbert space.

• 호남수학학술지
• /
• 제44권2호
• /
• pp.244-258
• /
• 2022

In this work, by using an integral identity together with both the Hölder and the power-mean integral inequalities we establish several new inequalities for n-times differentiable arithmetic-harmonically-convex function. Then, using this inequalities, we obtain some new inequalities connected with means. In special cases, the results obtained coincide with the well-known results in the literature.

• Nonlinear Functional Analysis and Applications
• /
• 제28권1호
• /
• pp.81-93
• /
• 2023

By utilizing a certain Libera integral operator considered on analytic multivalent functions in the unit disk U. Using the hypergeometric function and the Libera integral operator, we included a new convolution operator that expands on some previously specified operators in U, which broadens the scope of certain previously specified operators. We introduced and investigated the properties of new subclasses of functions f (z) ∈ A_p using this operator.

• Korean Journal of Mathematics
• /
• 제32권3호
• /
• pp.453-466
• /
• 2024

In the present paper, we define the class of (h₁, h₂, h₂)-preinvex functions on co-ordinates and prove certain new Hermite-Hadamard and Fejér type inequalities for such mappings. As a consequence, we derive analogous Hadamard-type results on convex and s-convex functions in three co-ordinates. We also discuss some intriguing aspects of the associated H function.

• 대한수학회논문집
• /
• 제22권1호
• /
• pp.111-119
• /
• 2007

We consider the growth norm of a measurable function f defined by defined by $${\parallel}f{\parallel}-\sigma=ess\;sup\{\delta_D(z)^\sigma{\mid}f(z)\mid:z{\in}D\}$$, where $\delta_D(z)$ denote the distance from z to ${\partial}D$. We prove some kind of optimal growth norm estimates for a on convex domains.

• 대한수학회논문집
• /
• 제35권3호
• /
• pp.789-797
• /
• 2020

By considering a certain univalent function in the open unit disk 𝕌, that maps 𝕌 onto a strip domain, we introduce a new class of analytic and close-to-convex functions by means of a certain non-homogeneous Cauchy-Euler-type differential equation. We determine the coefficient bounds for functions in this new class. Relevant connections of some of the results obtained with those in earlier works are also provided.