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Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2011, Volume 381, Issue 2, pp. 530 - 537
We obtain some results on generalized Hyers–Ulam stability of the linear differential equation in a Banach space. As a consequence we improve some known... 
Hyers–Ulam stability | Differential equation in Banach spaces | Hyers-Ulam stability | MATHEMATICS | MATHEMATICS, APPLIED | FUNCTIONAL-EQUATIONS | CONSTANT-COEFFICIENTS | 1ST-ORDER | OPERATORS
Journal Article
Numerical Algorithms, ISSN 1017-1398, 11/2016, Volume 73, Issue 3, pp. 775 - 789
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 10/2015, Volume 268, pp. 422 - 431
We consider a parameterized probability distribution and denote by ( ) the squared -norm of ( ). The properties of ( ) are useful in studying the Rényi... 
Hypergeometric function | Probability distribution | Entropy | Heun function | Positive linear operator | MATHEMATICS, APPLIED | INEQUALITIES | GRUSS-TYPE | EQUATION | CONJECTURE
Journal Article
Results in Mathematics, ISSN 1422-6383, 12/2019, Volume 74, Issue 4, pp. 1 - 9
This is a continuation of the author’s paper “Convexity properties of some entropies”, published in Raşa (Results Math 73:105, 2018). We consider the sum... 
entropies | inequalities | 26A51 | Mathematics | Bernstein polynomials | log -convex function | 39B62 | functional equations | 39B22 | 94A17 | Mathematics, general | 05A19 | combinatorial identities | MATHEMATICS | MATHEMATICS, APPLIED | log-convex function | CONJECTURE
Journal Article
Periodica Mathematica Hungarica, ISSN 0031-5303, 12/2017, Volume 75, Issue 2, pp. 159 - 166
It is well-known that the Shannon entropies of some parameterized probability distributions are concave functions with respect to the parameter. In this paper... 
Entropies | 60E15 | 26A51 | Inequalities | 94A17 | Mathematics, general | Mathematics | Concavity | Complete monotonicity | MATHEMATICS | MATHEMATICS, APPLIED | OPERATORS | CONJECTURE | Distribution (Probability theory)
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 11/2012, Volume 219, Issue 4, pp. 1562 - 1568
We obtain some stability results for the linear differential operator of order one in Banach spaces. As a consequence we derive a result on Hyers–Ulam... 
Linear differential operator | Riccati equation | Hyers–Ulam stability | Liénard equation | Hyers-Ulam stability | MATHEMATICS, APPLIED | FUNCTIONAL-EQUATIONS | CONSTANT-COEFFICIENTS | Lienard equation | 1ST-ORDER
Journal Article
by Kappos, Ludwig and Bar-Or, Amit and Cree, Bruce A C and Fox, Robert J and Giovannoni, Gavin and Gold, Ralf and Vermersch, Patrick and Arnold, Douglas L and Arnould, Sophie and Scherz, Tatiana and Wolf, Christian and Wallström, Erik and Dahlke, Frank and Achiron, Anat and Achtnichts, Lutz and Agan, Kadriye and Akman-Demir, Gulsen and Allen, Alison B and Antel, Jack P and Antiguedad, Alfredo Rodriguez and Apperson, Michelle and Applebee, Angela M and Ayuso, Guillermo Izquierdo and Baba, Masayuki and Bajenaru, Ovidiu and Balasa, Rodica and Balci, Belgin Petek and Barnett, Michael and Bass, Ann and Becker, Veit U and Bejinariu, Mihaela and Bergh, Florian Then and Bergmann, Arnfin and Bernitsas, Evanthia and Berthele, Achim and Bhan, Virender and Bischof, Felix and Bjork, Randall John and Blevins, Gregg and Boehringer, Matthias and Boerner, Thomas and Bonek, Robert and Bowen, James D and Bowling, Allen and Boyko, Alexey N