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On approximate solution of Drygas functional equation according to the Lipschitz criteria

Acta Universitatis Sapientiae, Mathematica, ISSN 2066-7752, 08/2019, Volume 11, Issue 1, pp. 66 - 77

Abstract Let G be an Abelian group with a metric d and E be a normed space. For any f : G → E we define the Drygas difference of the function f by the formula...

Lipschitz space | 65Q20 | Drygas functional equation | stability | 41A65 | 39B82

Lipschitz space | 65Q20 | Drygas functional equation | stability | 41A65 | 39B82

Journal Article

Mathematika, ISSN 0025-5793, 2017, Volume 63, Issue 2, pp. 383 - 432

Let X be a vector space and let φ:X→R∪{−∞,+∞} be an extended real‐valued function. For every function f:X→R∪{−∞,+∞}, let us define the φ‐envelope of f by...

49J53 | 41A65 (primary) | 52A41 | MATHEMATICS | MATHEMATICS, APPLIED | DECONVOLUTION | WEAK CONVEXITY | POLARITIES | DUALITY | CONVEX-FUNCTIONS | FORMULA | CONVOLUTION

49J53 | 41A65 (primary) | 52A41 | MATHEMATICS | MATHEMATICS, APPLIED | DECONVOLUTION | WEAK CONVEXITY | POLARITIES | DUALITY | CONVEX-FUNCTIONS | FORMULA | CONVOLUTION

Journal Article

Numerical Functional Analysis and Optimization, ISSN 0163-0563, 10/2019, Volume 40, Issue 14, pp. 1703 - 1719

In this article, we first discuss the subduality and orthogonality of the cones and the dual cones when the norm is monotone in Banach spaces. Then, under...

47H10 | Cone | 47J20 | metric projection | 06B30 | 41A65 | complementarity problem | variational inequality | 47H07 | Banach spaces | Intervals | Cones | Banach space | Orthogonality

47H10 | Cone | 47J20 | metric projection | 06B30 | 41A65 | complementarity problem | variational inequality | 47H07 | Banach spaces | Intervals | Cones | Banach space | Orthogonality

Journal Article

ESAIM: Mathematical Modelling and Numerical Analysis, ISSN 0764-583X, 07/2017, Volume 51, Issue 4, pp. 1367 - 1385

This paper introduces a quasi-interpolation operator for scalar-and vector-valued finite element spaces constructed on affine, shape-regular meshes with some...

Quasi-interpolation | Finite elements | Best approximation | MATHEMATICS, APPLIED | best approximation | finite elements | Finite element method | Interpolation | Approximation | Mathematical analysis | Sobolev space | Boundary conditions | Smoothness | Numerical Analysis | Mathematics

Quasi-interpolation | Finite elements | Best approximation | MATHEMATICS, APPLIED | best approximation | finite elements | Finite element method | Interpolation | Approximation | Mathematical analysis | Sobolev space | Boundary conditions | Smoothness | Numerical Analysis | Mathematics

Journal Article

Constructive Approximation, ISSN 0176-4276, 10/2018, Volume 48, Issue 2, pp. 337 - 369

This paper is devoted to discretization of integral norms of functions from a given finite dimensional subspace. This problem is very important in...

Primary 41A65 | Sparse approximation | Discretization | Numerical Analysis | Analysis | Secondary 42A10 | 46B20 | Chaining | Mathematics | Entropy | SPARSE TRIGONOMETRIC APPROXIMATION | MATHEMATICS | SUBMATRICES

Primary 41A65 | Sparse approximation | Discretization | Numerical Analysis | Analysis | Secondary 42A10 | 46B20 | Chaining | Mathematics | Entropy | SPARSE TRIGONOMETRIC APPROXIMATION | MATHEMATICS | SUBMATRICES

Journal Article

Journal of Interdisciplinary Mathematics, ISSN 0972-0502, 07/2019, Volume 22, Issue 5, pp. 689 - 696

For a bounded subset K of a metric space (X, d), an element k 0 ϵ K is called a farthest point to an x ϵ X if . The set of all farthest points to x in K is...

