• 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.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.599-610
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• 2018

We aim to present some formulas for Saigo hypergeometric fractional integral and differential operators involving (p, q)-extended Bessel function $J_{{\nu},p,q}(z)$, which are expressed in terms of Hadamard product of the (p, q)-extended Gauss hypergeometric function and the Fox-Wright function $_p{\Psi}_q(z)$. A number of interesting special cases of our main results are also considered. Further, it is emphasized that the results presented here, which are seemingly complicated series, can reveal their involved properties via those of the two known functions in their respective Hadamard product.

• Journal of applied mathematics & informatics
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• v.36 no.3_4
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• pp.285-299
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• 2018

In this article, we present the Stancu generalization of (p, q)-$Sz{\acute{a}}sz$-Mirakyan Kantorovich type linear positive operators. Using Korovkin's result, approximation properties are investigated. First, we evaluate moments and direct results. By choosing p and q, the convergence rate have been estimated for better approximation. For the particular case ${\alpha}=0$, ${\beta}=0$ we obtain results for (p, q)-$Sz{\acute{a}}sz$-Mirakyan Kantorovich type operators.

• The Pure and Applied Mathematics
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• v.12 no.2 s.28
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• pp.125-131
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• 2005

In this paper, we introduce the concept of derivative of the function f : $\mathbb{Q}p{\to} R$ where $\mathbb{Q}p$ is the field of the p-adic numbers and R is the set of real numbers. And some basic theorems on derivatives are given.

• 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.

• Nonlinear Functional Analysis and Applications
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• v.26 no.2
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• pp.381-392
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• 2021

During the last several decades, a great variety of fractional kinetic equations involving diverse special functions have been broadly and usefully employed in describing and solving several important problems of physics and astrophysics. In this paper, we aim to find solutions of a type of fractional kinetic equations associated with the (p, q)-extended 𝜏 -hypergeometric function and the (p, q)-extended 𝜏 -confluent hypergeometric function, by mainly using the Laplace transform. It is noted that the main employed techniques for this chosen type of fractional kinetic equations are Laplace transform, Sumudu transform, Laplace and Sumudu transforms, Laplace and Fourier transforms, P_𝛘-transform, and an alternative method.

• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.275-292
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• 2015

This paper is mainly concerned with the existence of solution for nonlinear impulsive fractional dynamic equations on a special time scale.We introduce the new concept and propositions of fractional q-integral, q-derivative, and α-Lipschitz in the paper. By using a new fixed point theorem, we obtain some new existence results of solutions via some generalized singular Gronwall inequalities on time scales. Further, an interesting example is presented to illustrate the theory.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.3
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• pp.235-242
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• 2022

In this paper, we consider the existence of nonconstant warping functions on a warped product manifold M = B × _f² F, where B is a q(> 2)-dimensional base manifold with a nonconstant scalar curvature S_B(x) and F is a 3- dimensional fiber Einstein manifold and discuss that the resulting warped product manifold is an Einstein manifold, using the existence of the solution of some partial differential equation.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.29B no.7
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• pp.52-61
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• 1992

An iterative scheme for computing the three-dimensional position and the surface orientation of an opaque object from a singel shaded image is proposed. This method demonstrates that calculating the depth(distance) between the camera and the object from one shaded video image is possible. Most previous research works on $'Shape from Shading$' problem, even in the $'Photometric Stereo Method$', invoved the determination of surface orientation only. To measure the depth of an object, depth of the object, and the reflectance properties of the surface. Assuming that the object surface is uniform Lambertian the measured intensity level at a given image pixel*x,y0becomes a function of surface orientation and depth component of the object. Derived Image Irradiance Equation can`t be solved without further informations since three unknown variables(p,q and D) are in one nonlinear equation. As an additional constraints we assume that surface satisfy smoothness conditions. Then equation can be solved relaxatively using standard methods of TEX>$'Calculus of VariationTEX>$'. After checking the sensitivity of the algorithm to the errors ininput parameters, the theoretical results is tested by experiments. Three objects (plane, cylinder, and sphere)are used. Thees initial results are very encouraging since they match the theoretical calculations within 20$\%$ error in simple experiments.> error in simple experiments.

• Smart Structures and Systems
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• v.19 no.2
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• pp.195-202
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• 2017

The aim of this paper is to develop a novel method to determine the severity of a damage in a thin plate. This paper presents a novel fault detection and diagnosis approach employing a new electromagnetic acoustic transducer, called EMAT, together with a complex signal processing method. The method consists in the recognition of a fault that exists within the structure, the fault location, i.e. the identification of the geometric position of damage, and the determining the significance of the damage, which indicates the importance or severity of the defect. The main scientific novelties presented in this paper is: to develop of a new type of electromagnetic acoustic transducer; to incorporate wavelet transforms for signal representation enhancements; to investigate multi-parametric analysis for noise identification and defect classification; to study attenuation curves properties for defect localization improvement; flaw sizing and location algorithm development.