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010   $a3-319-58795-1
024 7 $a10.1007/978-3-319-58795-0
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035   $a(DE-He213)978-3-319-58795-0
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100   $a20170627d2017      u|         0
101 0 $aeng
135   $aurnn#008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aApproximation with Positive Linear Operators and Linear Combinations /$fby Vijay Gupta, Gancho Tachev
205   $a1st ed. 2017.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017.
215   $a1 online resource (XIII, 186 p. 2 illus. in color.)
225 1 $aDevelopments in Mathematics,$x2197-795X ;$v50
311 08$a3-319-58794-3 
320   $aIncludes bibliographical references and index.
327   $a1. Moments and Linear Combinations of Positive Linear Operators -- 2. Direct Estimates for Approximation by Linear Combinations -- 3. Inverse Estimates and Saturation Results for Linear Combinations -- 4. Voronovskaja Type Estimates -- 5. Pointwise Estimates for Linear Combinations -- 6. Voronovskaja's Theorem in Terms of Weighted Modulus of Continuity -- 7. Direct Estimates for Some New Operators -- 8. Convergence for Operators Based on P?lt?anea Basis -- Bibliography -- Index. .
330   $aThis book presents a systematic overview of approximation by linear combinations of positive linear operators, a useful tool used to increase the order of approximation. Fundamental and recent results from the past decade are described with their corresponding proofs. The volume consists of eight chapters that provide detailed insight into the representation of monomials of the operators Ln , direct and inverse estimates for a broad class of positive linear operators, and case studies involving finite and unbounded intervals of  real and complex functions. Strong converse inequalities of Type A in terminology of Ditzian?Ivanov for linear combinations of Bernstein and Bernstein?Kantorovich operators and various Voronovskaja-type estimates for some linear combinations are analyzed and explained. Graduate students and researchers in approximation theory will find the list of open problems in approximation of linear combinations useful. The book serves as a reference for graduate and postgraduate courses as well as a basis for future study and development.  .
410  0$aDevelopments in Mathematics,$x2197-795X ;$v50
606   $aApproximation theory
606   $aNumerical analysis
606   $aFunctional analysis
606   $aApproximations and Expansions
606   $aNumerical Analysis
606   $aFunctional Analysis
615  0$aApproximation theory.
615  0$aNumerical analysis.
615  0$aFunctional analysis.
615 14$aApproximations and Expansions.
615 24$aNumerical Analysis.
615 24$aFunctional Analysis.
676   $a511.4
700   $aGupta$b Vijay$4aut$4http://id.loc.gov/vocabulary/relators/aut$0721656
702   $aTachev$b Gancho$4aut$4http://id.loc.gov/vocabulary/relators/aut
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910254280603321
996   $aApproximation with Positive Linear Operators and Linear Combinations$91935693
997   $aUNINA