Farthest point map | 41A65 | Remotal set | Isolated point | Farthest point | 54C60 | Uniquely remotal set | 54H25

Farthest point map | 41A65 | Remotal set | Isolated point | Farthest point | 54C60 | Uniquely remotal set | 54H25

Journal Article

Results in Mathematics, ISSN 1422-6383, 9/2019, Volume 74, Issue 3, pp. 1 - 14

Let X be a real Banach space, C a closed bounded convex subset of X with the origin as an interior point, and $$p_C$$ pC the Minkowski functional generated by...

property ( $$\varepsilon _$$ ε ∗ ) | Minkowski functional | generalized best approximation | 41A65 | Mathematics, general | proximinal subspace | Mathematics | MATHEMATICS | MATHEMATICS, APPLIED | property (epsilon())

property ( $$\varepsilon _$$ ε ∗ ) | Minkowski functional | generalized best approximation | 41A65 | Mathematics, general | proximinal subspace | Mathematics | MATHEMATICS | MATHEMATICS, APPLIED | property (epsilon())

Journal Article

Integral Equations and Operator Theory, ISSN 0378-620X, 6/2018, Volume 90, Issue 3, pp. 1 - 23

Given a Krein space $$\mathcal {H}$$ H and B, C in $$L(\mathcal {H}),$$ L(H), the bounded linear operators on $$\mathcal {H},$$ H, the...

Operator approximation | Moore–Penrose inverse | Analysis | Krein spaces | 47A58 | 41A65 | Mathematics | 47B50 | MATHEMATICS | PROJECTIONS | Moore-Penrose inverse | RANGE

Operator approximation | Moore–Penrose inverse | Analysis | Krein spaces | 47A58 | 41A65 | Mathematics | 47B50 | MATHEMATICS | PROJECTIONS | Moore-Penrose inverse | RANGE

Journal Article

Results in Mathematics, ISSN 1422-6383, 11/2017, Volume 72, Issue 3, pp. 1033 - 1040

The present note supplements information contained in three earlier papers with the same title. Here we consider certain aspects of (in)decomposability of...

41A36 | composition | 41A63 | 41A65 | Mathematics, general | Mathematics | decomposition | Positive linear operators | MATHEMATICS | MATHEMATICS, APPLIED | BERNSTEIN OPERATORS

41A36 | composition | 41A63 | 41A65 | Mathematics, general | Mathematics | decomposition | Positive linear operators | MATHEMATICS | MATHEMATICS, APPLIED | BERNSTEIN OPERATORS

Journal Article

Constructive Approximation, ISSN 0176-4276, 2/2019, Volume 49, Issue 1, pp. 103 - 122

For a conditional quasi-greedy basis $$\mathcal {B}$$ B in a Banach space, the associated conditionality constants $$k_{m}[\mathcal {B}]$$ k m [ B ] verify the...

Cotype | Reflexivity | Finite representability | Mathematics | Thresholding greedy algorithm | Banach spaces | Superreflexivity | Conditional basis | Type | 46B15 | Numerical Analysis | Analysis | Super property | 41A65 | Quasi-greedy basis | Conditionality constants | MATHEMATICS

Cotype | Reflexivity | Finite representability | Mathematics | Thresholding greedy algorithm | Banach spaces | Superreflexivity | Conditional basis | Type | 46B15 | Numerical Analysis | Analysis | Super property | 41A65 | Quasi-greedy basis | Conditionality constants | MATHEMATICS

Journal Article

Aequationes mathematicae, ISSN 0001-9054, 8/2017, Volume 91, Issue 4, pp. 745 - 758

A generalized solution operator is a mapping abstractly describing a computational problem and its approximate solutions. It assigns a set of $$\varepsilon $$...

Approximation | 54E99 | Quantale | Analysis | 41A65 | Solution operator | 06F07 | Mathematics | Generalized metric | Combinatorics | MATHEMATICS | MATHEMATICS, APPLIED

Approximation | 54E99 | Quantale | Analysis | 41A65 | Solution operator | 06F07 | Mathematics | Generalized metric | Combinatorics | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 3/2019, Volume 42, Issue 2, pp. 467 - 483

The problem of finding a solution of a variational inequality over the set of common fixed points of a nonexpansive semigroup is considered in a real and...