and Boz, Cavit and Bracknies, Vera and Braune, Stefan and Brescia Morra, Vincenzo and Brochet, Bruno and Brola, Waldemar and Brownstone, Paul Kenneth and Brozman, Miroslav and Brunet, Donald and Buraga, Ioan and Burnett, Margaret and Buttmann, Mathias and Butzkueven, Helmut and Cahill, Jonathan and Calkwood, Jonathan C and Camu, William and Cascione, Mark and Castelnovo, Giovani and Centonze, Diego and Cerqueira, Joao and Chan, Andrew and Cimprichova, Andrea and Cohan, Stanley and Comi, Giancarlo and Conway, Jill and Cooper, Joanna A and Corboy, John and Correale, Jorge and Costell, Brian and Cottrell, David A and Coyle, Patricia K and Craner, Matthew and Cui, Liying and Cunha, Luis and Czlonkowska, Anna and da Silva, Ana Martins and de Sa, Joao and de Seze, Jérôme and Debouverie, Marc and Debruyne, Jan and Decoo, Danny and Defer, Gilles and Derfuss, Tobias and Deri, Norma H and Dihenia, Bhupesh and Dioszeghy, Peter and Donath, Vladimir and Dubois, Benedicte and Duddy, Martin and Duquette, Pierre and Edan, Gilles and Efendi, Husnu and Elias, Stanton and Emrich, Peter J and Estruch, Bonaventura Casanova and ... and EXPAND Clinical Investigators and Institute of Neuroscience and Physiology and Sahlgrenska akademin and Göteborgs universitet and Gothenburg University and Sahlgrenska Academy and Institutionen för neurovetenskap och fysiologi
The Lancet, ISSN 0140-6736, 03/2018, Volume 391, Issue 10127, pp. 1263 - 1273
Journal Article
Results in Mathematics, ISSN 1422-6383, 9/2018, Volume 73, Issue 3, pp. 1 - 5
We consider a family of probability distributions depending on a real parameter x, and study the logarithmic convexity of the sum of the squared probabilities.... 
entropies | 26A51 | 94A17 | Mathematics, general | Mathematics | Probability distribution | 26D05 | log-convex function | MATHEMATICS | MATHEMATICS, APPLIED | OPERATORS | Analysis | Distribution (Probability theory)
Journal Article
Mediterranean Journal of Mathematics, ISSN 1660-5446, 10/2019, Volume 16, Issue 5, pp. 1 - 10
We consider some connections between the classical sequence of Bernstein polynomials and the Taylor expansion at the point 0 of a $$C^\infty $$ C∞ function f... 
Bernstein operators | Extrapolation | 41A36 | 41A63 | Voronovskaja’s formula | 41A10 | Mathematics, general | Taylor series | Mathematics | 41A28 | MATHEMATICS | MATHEMATICS, APPLIED | Voronovskaja's formula
Journal Article
Positivity, ISSN 1385-1292, 07/2018, Volume 22, Issue 3, pp. 829 - 835
To access, purchase, authenticate, or subscribe to the full-text of this article, please visit this link: http://dx.doi.org/10.1007/s11117-017-0547-0 We extend... 
Uniquely ergodic operator | semigroups | Linking operators | Kantorovich modification | Iterates of operators
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 04/2014, Volume 412, Issue 1, pp. 103 - 108
We obtain the infimum of the Hyers–Ulam stability constants for Stancu, Bernstein and Kantorovich operators and prove that in a class of certain positive... 
Operators | Approximation | Hyers–Ulam stability | Best constant | Hyers-Ulam stability | MATHEMATICS | ORDER | MATHEMATICS, APPLIED | DIFFERENTIAL OPERATOR | COEFFICIENTS | FUNCTIONAL-EQUATION
Journal Article
Positivity, ISSN 1385-1292, 7/2018, Volume 22, Issue 3, pp. 829 - 835
We extend to the context of $$L^p$$ Lp spaces and $$C_0$$ C0 -semigroups of operators our previous results from Heilmann and Raşa (Positivity 21:897–910, 2017.... 
