Topics in Uniform Approximation of Continuous Functions

Bucur, Ileana; Paltineanu, Gavriil

doi:10.1007/978-3-030-48412-5

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2024

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Cited by 9 publications

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“…A nice account on the present state of art is offered by the authoritative monograph of F. Altomare and M. Campiti [2] and the excellent survey of F. Altomare [1]. See also [4].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear versions of Korovkin's abstract theorems

Gal¹,

Niculescu²

2021

Preprint

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“…A nice account on the present state of art is offered by the authoritative monograph of F. Altomare and M. Campiti [2] and the excellent survey of F. Altomare [1]. See also [4].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear versions of Korovkin's abstract theorems

Gal¹,

Niculescu²

2021

Preprint

View full text Add to dashboard Cite

show abstract

On the Dual of a Weighted Space of Vector Functions and Some Approximation Results

Bucur

Paltineanu

2023

Mediterr. J. Math.

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A New Look on Korovkin Theorem

Bucur

2024

Mediterr. J. Math.

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Giving a sequence $$P=(P_{n})_{n}$$ P = ( P n ) n of kernels on a measurable space (or just a semigroup $$(P_{t})_{t\in (0,\infty )}$$ ( P t ) t ∈ ( 0 , ∞ ) ), we are interested to describe the “semi-excessive” functions w.r. to P, i.e., measurable functions f, such that $$\lim \nolimits _{n\rightarrow \infty } P_{n}(f)=f$$ lim n → ∞ P n ( f ) = f (or $$\lim \nolimits _{t\rightarrow 0} P_{t}(f)=f$$ lim t → 0 P t ( f ) = f ). We extend in this frame the famous Korovkin result on the uniform convergence of $$P_{n}(f)$$ P n ( f ) to f on a class of measurable functions f, but beside that, we give a pointwise convergence result which may be a useful tool in Probabilistic Potential Theory as well Right Processes.

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Topics in Uniform Approximation of Continuous Functions

Cited by 9 publications

References 0 publications

Nonlinear versions of Korovkin's abstract theorems

Nonlinear versions of Korovkin's abstract theorems

On the Dual of a Weighted Space of Vector Functions and Some Approximation Results

A New Look on Korovkin Theorem

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