Nonexpansive semigroup | Explicit method | Variational inequality | Common fixed point | 47H20 | Accretive mapping | 41A65 | Mathematics, general | Mathematics | Applications of Mathematics | 47H17 | MATHEMATICS

Nonexpansive semigroup | Explicit method | Variational inequality | Common fixed point | 47H20 | Accretive mapping | 41A65 | Mathematics, general | Mathematics | Applications of Mathematics | 47H17 | MATHEMATICS

Journal Article

Computational Methods in Applied Mathematics, ISSN 1609-4840, 01/2016, Volume 16, Issue 1, pp. 51 - 75

We construct mollification operators in strongly Lipschitz domains that do not invoke non-trivial extensions, are stable for any real number , and commute with...

65D05 | Finite Element Approximation | De Rham Diagram | 65N30 | Mollification | 41A65 | De rham diagram | Finite element approximation | MATHEMATICS, APPLIED | FINITE | FLUID | REGULARITY | MAXWELL EQUATIONS | ELEMENT EXTERIOR CALCULUS

65D05 | Finite Element Approximation | De Rham Diagram | 65N30 | Mollification | 41A65 | De rham diagram | Finite element approximation | MATHEMATICS, APPLIED | FINITE | FLUID | REGULARITY | MAXWELL EQUATIONS | ELEMENT EXTERIOR CALCULUS

Journal Article

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Interpolation and Approximation of Continuous Functions with Values in the Unit Interval

Numerical Functional Analysis and Optimization, ISSN 0163-0563, 02/2019, Volume 40, Issue 3, pp. 319 - 325

We give applications of a Stone-Weierstrass type theorem concerning uniform density of certain subsets with property V in and establish a simultaneous...

Primary 41A65 | Interpolation | semi-algebra of type 0 | Secondary 41A05 | property V | MATHEMATICS, APPLIED | SEMI-ALGEBRAS | Approximation | Mathematical analysis | Continuity (mathematics)

Primary 41A65 | Interpolation | semi-algebra of type 0 | Secondary 41A05 | property V | MATHEMATICS, APPLIED | SEMI-ALGEBRAS | Approximation | Mathematical analysis | Continuity (mathematics)

Journal Article

Applicable Analysis, ISSN 0003-6811, 10/2019, Volume 98, Issue 13, pp. 2486 - 2496

We consider some Korovkin-type approximation results for sequences of linear continuous operators in spaces of vector-valued and set-valued continuous...

41A36 | 41A25 | approximation of vector-valued functions | 41A63 | 41A65 | Korovkin approximation | approximation of set-valued functions | MATHEMATICS, APPLIED | THEOREM | Operators (mathematics) | Approximation | Mathematical analysis | Continuity (mathematics)

41A36 | 41A25 | approximation of vector-valued functions | 41A63 | 41A65 | Korovkin approximation | approximation of set-valued functions | MATHEMATICS, APPLIED | THEOREM | Operators (mathematics) | Approximation | Mathematical analysis | Continuity (mathematics)

Journal Article

Constructive Approximation, ISSN 0176-4276, 10/2019, Volume 50, Issue 2, pp. 293 - 321

We prove asymptotic evaluations for univariate and multivariate positive linear operators. Our proofs are different from what has been used so far. As...

Cesàro and Volterra operator | 41A35 | 41A36 | 41A25 | Korovkin approximation theorem | Numerical Analysis | Analysis | 41A65 | Mathematics | Asymptotic evaluations for univariate and multivariate positive operators | Positive linear operators | Iterates | MATHEMATICS | Cesaro and Volterra operator

Cesàro and Volterra operator | 41A35 | 41A36 | 41A25 | Korovkin approximation theorem | Numerical Analysis | Analysis | 41A65 | Mathematics | Asymptotic evaluations for univariate and multivariate positive operators | Positive linear operators | Iterates | MATHEMATICS | Cesaro and Volterra operator

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 9/2019, Volume 182, Issue 3, pp. 885 - 905

Given an open subset of a Banach space and a Lipschitz real-valued function defined on its closure, we study whether it is possible to approximate this...

