• Nonlinear Functional Analysis and Applications
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• 제29권2호
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• pp.361-391
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• 2024

In this paper, a pair of ω-compatible self mappings in the setting of modular G-metric space is defined. We prove the existence and uniqueness of common fixed point of pairs of ω-compatible self mappings in a G-complete modular G-metric space. Furthermore, we give an example to justify our claims. The results established in this paper extend, improve, generalize and complement some existing results in literature.

• 한국주거학회논문집
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• 제16권1호
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• pp.65-72
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• 2005

With the changing consciousness of community people and the rising standard of living, there has recently been an emphasis on the creation of public facilities' new functions and their role as local community facilities. This changing trends are accordingly requiring a change in spatial structure of the public facilities. In this study, an analysis was conducted with 24 public facilities situated in the Buk-gu district of Daegu to identify the adequacy of their space scale after functional variation. The results of this study are summarized as follows. 1) The site area of public facilities has been being widened after functional variation since more spaces are needed to provide an outdoor resting space with community people, expand a parking space, and operate a community center. 2) The factors that had a direct effect on the change in the use of space are the reduced space for administrative work and the expanded scope of the community center's function. Specifically, the areas of activities for civil service and administrative work and for reserve forces have been reduced due to reduction of function, and floor division by each function group has been becoming stricter due to addition of a community center's function. 3) It was shown that in terms of the space for functions of public facilities, spaces for civil service and waiting have increased mostly after function variation. After functional variation, the scale of spaces for civil service and administrative work has been being planned within the range of $200\~300 m^2$, regardless of the number of population to be covered by public facilities. 4) The space for public use is showing the greatest increase in public facilities which have been built after functional variation. The major factors seem to be the increased moving passages, the expanded convenient facilities for community people, and the increased convenient facilities for disabled. Facilities scale plans have been being made more systematically, compared to the conventional facilities.

• 충청수학회지
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• 제20권2호
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• pp.173-182
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• 2007

In this paper, we prove the Cauchy-Rassias stability of derivations on quasi-Banach algebras associated to the Cauchy functional equation and the Jensen functional equation. We use the Cauchy-Rassias inequality that was first introduced by Th. M. Rassias in the paper "On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300".

• 충청수학회지
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• 제26권4호
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• pp.887-900
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• 2013

In this paper, we investigate the stability for the functional equation f(3x+y)-3f(2x+y)+3f(x+y)-f(y)=0 in the sense of M. S. Moslehian and Th. M. Rassias.

• 호남수학학술지
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• 제30권1호
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• pp.185-195
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• 2008

We consider a system of trigonometric functional equations in the spaces of generalized functions such as Schwartz distributions and Gelfand generalized functions. As a consequence we find locally integrable solutions of the n-dimensional trigonometric functional equation.

• 한국수학교육학회지시리즈B:순수및응용수학
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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.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제29권2호
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• pp.189-199
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• 2022

In this paper, we introduce a new generalized (a, b)-cubic Euler-Lagrange-Jensen functional equation and obtain its general solution. Furthermore, we prove the Hyers-Ulam stability of the new generalized (a, b)-cubic Euler-Lagrange-Jensen functional equation in orthogonality normed spaces.

• Journal of applied mathematics & informatics
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• 제41권3호
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• pp.469-485
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• 2023

In this paper, we investigate the Hyers-Ulam-Rassias stability for a Drygas functional equation g(u + v) + g(u - v) = 2g(u) + g(v) + g(-v) in the setting of quasi-Banach space using fixed point approach. Also, we give general results on hyperstability of a Drygas functional equation. The results obtain in this paper extend various previously known results in the setting of quasi-Banach space. Some examples are also illustrated.

• Kyungpook Mathematical Journal
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• 제59권2호
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• pp.259-275
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• 2019

The aim of this paper is to prove that Marcinkiewicz integral operators are bounded from ${\dot{K}}^{{\alpha}({\cdot}),q({\cdot})}_{p({\cdot})}({\mathbb{R}}^n)$ to ${\dot{K}}^{{\alpha}({\cdot}),q({\cdot})}_{p({\cdot})}({\mathbb{R}}^n)$ when the parameters ${\alpha}({\cdot})$, $p({\cdot})$ and $q({\cdot})$ satisfies some conditions. Also, we prove the boundedness of ${\mu}$ on variable Herz-type Hardy spaces $H{\dot{K}}^{{\alpha}({\cdot}),q({\cdot})}_{p({\cdot})}({\mathbb{R}}^n)$.

• Nonlinear Functional Analysis and Applications
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• 제26권2호
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• pp.303-322
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• 2021

The concepts of new classes of mappings are introduced in the spaces which are more general space than the usual metric spaces. The existence and uniqueness of common fixed points and fixed point results are established in the setting of complete complex valued b-metric spaces. An illustration is given by establishing the existence of solution of periodic differential equations in the framework of a complete complex valued b-metric spaces.