Optimal Recovery of Operators in Function L-Spaces

Бабенко, В. Ф.; Коваленко, О. В.; Полищук, М. В.

doi:10.1007/s10476-021-0065-y

Cited by 6 publications

(6 citation statements)

References 19 publications

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“…Observe that semi-continuity of d X,M (•, y) (see inequality ( 6)) can be substituted by a more general inequality (7) d…”

Section: Hausdorffness Conditions In Terms Of Semi-continuity Of the ...mentioning

confidence: 99%

“…Let T be a metric compact and µ be a measure defined on the σ-algebra of Borel sets of T . Let also an L-space (the definition can be found in [4,5,7,37]) (X, h X ) be given, and C(T, X) be the space of continuous functions x : T → X. In the space C(T, X) consider a C(T, R)valued metric, setting h C(T,X) (x, y) = h X (x(•), y(•)), where C(T, R) is considered as a partially ordered monoid with pointwise addition and partial order.…”

Section: Applicationsmentioning

confidence: 99%

“…In particular, we consider the questions of existence of solutions of the Fredholm integral equation in L-spaces (i.e. semi-linear metric spaces with two additional axioms, which connect the metric with the algebraic operations), see [4,5,7,37]. We obtain significantly more general than in [4] conditions for existence and uniqueness of a solution of the Fredholm integral equation.…”

Section: Introductionmentioning

confidence: 99%

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Fixed Points Theorems in Hausdorff M-distance Spaces

Бабенко¹,

Коваленко²

2021

Preprint

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We prove fixed point theorems in a space with a distance function that takes values in a partially ordered monoid. On the one hand, such an approach allows one to generalize some fixed point theorems in a broad class of spaces, including metric and uniform spaces. On the other hand, compared to the so-called cone metric spaces and K-metric spaces, we do not require that the distance function range has a linear structure. We also consider several applications of the obtained fixed point theorems. In particular, we consider the questions of the existence of solutions of the Fredholm integral equation in L-spaces.

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“…Observe that semi-continuity of d X,M (•, y) (see inequality ( 6)) can be substituted by a more general inequality (7) d…”

Section: Hausdorffness Conditions In Terms Of Semi-continuity Of the ...mentioning

confidence: 99%

Section: Applicationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Fixed Points Theorems in Hausdorff M-distance Spaces

Бабенко¹,

Коваленко²

2021

Preprint

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show abstract

“…Let T be a metric compact and µ be a measure defined on the σ-algebra of Borel sets of T . Let also an L-space (the definition can be found in [24,2,3,4]) (X, h X ) be given, and C(T, X) be the space of continuous functions x : T → X. In the space C(T, X) consider a C(T, R)-valued metric, setting h…”

Section: 3mentioning

confidence: 99%

Fixed Point Theorems in M-distance Spaces

Babenko,

Kovalenko

2021

Preprint

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“…In papers [3,4,6] questions of numerical analysis and optimal recovery of operators in spaces of functions taking values in semi-linear metric spaces (see [11,2] for definitions and some properties of L-spaces) were studied. In [6] the notion of a (λ, ϕ)-additive operator was introduced in connection to problems of optimal recovery of monotone operators in partially ordered Lspaces.…”

Section: Introductionmentioning

confidence: 99%