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