• 충청수학회지
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• 제29권3호
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• pp.385-396
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• 2016

Characterizations of probability distributions by different regression conditions on generalized order statistics has attracted the attention of many researchers. We present here, characterization of Pareto and Weibull distributions based on the conditional expectation of generalized order statistics extending the characterization results reported by Jin and Lee (2014). We also present a characterization of the power function distribution based on the conditional expectation of lower generalized order statistics.

• Kyungpook Mathematical Journal
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• 제64권2호
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• pp.219-233
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• 2024

In this paper, we study the generalized Fourier-Feynman transform (GFFT) for functions on the general Wiener space C_a,b[0, T]. We establish an explicit evaluation formula for the analytic GFFT of bounded cylinder functions on C_a,b[0, T]. We start by examining certain cylinder functions which belong in a Banach algebra of bounded functions on C_a,b[0, T]. We then obtain an explicit formula for the analytic GFFT of the bounded cylinder functions.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제4권1호
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• pp.47-60
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• 1997

In the theory of the conditional Wiener integral, the integrand is a functional of the standard Wiener process. In this paper we consider a conditional function space integral for functionals of more general stochastic process and the generalized Kac-Feynman integral equation. We first show that the existence of a partial differential equation. We then show that the generalized Kac-Feynman integral equation is equivalent to the partial differential equation.

• Kyungpook Mathematical Journal
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• 제59권2호
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• pp.325-333
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• 2019

Motivated by the results on generating functions investigated by H. Exton and many other authors, we derive certain (presumably) new generating functions for generalized Mittag-Leffler-type functions. Specifically, we introduce a new class of generating relations (which are partly bilateral and partly unilateral) involving the generalized Mittag-Leffler function. Also we present some special cases of our main result.

• Korean Journal of Mathematics
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• 제29권4호
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• pp.715-723
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• 2021

In this paper we wish to introduce the concept of generalized relative index-pair (𝛼, 𝛽) of a p-adic entire function with respect to another p-adic entire function and then prove some results relating to the growth rates of composition of two p-adic entire functions with their corresponding left and right factors.

• 호남수학학술지
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• 제39권3호
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• pp.349-361
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• 2017

By means of the Oberhettinger integral, certain generalized integral formulae involving product of generalized k-Bessel function $w^{{\gamma},{\alpha}}_{k,v,b,c}(z)$ and general class of polynomials $S^m_n[x]$ are derived, the results of which are expressed in terms of the generalized Wright hypergeometric functions. Several new results are also obtained from the integrals presented in this paper.

• 대한수학회논문집
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• 제32권3호
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• pp.601-617
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• 2017

We give a function associated with generalized Ostrowski type inequality and its integral representation for local fractional calculus. Then, using this function and its integral representation, we establish several inequalities of generalized Ostrowski type for twice local fractional differentiable functions. We also consider some special cases of the main results which are further applied to a concrete function to yield two interesting inequalities associated with two generalized means.

• Korean Journal of Mathematics
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• 제11권1호
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• pp.17-30
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• 2003

In this paper, we use a generalized Brownian motion process to define a translation theorem. First we establish the translation theorem for function space integrals. We then obtain the general translation theorem for functionals on function space.

• East Asian mathematical journal
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• 제33권1호
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• pp.83-102
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• 2017

The main purpose of this paper is to introduce a pair new class of primal and dual problem associated with an operator. We prove the sufficient optimality theorem, weak duality theorem and strong duality theorem for these problems. The equivalence between the generalized optimization problems and the generalized variational inequality problems is studied in ordered topological vector space modeled in Hilbert spaces. We introduce the concept of partial differential associated (PDA)-operator, PDA-vector function and PDA-antisymmetric function to show the existence of a new class of function called, ($T_{\eta};{\xi}_{\theta}$)-invex functions. We discuss first and second kind of ($T_{\eta};{\xi}_{\theta}$)-invex functions and establish their existence theorems in ordered topological vector spaces.

• Journal of applied mathematics & informatics
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• 제29권3_4호
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• pp.763-779
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• 2011

In this paper we apply the Exp-function method to obtain traveling wave solutions of three nonlinear partial differential equations, namely, generalized sinh-Gordon equation, generalized form of the famous sinh-Gordon equation, and double combined sinh-cosh-Gordon equation. These equations play a very important role in mathematical physics and engineering sciences. The Exp-Function method changes the problem from solving nonlinear partial differential equations to solving a ordinary differential equation. Mainly we try to present an application of Exp-function method taking to consideration rectifying a commonly occurring errors during some of recent works.