• International Journal of Fuzzy Logic and Intelligent Systems
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• v.5 no.2
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• pp.164-168
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• 2005

As a generalization of the notions of fuzzy $\alpha-irresolute$, fuzzy preirresolute, fuzzy irresolute and fuzzy $\beta-irresolute$ functions, we introduce the notion of fuzzy $\beta\alpha-continuous$ functions and investigate the relationships between fuzzy $\beta\alpha-continuous$ functions and fuzzy separation axioms.

• Journal of Applied and Pure Mathematics
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• v.4 no.5_6
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• pp.269-286
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• 2022

In this article we exhibit univariate and multivariate quantitative approximation by Kantorovich-Choquet type quasi-interpolation neural network operators with respect to supremum norm. This is done with rates using the first univariate and multivariate moduli of continuity. We approximate continuous and bounded functions on ℝ^N , N ∈ ℕ. When they are also uniformly continuous we have pointwise and uniform convergences. Our activation functions are induced by the arctangent, algebraic, Gudermannian and generalized symmetrical sigmoid functions.

• Journal of the Korean Mathematical Society
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• v.52 no.1
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• pp.177-190
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• 2015

Let X be a completely regular Hausdorff space, and E and F be Banach spaces. Let $C_{rc}(X,E)$ be the Banach space of all continuous functions $f:X{\rightarrow}E$ such that f(X) is a relatively compact set in E. We establish an integral representation theorem for bounded linear operators $T:C_{rc}(X,E){\rightarrow}F$. We characterize continuous operators from $C_{rc}(X,E)$, provided with the strict topologies ${\beta}_z(X,E)$ ($z={\sigma},{\tau}$) to F, in terms of their representing operator-valued measures.

• East Asian mathematical journal
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• v.24 no.4
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• pp.317-328
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• 2008

In this paper we introduce ${\pi}G{\alpha}$-LC sets, ${\pi}G{\alpha}-LC^*$ sets and ${\pi}G{\alpha}-LC^{**}$ sets and different notions of generalizations of continuous functions in topological space and discuss some of their properties. Further we prove pasting lemma for ${\pi}G{\alpha}-LC^{**}$ continuous functions and ${\pi}G{\alpha}-LC^{**}$ irresolute functions.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.3
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• pp.263-269
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• 1999

In this paper, an unifying design algorithm is presented for efficient digital implementation of continuous PID controller using general discrete orthogonal functions. The proposed algorithm is an algebraic method to determine controller parameters, which can unify controller design procedures divided into three ways. A set of linear equations for the controller design are derived from simple algebraic transformation based on general discrete orthogonal functions. By solving these equations, all of the controller parameters can be determined directly and simultaneously, which thus makes the design procedure systematic and straightforward. It does not involve any trial and error procedure, hence the difficulty of conventional approach can be avoided. The simulation results and discussions are given to demonstrate the efficiency of the proposed method.

• The Pure and Applied Mathematics
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• v.9 no.1
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• pp.39-45
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• 2002

In this paper, we study the space of almost continuous functions with the topology of uniform convergence. And we investigate some properties of this space.

• Bulletin of the Korean Mathematical Society
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• v.48 no.5
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• pp.1105-1109
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• 2011

We establish a result concerning simultaneous approximation and interpolation from certain uniformly dense subsets of the space of vector-valued continuous functions vanishing at infinity on locally compact Hausdorff spaces.

• Bulletin of the Korean Mathematical Society
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• v.39 no.4
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• pp.543-559
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• 2002

Some inequalities and approximations for the finite filbert transform by the use of Ostrowski type inequalities for absolutely continuous functions are given.

• Bulletin of the Korean Mathematical Society
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• v.46 no.2
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• pp.359-365
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• 2009

We prove a universality theorem from which we deduce the existence of $H{\ddot{o}}lder$ continuous universal primitives in the sense of Marcinkiewicz.

• Bulletin of the Korean Mathematical Society
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• v.42 no.2
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• pp.213-230
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• 2005

Companions of Ostrowski's integral inequality for absolutely continuous functions and applications for composite quadrature rules and for p.d.J.'s are provided.