• 충청수학회지
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• 제24권3호
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• pp.409-415
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• 2011

We introduce the notion of weakly quasi generalized continuous functions, and investigate properties for the continuity.

• 호남수학학술지
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• 제32권4호
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• pp.619-624
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• 2010

We introduce the notions of bigeneralized topological spaces and quasi generalized open sets, and study some basic properties for the sets. We also introduce the notion of quasi generalized continuity on bigeneralized topological spaces, and investigate characterizations for the continuity.

• Korean Journal of Mathematics
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• 제13권2호
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• pp.241-248
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• 2005

Some of the generalized continuous functions and their basic properties are introduced in concern with the cover theory. The open property of a function is a crucial tool for the survey of this area.

• East Asian mathematical journal
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• 제26권1호
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• pp.49-58
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• 2010

In this paper, we consider and study a new class of generalized vector quasi-variational type inequalities and obtain some existence theorems for both under compact and noncompact assumptions in topological vector spaces without using monotonicity. For the noncompact case, we use the concept of escaping sequences.

• Journal of Applied and Pure Mathematics
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• 제4권3_4호
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• pp.185-209
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• 2022

Here we exhibit multivariate quantitative approximations of Banach space valued continuous multivariate functions on a box or ℝ^N, N ∈ ℕ, by the multivariate normalized, quasi-interpolation, Kantorovich type and quadrature type neural network operators. We treat also the case of approximation by iterated operators of the last four types. These approximations are achieved by establishing multidimensional Jackson type inequalities involving the multivariate modulus of continuity of the engaged function or its high order Fréchet derivatives. Our multivariate operators are defined by using a multidimensional density function induced by the generalized symmetrical sigmoid function. The approximations are point-wise and uniform. The related feed-forward neural network is with one hidden layer.