• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1111-1126
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• 2023

In this paper, we define a new subclass of k-uniformly starlike functions of order γ (0 ≤ γ < 1) by using certain generalized q-integral operator. We explore geometric interpretation of the functions in this class by connecting it with conic domains. We also investigate q-sufficient coefficient condition, q-Fekete-Szegö inequalities, q-Bieberbach-De Branges type coefficient estimates and radius problem for functions in this class. We conclude this paper by introducing an analogous subclass of k-uniformly convex functions of order γ by using the generalized q-integral operator. We omit the results for this new class because they can be directly translated from the corresponding results of our main class.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 1999.05a
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• pp.141-146
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• 1999

A new method, so called MMA(Method of Moving Asymptotes) was applied to the optimization problems of non-linear functions and non-linear structures. In each step of the iterative process, tile MMA generates a strictly convex approximation subproblems and solves them by using the dual problems. The generation of these subproblems is controlled by so called 'moving asymptotes', which may both make no oscillation and speed up tile convergence rate of optimization process. By contrast in generalized dual function, the generated function by MMA is always explicit type. Both the objective and behaviour constraints which were approximated are optimized by dual function. As the results of some examples, it was found that this method is very effective to obtain the global solution for problems with many local solutions. Also it was found that MMA is a very effective approximate method using the original function and its 1st derivatives.

• Interaction and multiscale mechanics
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• v.6 no.2
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• pp.137-156
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• 2013

In this paper, a meshfree shell adaptive procedure is developed for the applications in the sheet metal forming simulation. The meshfree shell formulation is based on the first-order shear deformable shell theory and utilizes the degenerated continuum and updated Lagrangian approach for the nonlinear analysis. For the sheet metal forming simulation, an h-type adaptivity based on the meshfree background cells is considered and a geometric error indicator is adopted. The enriched nodes in adaptivity are added to the centroids of the adaptive cells and their shape functions are computed using a first-order generalized meshfree (GMF) convex approximation. The GMF convex approximation provides a smooth and non-negative shape function that vanishes at the boundary, thus the enriched nodes have no influence outside the adapted cells and only the shape functions within the adaptive cells need to be re-computed. Based on this concept, a multi-level refinement procedure is developed which does not require the constraint equations to enforce the compatibility. With this approach the adaptive solution maintains the order of meshfree approximation with least computational cost. Two numerical examples are presented to demonstrate the performance of the proposed method in the adaptive shell analysis.

• Bulletin of the Korean Mathematical Society
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• v.47 no.4
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• pp.675-685
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• 2010

In this paper, we consider a new class of regularized (nonconvex) generalized mixed variational inequality problems in real Hilbert space. We give the concepts of partially relaxed strongly mixed monotone and partially relaxed strongly $\theta$-pseudomonotone mappings, which are extension of the concepts given by Xia and Ding [19], Noor [13] and Kazmi et al. [9]. Further we use the auxiliary principle technique to suggest a two-step iterative algorithm for solving regularized (nonconvex) generalized mixed variational inequality problem. We prove that the convergence of the iterative algorithm requires only the continuity, partially relaxed strongly mixed monotonicity and partially relaxed strongly $\theta$-pseudomonotonicity. The theorems presented in this paper represent improvement and generalization of the previously known results for solving equilibrium problems and variational inequality problems involving the nonconvex (convex) sets, see for example Noor [13], Pang et al. [14], and Xia and Ding [19].

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

• Nonlinear Functional Analysis and Applications
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• v.26 no.5
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• pp.887-902
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• 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
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• v.32 no.1
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• pp.47-59
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• 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.

• Journal of the Korea Safety Management & Science
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• v.16 no.2
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• pp.217-230
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• 2014

The purpose of this study is to develop the Generalized Depreciation Function (GDF) and Winfrey Depreciation Function (WDF) by reviewing methods for the depreciation accountings. The Depreciation Accounting Models (DAM), including straight-line model, declining-balance model, sum-of-the-year-digit model and sinking fund model presented in this paper, are reclassified into the charging pattern of increasing type, decreasing type and constant type. This paper also discusses the development of the GDFs based on convex type, concave type and constant type according to the demand pattern of product, frequency of plant usage, deterioration of time, relative inadequacy, Capital Expenditure (CAPEX) and Operating Expenditure (OPEX) of the Total Productive Maintenance (TPM). The WDFs presented in this paper depict a sudden degradation of plant performance by measuring the change of TPM activity at the midpoint of useful life of asset. The WDFs are classified into left-modal type, symmetrical type and right-modal type by varying the value of skewness and kurtosis. Moreover, three increasing patterns, such as convex, concave and linear types, are used in this paper to present the distinct identification of WFDs by using Instantaneous Depreciation Rate (IDR) in terms of Performance Depreciation Function (PDF) and Depreciation Density Function (DDF). In order to have better understanding of depreciation models, the numerical examples are used for evaluating the Net Operating Less Adjusted Tax (NOPLAT) and Economic Value Added (EVA). It is concluded that the depreciation models showing a large dispersion of EVA require the adjustment of NOPLAT and Invested Capital (IC) based on the objective cash basis and net operating activity for reducing the variation of EVA.

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

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