C_0$$ C 0 -semigroups | Mathematics | Linking operators | Kantorovich modification | Operator Theory | 37A30 | Fourier Analysis | 41A36 | Potential Theory | Calculus of Variations and Optimal Control; Optimization | Iterates of operators | Uniquely ergodic operator | Econometrics
Journal Article
Positivity, ISSN 1385-1292, 07/2018, Volume 22, Issue 3, pp. 829 - 835
Journal Article
Positivity, ISSN 1385-1292, 2018, Volume 23, Issue 1, pp. 233 - 246
This paper is a natural continuation of Acar et al. (Mediterr J Math 14:6, 2017, 10.1007/s00009-016-0804-7) where Szasz-Mirakyan operators preserving... 
Uniform convergence | Szász–Mirakyan operators | Voronovskaya type theorem | Weighted modulus of continuity | MATHEMATICS | Szasz-Mirakyan operators
Journal Article
Aequationes mathematicae, ISSN 0001-9054, 8/2016, Volume 90, Issue 4, pp. 719 - 726
We prove that the kernels of Bernstein, Stancu and Kantorovich operators are proximinal sets, therefore the infimum of Hyers–Ulam constants is also a... 
41A44 | 41A35 | Analysis | best constant | Mathematics | Combinatorics | Hyers–Ulam stability | proximinal set | 39B82 | MATHEMATICS | MATHEMATICS, APPLIED | DIFFERENTIAL OPERATOR | COEFFICIENTS | Hyers-Ulam stability | Linear operators | Infimum | Kernels | Operators | Stability | Norms | Constants
Journal Article
Mediterranean Journal of Mathematics, ISSN 1660-5446, 4/2019, Volume 16, Issue 2, pp. 1 - 11
We describe a unifying approach for studying the power series of the positive linear operators from a certain class. For the same operators, we give simpler... 
Ergodic theorem | 47D06 | 37A30 | Eigenstructure | Mathematics, general | Mathematics | Primary 41A36 | positive linear operator | Power series | 15A18 | C_{0}$$ C 0 -semigroup | C-semigroup | MATHEMATICS | MATHEMATICS, APPLIED | C-0-semigroup | BERNSTEIN OPERATORS | GEOMETRIC SERIES
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2017, Volume 453, Issue 1, pp. 620 - 628
We suggest a somewhat new approach to the issue of Hyers–Ulam stability. Namely, let , be (real or complex) linear spaces, be a linear operator, , and and be... 
Differential equation | Hyers–Ulam stability | Linear operator | Boundedness | Semigauge | MATHEMATICS | MATHEMATICS, APPLIED | CONSTANT-COEFFICIENTS | Y | Hyers-Ulam stability | LINEAR-DIFFERENTIAL EQUATIONS | 1ST-ORDER | OPERATORS | Differential equations
Journal Article
Positivity, ISSN 1385-1292, 9/2017, Volume 21, Issue 3, pp. 897 - 910
We consider Markov operators L on C[0, 1] such that for a certain $$c \in [0,1)$$ c ∈ [ 0 , 1 ) , $$\Vert (Lf)' \Vert \le c \Vert f' \Vert $$ ‖ ( L f ) ′ ‖ ≤ c... 
Operator Theory | 37A30 | Fourier Analysis | 41A36 | Potential Theory | Calculus of Variations and Optimal Control; Optimization | Iterates of operators | Uniquely ergodic operator | Mathematics | Dual functionals | Econometrics | Kantorovich modification | MATHEMATICS | LINEAR-OPERATORS | BERNSTEIN-DURRMEYER OPERATORS | Functionals | Markov processes | Operators
Journal Article
Results in Mathematics, ISSN 1422-6383, 3/2019, Volume 74, Issue 1, pp. 1 - 12
In this paper we consider a link between Baskakov–Durrmeyer type operators and corresponding Kantorovich type modifications of their classical variants. We... 
Kantorovich modifications of operators | Baskakov–Durrmeyer type operators | 41A36 | 41A10 | Mathematics, general | Mathematics | Linking operators | 41A28 | MATHEMATICS | MATHEMATICS, APPLIED | APPROXIMATION | Baskakov-Durrmeyer type operators | BERNSTEIN
Journal Article
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