• Kyungpook Mathematical Journal
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• v.59 no.3
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• pp.433-443
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• 2019

In this work, we evaluate the Mellin transform of the Marichev-Saigo-Maeda fractional integral operator with Appell's function $F_3$ type kernel. We then discuss six special cases of the result involving the Saigo fractional integral operator, the $Erd{\acute{e}}lyi$-Kober fractional integral operator, the Riemann-Liouville fractional integral operator and the Weyl fractional integral operator. We obtain new and known results as special cases of our main results. Finally, we obtain the images of S-generalized Gauss hypergeometric function under the operators of our study.

• Journal of the Korean Mathematical Society
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• v.53 no.1
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• pp.147-159
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• 2016

In this paper, subordination results of analytic function $f{\in}{\mathcal{A}}_p$ involving linear operator ${\mathcal{K}}^{{\delta},{\lambda}}_{c,p}$ are obtained. By applying the differential subordination method, results are derived under some sufficient subordination conditions. On using some hypergeometric identities, corollaries of the main results are derived. Furthermore, convolution preserving properties for a class of multivalent analytic function associated with the operator ${\mathcal{K}}^{{\delta},{\lambda}}_{c,p}$ are investigated.

• Communications of the Korean Mathematical Society
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• v.36 no.2
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• pp.267-276
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• 2021

The aim of the present investigation is to establish the composition formulas for the pathway fractional integral operator connected with Hurwitz-Lerch zeta function and extended Wright-Bessel function. Some interesting special cases have also been discussed.

• Journal of the Chungcheong Mathematical Society
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• v.8 no.1
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• pp.29-36
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• 1995

• Korean Journal of Mathematics
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• v.29 no.2
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• pp.211-225
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• 2021

In the present paper we introduce some sequence spaces over n-normed spaces defined by fractional difference operator and Musielak-Orlicz function 𝓜 = (𝕱_i). We also study some topological properties and prove some inclusion relations between these spaces.

• East Asian mathematical journal
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• v.33 no.1
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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.

• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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• pp.465-475
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• 1996

Fix t > 0. Denote by $C^t$ the space of $R$-valued continuous functions x on [0,t]. Let $C_0^t$ be the Wiener space - $C_0^t = {x \in C^t : x(0) = 0}$ - equipped with Wiener measure m. Let F be a function from $C^t to C$.

• Bulletin of the Korean Mathematical Society
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• v.46 no.3
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• pp.439-446
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• 2009

We consider the univalence function classes T, $T_2,\;T_{2,{\mu}}$, and S(p). For these classes we shall study some univalence properties for a general integral operator. Furthermore we shall extend some known univalence criteria, i.e., Becker-type criteria.

• Journal of the Korean Mathematical Society
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• v.34 no.3
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• pp.569-579
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• 1997

We investigate the existence of the operator-valued Feynman integral when a Wiener functional is given by a Fourier transform of complex Borel measure.

• Bulletin of the Korean Mathematical Society
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• v.53 no.3
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• pp.903-924
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• 2016

In the present paper, using a simple formula for the conditional expectations given a generalized conditioning function over an analogue of vector-valued Wiener space, we prove that the analytic operator-valued Feynman integrals of certain classes of functions over the space can be expressed by the conditional analytic Feynman integrals of the functions. We then provide the conditional analytic Feynman integrals of several functions which are the kernels of the analytic operator-valued Feynman integrals.