54C30 | 58C25 | Mathematics | Theory of Computation | Optimization | Smooth approximation | Calculus of Variations and Optimal Control; Optimization | 41A30 | Operations Research/Decision Theory | Almost classical solution | 41A65 | Eikonal equation | 26A16 | Lipschitz function | 26B05 | Applications of Mathematics | Engineering, general | 41A29 | SPACE | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | EXTENSION | REGULARIZATION | Banach space | Mathematical functions | Functional Analysis

54C30 | 58C25 | Mathematics | Theory of Computation | Optimization | Smooth approximation | Calculus of Variations and Optimal Control; Optimization | 41A30 | Operations Research/Decision Theory | Almost classical solution | 41A65 | Eikonal equation | 26A16 | Lipschitz function | 26B05 | Applications of Mathematics | Engineering, general | 41A29 | SPACE | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | EXTENSION | REGULARIZATION | Banach space | Mathematical functions | Functional Analysis

Journal Article

Archiv der Mathematik, ISSN 0003-889X, 7/2018, Volume 111, Issue 1, pp. 61 - 69

Let $$k\in \mathbb {N}$$ k∈N and $$\Lambda _{k}\subseteq \left[ 0,1\right] ^{k}$$ Λk⊆0,1k be a compact non-empty set and X, Y be non-null normed spaces. We...

Primary 41A65 | 41A35 | 41A36 | Korovkin approximation theorem | Secondary 41A10 | Mathematics, general | Mathematics | Multivariate Bernstein type operators | MATHEMATICS

Primary 41A65 | 41A35 | 41A36 | Korovkin approximation theorem | Secondary 41A10 | Mathematics, general | Mathematics | Multivariate Bernstein type operators | MATHEMATICS

Journal Article

Constructive Approximation, ISSN 0176-4276, 12/2018, Volume 48, Issue 3, pp. 415 - 451

We obtain Lebesgue-type inequalities for the greedy algorithm for arbitrary complete seminormalized biorthogonal systems in Banach spaces. The bounds are given...

Non-linear approximation | Mathematics | Lebesgue-type inequality | 41A46 | 46B15 | Numerical Analysis | Analysis | 41A65 | 46B45 | Greedy algorithm | Quasi-greedy basis | Biorthogonal system | Discrete Lorentz space | 41A17 | MATHEMATICS | BASES | BIORTHOGONAL SYSTEMS | M-TERM APPROXIMATION | Democracy | Algorithms

Non-linear approximation | Mathematics | Lebesgue-type inequality | 41A46 | 46B15 | Numerical Analysis | Analysis | 41A65 | 46B45 | Greedy algorithm | Quasi-greedy basis | Biorthogonal system | Discrete Lorentz space | 41A17 | MATHEMATICS | BASES | BIORTHOGONAL SYSTEMS | M-TERM APPROXIMATION | Democracy | Algorithms

Journal Article

Set-Valued and Variational Analysis, ISSN 1877-0533, 3/2019, Volume 27, Issue 1, pp. 213 - 222

The paper is concerned with local approximative and geometric properties of sets, with particular emphasis on strict solarity of such sets under certain...

54C65 | Chebyshev set | Bounded solarity | Mathematics | Sun | Optimization | Selection of the metric projection operator | Radial continuity | Analysis | Near-best approximation | 41A65 | Best approximation | Strict sun | MATHEMATICS, APPLIED | MONOTONE PATH-CONNECTEDNESS | CHEBYSHEV SETS

54C65 | Chebyshev set | Bounded solarity | Mathematics | Sun | Optimization | Selection of the metric projection operator | Radial continuity | Analysis | Near-best approximation | 41A65 | Best approximation | Strict sun | MATHEMATICS, APPLIED | MONOTONE PATH-CONNECTEDNESS | CHEBYSHEV SETS

Journal Article

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