• 호남수학학술지
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• 제32권4호
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• pp.537-544
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• 2010

We prove the superstability of a functional inequality associated with general exponential functions as follows; ${\mid}f(x+y)-a^{x^2y+xy^2}g(x)f(y){\mid}{\leq}H_p(x,y)$. It is a generalization of the superstability theorem for the exponential functional equation proved by Baker.

• Nonlinear Functional Analysis and Applications
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• 제26권1호
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• pp.71-81
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• 2021

The main object of this present paper is to study some majorization problems for certain classes of analytic functions defined by means of q-calculus operator associated with exponential function.

• 대한수학회논문집
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• 제38권4호
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• pp.1141-1151
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• 2023

Let C_a,b[0, T] denote the space of continuous sample paths of a generalized Brownian motion process (GBMP). In this paper, we study the structures which exist between the analytic generalized Fourier-Feynman transform (GFFT) and the generalized convolution product (GCP) for functions on the function space C_a,b[0, T]. For our purpose, we use the exponential type functions on the general Wiener space C_a,b[0, T]. The class of all exponential type functions is a fundamental set in L₂(C_a,b[0, T]).

• 대한수학회논문집
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• 제38권1호
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• pp.163-178
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• 2023

We use the theory of differential subordination to explore various inequalities that are satisfied by an analytic function p defined on the unit disc so that the function p is subordinate to the function e^z. These results are applied to find sufficient conditions for the normalised analytic functions f defined on the unit disc to satisfy the subordination zf'(z)/f(z) ≺ e^z.

• Korean Journal of Mathematics
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• 제30권2호
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• pp.199-203
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• 2022

Let f(z) be an entire function of exponential type τ such that ║f║ = 1. Also suppose, in addition, that f(z) ≠ 0 for ℑz > 0 and that $h_f(\frac{\pi}{2})=0$. Then, it was proved by Gardner and Govil [Proc. Amer. Math. Soc., 123(1995), 2757-2761] that for y = ℑz ≤ 0 $${\parallel}D_{\zeta}[f]{\parallel}{\leq}\frac{\tau}{2}({\mid}{\zeta}{\mid}+1)$$, where D_ζ[f] is referred to as polar derivative of entire function f(z) with respect to ζ. In this paper, we prove an inequality in the opposite direction and thereby obtain some known inequalities concerning polynomials and entire functions of exponential type.

• Journal of Information Science Theory and Practice
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• 제1권3호
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• pp.6-11
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• 2013

A new explanation, using exponential functions, is given for the S-shaped functional relation between the mean citation score and the proportion of top 10% (and other percentages) publications for the 500 Leiden Ranking universities. With this new model we again obtain an explanation for the concave or convex relation between the proportion of top $100{\theta}%$ publications, for different fractions of ${\theta}$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권4호
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• pp.363-372
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• 2010

In this paper we obtain the Hyers-Ulam stability of functional equations $f(x+y)=f(x)+f(y)+In\;{\alpha}^{2xy-1}$ and $f(x+y)=f(x)+f(y)+In\;{\beta(x,y)^{-1}$ which is related to the exponential and beta functions.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제19권2호
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• pp.193-198
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• 2012

We show that every unbounded approximate Pexiderized exponential type function has the exponential type. That is, we obtain the superstability of the Pexiderized exponential type functional equation $$f(x+y)=e(x,y)g(x)h(y)$$. From this result, we have the superstability of the exponential functional equation $$f(x+y)=f(x)f(y)$$.

• 융합신호처리학회논문지
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• 제10권1호
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• pp.60-65
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• 2009

본 논문에서는 Chebychev 항등식과 Bessel 계수로부터 유도 될 수 있는 새로운 지수펄스모형함수를 제안하고 그 특성을 고찰한다. 제안된 지수펄스모형함수는 매개변수 변화에 따라 시간과 주파수영역에서 서로 다른 특성을 갖는 다양한 펄스 모형함수를 발생시킬 수 있다. 그리고 지수펄스모형함수의 미분함수로부터 여러 형태를 갖는 새로운 펄스모형함수를 얻을 수 있다. 미분으로부터 얻어지는 지수펄스함수의 짝수 계와 홀수 계 미분 함수간은 직교성을 유지한다. 이러한 기본적인 특성을 통상적인 Gaussian 펄스 모형함수와 비교 분석함으로써 그 유용성을 확인한다. 통신시스템의 요구 설계조건에 따라 최적의 지수펄스파형을 선택하여 사용할 수 있다.

• 대한수학회논문집
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• 제37권4호
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• pp.1041-1053
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• 2022

In this paper, sharp lower and upper bounds on the third order Hermitian-Toeplitz determinant for the classes of Sakaguchi functions and some of its subclasses related to right-half of lemniscate of Bernoulli, reverse lemniscate of Bernoulli and exponential functions are investigated.