• 대한수학회보
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• 제56권4호
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• pp.939-959
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• 2019

Using generalized graded crossed products, we give necessary and sufficient conditions for a simple algebra over a Henselian valued field (under some hypotheses) to have Kummer subfields. This study generalizes some known works. We also study many properties of generalized graded crossed products and conditions for embedding a graded simple algebra into a matrix algebra of a graded division ring.

• Communications for Statistical Applications and Methods
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• 제26권3호
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• pp.305-313
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• 2019

Generalized canonical correlation analysis (GCCA) extends the canonical correlation analysis (CCA) to the case of more than two sets of variables and there have been many studies on how two-set canonical solutions can be generalized. In this paper, we derive certain stationary equations which can lead the higher-order solutions of several GCCA methods and suggest a type of iterative procedure to obtain the canonical coefficients. In addition, with some numerical examples we present the methods for graphical display, which are useful to interpret the GCCA results obtained.

• 대한수학회보
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• 제56권5호
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• pp.1099-1115
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• 2019

In the present paper, we establish certain $L^p$ bounds for the generalized parametric Marcinkiewicz integral operators associated to surfaces generated by polynomial compound mappings with rough kernels in Grafakos-Stefanov class ${\mathcal{F}}_{\beta}(S^{n-1})$. Our main results improve and generalize a result given by Al-Qassem, Cheng and Pan in 2012. As applications, the corresponding results for the generalized parametric Marcinkiewicz integral operators related to the Littlewood-Paley $g^*_{\lambda}$-functions and area integrals are also presented.

• 대한수학회논문집
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• 제36권2호
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• pp.299-312
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• 2021

The main aim of this paper is to introduce and study the generalized Laguerre polynomials and prove that these polynomials are characterized by the generalized hypergeometric function. Also we investigate some properties and formulas for these polynomials such as explicit representations, generating functions, recurrence relations, differential equation, Rodrigues formula, and orthogonality.

• Korean Journal of Mathematics
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• 제29권1호
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• pp.121-136
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• 2021

In this paper we wish to prove some results relating to the growth rates of composite entire and meromorphic functions with their corresponding left and right factors on the basis of their generalized order (��, ��) and generalized lower order (��, ��), where �� and �� are continuous non-negative functions defined on (-∞, +∞).

• Nonlinear Functional Analysis and Applications
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• 제26권1호
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• pp.93-104
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• 2021

In this paper, we present a fixed point theorem for a family of generalized condensing multimaps which have ranges of the Zima-Hadžić type in Hausdorff KKM uniform spaces. It extends Himmelberg et al. type fixed point theorem. As applications, we obtain some new collective fixed point theorems for various type generalized condensing multimaps in abstract convex uniform spaces.

• Kyungpook Mathematical Journal
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• 제61권1호
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• pp.169-179
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• 2021

In this paper, we extend the definition of p-harmonic maps between two Riemannian manifolds. We prove a Liouville type theorem for generalized p-harmonic maps. We present some new properties for the generalized stress p-energy tensor. We also prove that every generalized p-harmonic map from a complete Riemannian manifold into a Riemannian manifold admitting a homothetic vector field satisfying some condition is constant.

• Nonlinear Functional Analysis and Applications
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• 제26권3호
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• pp.601-610
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• 2021

A convergence theorem for a generalized 𝜑-weakly contractive mapping is proved which satisfy a generalized contraction condition on a complete metrically convex metric space. The result in this paper generalizes the relevant results due to Rhoades [18], Alber and Guerre-Delabriere [1], Khan and Imdad [14], Xue [20] and others. An illustrative example is also furnished in support of our main result.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제28권4호
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• pp.343-353
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• 2021

In this paper, we obtain some inequalities concerning the class of generalized derivative and generalized polar derivative which are analogous respectively to the ordinary derivative and polar derivative of polynomials.

• 대한수학회논문집
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• 제37권4호
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• pp.977-988
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• 2022

The Padovan sequence is the third-order linear recurrence (𝓟_n)_n≥0 defined by 𝓟_n = 𝓟_n-2 + 𝓟_n-3 for all n ≥ 3 with initial conditions 𝓟₀ = 0 and 𝓟₁ = 𝓟₂ = 1. In this paper, we investigate a generalization of the Padovan sequence called the k-generalized Padovan sequence which is generated by a linear recurrence sequence of order k ≥ 3. We present recurrence relations, the generalized Binet formula and different arithmetic properties for the above family of sequences.