• Korean Journal of Mathematics
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• v.30 no.2
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• pp.231-238
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• 2022

In this paper we prove some results by using a simple but elegant techniques to improve and strengthen some generalizations and refinements of two widely known polynomial inequalities and thereby deduce some useful corollaries.

• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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• pp.903-920
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• 2022

In this paper, we propose and study an implicit iteration process for a finite family of total asymptotically quasi-nonexpansive mappings and a finite family of asymptotically quasi-nonexpansive mappings in the intermediate sense in convex metric spaces and establish some strong convergence results. Also, we give some applications of our result in the setting of convex metric spaces. The results of this paper are generalizations, extensions and improvements of several corresponding results.

• Journal of the Korean Mathematical Society
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• v.60 no.1
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• pp.71-90
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• 2023

We construct generalized Cauchy-Riemann equations of the first order for a pair of two ℝ-valued functions to deform a minimal graph in ℝ³ to the one parameter family of the two dimensional minimal graphs in ℝ⁴. We construct the two parameter family of minimal graphs in ℝ⁴, which include catenoids, helicoids, planes in ℝ³, and complex logarithmic graphs in ℂ². We present higher codimensional generalizations of Scherk's periodic minimal surfaces.

• Kyungpook Mathematical Journal
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• v.63 no.1
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• pp.15-27
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• 2023

A purely extending module is a generalization of an extending module. In this paper, we study several properties of purely extending modules and introduce the notion of purely essentially Baer modules. A module M is said to be a purely essentially Baer if the right annihilator in M of any left ideal of the endomorphism ring of M is essential in a pure submodule of M. We study some properties of purely essentially Baer modules and characterize von Neumann regular rings in terms of purely essentially Baer modules.

• Nonlinear Functional Analysis and Applications
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• v.28 no.2
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• pp.311-335
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• 2023

Fixed point theory is the center of focus for many mathematicians from last few decades. A lot of generalizations of the Banach contraction principle have been established. In this paper, we introduce the concepts of 𝜃-contraction and 𝜃-𝜑-contraction in quasi-metric spaces to study the existence of the fixed point for them.

• Honam Mathematical Journal
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• v.45 no.2
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• pp.269-284
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• 2023

In this paper we study generalizations of the concept of pure-direct-projectivity from module categories to Grothendieck categories. We examine for which categories or under what conditions pure-direct-projective objects are direct-projective, quasi-projective, pure-projective, projective and flat. We investigate classes all of whose objects are pure-direct-projective. We give applications of some of the results to comodule categories.

• Journal of the Korean Mathematical Society
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• v.61 no.2
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• pp.207-226
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• 2024

In this paper, the weighted L^p boundedness of multilinear commutators and multilinear iterated commutators generated by the multilinear singular integral operators with generalized kernels and BMO functions is established, where the weight is multiple weight. Our results are generalizations of the corresponding results for multilinear singular integral operators with standard kernels and Dini kernels under certain conditions.

• Nonlinear Functional Analysis and Applications
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• v.29 no.1
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• pp.99-111
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• 2024

In this paper, a new seven-parameter Mittag-Leffler function of a single complex variable is proposed as a generalization of the standard Mittag-Leffler function, certain generalizations of Mittag-Leffler function, hypergeometric function and confluent hypergeometric function. Certain essential analytic properties are mainly discussed, such as radius of convergence, order, type, differentiation, Mellin-Barnes integral representation and Euler transform in the complex plane. Its relation to Fox-Wright function and H-function is also developed.

• The Pure and Applied Mathematics
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• v.31 no.2
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• pp.235-249
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• 2024

We obtain a structured class of frames in separable Hilbert spaces which are generalizations of Gabor frames in L²(ℝ) in their construction aspects. For this, the concept of Gabor type unitary systems in [13] is generalized by considering a system of invertible operators in place of unitary systems. Pseudo Gabor like frames and pseudo Gabor frames are introduced and the corresponding frame operators are characterized.

• Animal cells and systems
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• v.6 no.3
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• pp.187-193
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• 2002

It has long been recognized that exposure to low levels of toxic chemicals could have beneficial effects, such as increased resistance to related chemicals or stimulation of growth or development. The notion of radiation hormesis, that exposure to low levels of ionizing radiation could produce beneficial effects, developed seriously in the late 1950’s, and was, to most radiation scientists, incredible. This was due in pan to the then prevailing ideas of radiobiological mechanisms, in part to the sweeping generalizations made by the leading proponents of the radiation hormesis concept, and in pan to the many failures to confirm reports of beneficial effects. More recent understanding of the mechanisms of radiation damage and repair, and discoveries of induction of gene expression by radiation and other genotoxic agents [the adaptive response] make it seem inevitable that under suitable conditions, irradiation will produce beneficial effects.