zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Szász-Mirakjan type operators providing a better error estimation. (English) Zbl 1182.41022
Modifying the coefficients of the classical Szasz-Mirakjan operators a new class of Szasz-Mirakjan type operators is obtained. Their convergence property is proved using the Korovkin type approximation theorem. Next, using a Shisha-Mond type theorem,the approximation order of the new operators is established in terms of modulus of continuity. It is proved that this order is better as the approximation order of the classical operators. Finally, a Voronovskaja type theorem for the generalized Szasz-Mirakjan type operators is proved.

MSC:
41A36Approximation by positive operators
WorldCat.org
Full Text: DOI
References:
[1] Agrawal, P. N.; Kasana, H. S.: On simultaneous approximation by szász--mirakjan operators. Bull. inst. Math. acad. Sinica 22, No. 2, 181-188 (1994) · Zbl 0859.41014
[2] Altomare, F.; Campiti, M.: Korovkin-type approximation theory and its application. Walter de gruyter studies in math. 17 (1994) · Zbl 0924.41001
[3] Bardaro, C.; Butzer, P. L.; Stens, R. L.; Vinti, G.: Convergence in variation and rates of approximation for Bernstein-type polynomials and singular convolution integrals. Analysis (Munich) 23, 299-340 (2003) · Zbl 1049.41015
[4] P.P. Korovkin, Linear operators and the theory of approximation, India, Delhi, 1960 · Zbl 0107.05302
[5] Devore, R. A.: The approximation of continuous functions by positive linear operators. Lecture notes in mathematics 293 (1972) · Zbl 0276.41011
[6] King, J. P.: Positive linear operators which preserve x2. Acta math. Hungar. 99, No. 3, 203-208 (2003) · Zbl 1027.41028
[7] Duman, O.; Orhan, C.: An abstract version of the Korovkin approximation theorem. Publ. math. Debrecen 69, 33-46 (2006) · Zbl 1121.41012
[8] M.A. Özarslan, O. Duman, MKZ type operators providing a better estimation on [1/2,1), Canadian Math. Bull. (2007) (in press)
[9] Totik, V.: Uniform approximation by szász--mirakjan type operators. Acta math. Hungar 41, No. 3--4, 291-307 (1983) · Zbl 0513.41013