• The Pure and Applied Mathematics
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• v.19 no.2
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• pp.87-102
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• 2012

In this paper, we consider the Fourier-type functionals introduced in [16]. We then establish the analytic Feynman integral for the Fourier-type functionals. Further, we get a series expansion of the analytic Feynman integral for the Fourier-type functional $[{\Delta}^kF]^{\^}$. We conclude by applying our series expansion to several interesting functionals.

• East Asian mathematical journal
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• v.29 no.5
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• pp.467-479
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• 2013

We develop a Fourier-Feynman theory for Fourier-type functionals ${\Delta}^kF$ and $\widehat{{\Delta}^kF}$ on Wiener space. We show that Fourier-Feynman transform and convolution of Fourier-type functionals exist. We also show that the Fourier-Feynman transform of the convolution product of Fourier-type functionals is a product of Fourier-Feynman transforms of each functionals.

• Bulletin of the Korean Mathematical Society
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• v.49 no.3
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• pp.609-619
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• 2012

In this paper we define the Fourier-type functionals via the Fourier transform on Wiener space. We investigate some properties of the Fourier-type functionals. Finally, we establish integral transform of the Fourier-type functionals which also can be expressed by other Fourier-type functionals.

• Honam Mathematical Journal
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• v.27 no.3
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• pp.421-429
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• 2005

Generalizing the results in [7] that considers several functional equations in the spaces of the Schwartz tempered distributions and the Fourier hyperfunctions we consider Pexider type functional equations in the space of distributions.

• Journal of the Korean Mathematical Society
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• v.50 no.2
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• pp.259-274
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• 2013

In this paper, we consider the Fourier-type functionals on Wiener space. We then establish the analytic Feynman integrals involving the ${\diamond}$-convolutions. Further, we give an approach to solution of the Schr$\ddot{o}$dinger equation via Fourier-type functionals. Finally, we use this approach to obtain solutions of the Schr$\ddot{o}$dinger equations for harmonic oscillator and double-well potential. The Schr$\ddot{o}$dinger equations for harmonic oscillator and double-well potential are meaningful subjects in quantum mechanics.

• The Pure and Applied Mathematics
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• v.28 no.4
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• pp.281-296
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• 2021

In this paper, we suggest a representation for an inverse transform of the generalized Fourier-Feynman transform on the function space C_a,b[0, T]. The function space C_a,b[0, T] is induced by the generalized Brownian motion process with mean function a(t) and variance function b(t). To do this, we study the generalized Fourier-Feynman transform associated with the Gaussian process Ƶ_k of exponential-type functionals. We then establish that a composition of the Ƶ_k-generalized Fourier-Feynman transforms acts like an inverse generalized Fourier-Feynman transform.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.1
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• pp.79-99
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• 2006

In this paper, we define a class of functional defined on a very general function space $C_{a,b}[0,T]$ like a Fresnel class of an abstract Wiener space. We then define the multiple $L_p$ analytic generalized Fourier-Feynman transform and the generalized convolution product of functionals on function space $C_{a,b}[0,T]$. Finally, we establish some relationships between the multiple $L_p$ analytic generalized Fourier-Feynman transform and the generalized convolution product for functionals in $\mathcal{F}(C_{a,b}[0,T])$.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.3
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• pp.361-370
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• 2008

We consider the Hyers-Ulam type stability of the Cauchy, Jensen, Pexider, Pexider-Jensen differences: $$(0.1){\hspace{55}}C(u):=u{\circ}A-u{\circ}P_1-u{\circ}P_2,\\(0.2){\hspace{55}}J(u):=2u{\circ}\frac{A}{2}-u{\circ}P_1-u{\circ}P_2,\\(0.3){\hspace{18}}P(u,v,w):=u{\circ}A-v{\circ}P_1-w{\circ}P_2,\\(0.4)\;JP(u,v,w):=2u{\circ}\frac{A}{2}-v{\circ}P_1-w{\circ}P_2$$, with respect to bounded distributions.

• 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.

• Macromolecular Research
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• v.16 no.1
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• pp.21-30
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• 2008

Based on the sheath-core bicomponent composite fibers with modified polystyrene (PS) and the modified polypropylene (PP), composite fibers obtained were further cross-linked and sulphonated with chlorosulphonic acid to produce strong acidic cation ion exchange fibers. The structures of the fibers obtained were characterized using Fourier transform infrared (FT-IR) spectroscopy, differential scanning calorimetry (DSC) etc. The optimal technology of the fibers obtained is discussed. The static absorption capacity of the sheath-core bicomponent composite cation exchange fibers for $Zn^{2+}$, $Cu^{2+}$ was determined. The absorption kinetics and major factors affecting the absorption capacities of $Zn^{2+}$, $Cu^{2+}$ were studied, and its chemical stability and regenerating properties were probed. The results suggest that cation exchange fibers with better mechanical properties and higher exchange capability were obtained. Moreover, this type of ion exchange fiber has good absorption properties and working stability to various metal ions. Hence, they have higher practicability.