• Journal of the Chungcheong Mathematical Society
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• 제31권1호
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• pp.183-191
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• 2018

This paper deals with binary ideal topological space and discuss about generalized binary closed sets and generalized kernel in the same topological space. Further it will discuss various types of characterizations of generalized binary closed sets and generalized kernel.

• Kyungpook Mathematical Journal
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• 제55권3호
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• pp.597-614
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• 2015

In this paper, we study some properties of the generalized Apostol type Hermite-based polynomials. which extend some known results. We also deduce some properties of the generalized Apostol-Bernoulli polynomials, the generalized Apostol-Euler polynomials and the generalized Apostol-Genocchi polynomials of high order. Numerous properties of these polynomials and some relationships between $F_n{^{({\alpha})}}(x;{\lambda};{\mu};{\nu};c)$ and $_HF_n{^{({\alpha})}}(x;{\lambda};{\mu};{\nu};c)$ are established. Some implicit summation formulae and general symmetry identities are derived by using different analytical means and applying generating functions.

• Journal of the Chungcheong Mathematical Society
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• 제26권1호
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• pp.111-123
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• 2013

Cameron and Storvick discovered change of scale formulas for Wiener integrals on classical Wiener space. Yoo and Skoug extended this result to an abstract Wiener space. In this paper, we investigate a change of scale formula for generalized Wiener integrals of various functions using the generalized Fourier-Feynman transform.

• The Pure and Applied Mathematics
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• 제14권2호
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• pp.111-125
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• 2007

For an odd mapping, we study a generalized additive functional equation in Banach spaces and Banach modules over a $C^*-algebra$. And we obtain generalized solutions of a generalized additive functional equation and so generalize the Cauchy-Rassias stability.

• Communications of the Korean Mathematical Society
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• 제24권4호
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• pp.529-537
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• 2009

Generalized Menger space introduced by the present authors is a generalization of Menger space as well as a probabilistic generalization of generalized metric space introduced by Branciari [Publ. Math. Debrecen 57 (2000), no. 1-2, 31-37]. In this paper we prove a Kannan type fixed point theorem in generalized Menger spaces. We also support our result by an example.

• Kyungpook Mathematical Journal
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• 제58권4호
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• pp.781-788
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• 2018

In the present paper, we have studied the Finslerian hypersurfaces and generalized ${\beta}$-conformal change of Finsler metric. The relations between the Finslerian hypersurface and the other which is Finslerian hypersurface given by generalized ${\beta}$-conformal change have been obtained. We have also proved that generalized ${\beta}$-conformal change makes three types of hypersurfaces invariant under certain conditions.

• Communications of the Korean Mathematical Society
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• 제36권1호
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• pp.41-50
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• 2021

This paper devoted to obtain some fractional integral properties of generalized Bessel function using pathway fractional integral operator. We also find the pathway transform of the generalized Bessel function in terms of Fox H-function.

• Communications of the Korean Mathematical Society
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• 제36권2호
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• pp.239-246
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• 2021

In this article, a study of generalized Bateman's matrix polynomials is presented. We obtained partial differential equations by using differential operators in the generalized Bateman's matrix polynomials for two variables. Then we introduced some different recurrence relationships of the generalized Bateman's matrix polynomials. Finally present the relationship between the generalized Bateman's matrix polynomials of one and two variables.

• East Asian mathematical journal
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• 제25권2호
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• pp.141-146
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• 2009

In this paper, we introduce a new generalized nonlinear quasivariational inequality and establish its equivalence with a xed point problem by using the resolvent operator technique. Utilizing this equivalence, we suggest two iterative schemes, prove two existence theorems of solutions for the generalized nonlinear quasivariational inequality involving generalized cocoercive mapping and establish some convergence results of the sequences generated by the algorithms. Our results include several previously known results as special cases.

• Bulletin of the Korean Mathematical Society
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• 제60권3호
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• pp.611-622
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• 2023

The main purpose of this paper is to study the hybrid mean value problem involving generalized Dedekind sums, generalized Hardy sums and Kloosterman sums. Some exact computational formulas are given by using the properties of Gauss sums and the mean value theorem of the Dirichlet L-function. A result of W. Peng and T. P. Zhang [12] is extended. The new results avoid the restriction that q is a prime.