• Honam Mathematical Journal
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• v.39 no.4
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• pp.575-590
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• 2017

A new class of functions called $R_{\theta}$-supercontinuous functions is introduced. Their basic properties are studied and their place in the hierarchy of strong variants of continuity, which already exist in the literature, is elaborated. The class of $R_{\theta}$-supercontinuous functions properly contains the class of $R_z$-supercontinuous functions [39] which in turn properly contains the class of $R_{cl}$-supercontinuous functions [43] and so includes all cl-supercontinuous (clopen continuous) functions ([38], [34]) and is properly contained in the class of $R_{\delta}$-supercontinuous functions [24].

• Communications of the Korean Mathematical Society
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• v.36 no.4
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• pp.651-669
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• 2021

In this paper, we investigate some basic results on the slice regular Besov spaces of hyperholomorphic functions on the unit ball 𝔹. We also characterize the boundedness, compactness and find the essential norm estimates for composition operators between these spaces.

• Nonlinear Functional Analysis and Applications
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• v.23 no.1
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• pp.63-72
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• 2018

We consider general base i_α and j_β which perform the roles of i and j do in quaternions. We give a representation and properties of a Fourier transformation of regular functions with values in generalized quaternions, referring the Fourier transformation using quaternions.

• Honam Mathematical Journal
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• v.37 no.4
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• pp.569-575
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• 2015

In this paper, we research some properties of quaternionic regular functions in Clifford analysis. We investigate the corresponding Cauchy-Riemann system and find regularities of some hypercomplex valued functions.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1401-1409
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• 2016

In complex analysis, the Bergman kernels for two biholomorphically equivalent complex domains satisfy the transformation formula. Recently new Bergman theory of slice regular functions of the quaternion variables has been investigated. In this paper we construct the transformation formula of the slice Bergman kernels under slice biregular functions in the setting of the quaternion variables.

• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.507-518
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• 2016

In this paper, using forms of conjugations, we give some algebraic properties of bicomplex numbers. We research differential operators, elementary functions and the analogous Cauchy-Riemann system in bicomplex number systems. Also, we investigate the definition and properties of regular functions with values in bicomplex settings in Clifford analysis.

• Bulletin of the Korean Mathematical Society
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• v.59 no.6
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• pp.1327-1337
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• 2022

Zero-difference balanced (ZDB) functions can be applied to many areas like optimal constant composition codes, optimal frequency hopping sequences etc. Moreover, it has been shown that the image set of some ZDB functions is a regular partial difference set, and hence provides strongly regular graphs. Besides, perfect nonlinear functions are zero-difference balanced functions. However, the converse is not true in general. In this paper, we use the decomposition of cyclotomic polynomials into irreducible factors over 𝔽_p, where p is an odd prime to generalize some recent results on ZDB functions. Also we extend a result introduced by Claude et al. [3] regarding zero-difference-p-balanced functions over 𝔽_pⁿ. Eventually, we use these results to construct some optimal constant composition codes.

• The Pure and Applied Mathematics
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• v.3 no.2
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• pp.103-111
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• 1996

Let $f(z)=z＋\alpha_2 z^2$＋…＋ \alpha_{n}z^n$＋… be regular and univalent in $\Delta$ = {z : │z│＜1}. In this paper, using the proper subordinate functions, we investigate the some relations between subordinations and conditions of functions belonging to subclasses of univalent functions.

• Bulletin of the Korean Mathematical Society
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• v.47 no.5
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• pp.1025-1036
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• 2010

A new class of generalized open sets in a topological space, called e-open sets, is introduced and some properties are obtained by Ekici [6]. This class is contained in the class of $\delta$-semi-preopen (or $\delta-\beta$-open) sets and weaker than both $\delta$-semiopen sets and $\delta$-preopen sets. In order to investigate some different properties we introduce two strong form of e-open sets called e-regular sets and e-$\theta$-open sets. By means of e-$\theta$-open sets we also introduce a new class of functions called strongly $\theta$-e-continuous functions which is a generalization of $\theta$-precontinuous functions. Some characterizations concerning strongly $\theta$-e-continuous functions are obtained.

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1299-1307
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• 2023

In this paper, we attempt to study several topological properties for the function space H(X), space of self-homeomorphisms on a metric space endowed with the regular topology. We investigate its metrizability and countability and prove their coincidence at X compact. Furthermore, we prove that the space H(X) endowed with the regular topology is a topological group when X is a metric, almost P-space. Moreover, we prove that the homeomorphism spaces of increasing and decreasing functions on ℝ under regular topology are open subspaces of H(ℝ) and are homeomorphic.