000046556 001__ 46556
000046556 005__ 20170504094950.0
000046556 0247_ $$2doi$$a10.1155/2015/915358
000046556 0248_ $$2sideral$$a90796
000046556 037__ $$aART-2015-90796
000046556 041__ $$aeng
000046556 100__ $$0(orcid)0000-0001-8331-5160$$aAdell, J.A.$$uUniversidad de Zaragoza
000046556 245__ $$aQuantitative estimates for positive linear operators in terms of the usual second modulus
000046556 260__ $$c2015
000046556 5060_ $$aAccess copy available to the general public$$fUnrestricted
000046556 5203_ $$aWe give accurate estimates of the constants Cn(A(I),x) appearing in direct inequalities of the form |Lnf(x)-f(x)|=Cn(A(I),x)?2 f;s(x)/n, f?A(I), x?I, and n=1,2,., where Ln is a positive linear operator reproducing linear functions and acting on real functions f defined on the interval I, A(I) is a certain subset of such functions, ?2(f;·) is the usual second modulus of f, and s(x) is an appropriate weight function. We show that the size of the constants Cn(A(I),x) mainly depends on the degree of smoothness of the functions in the set A(I) and on the distance from the point x to the boundary of I. We give a closed form expression for the best constant when A(I) is a certain set of continuous piecewise linear functions. As illustrative examples, the Szàsz-Mirakyan operators and the Bernstein polynomials are discussed.
000046556 536__ $$9info:eu-repo/grantAgreement/ES/MINECO-FEDER/MTM2011-23998
000046556 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/
000046556 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000046556 700__ $$0(orcid)0000-0001-6555-4432$$aLekuona, A.$$uUniversidad de Zaragoza
000046556 7102_ $$12007$$2265$$aUniversidad de Zaragoza$$bDepartamento de Métodos Estadísticos$$cEstadística e Investigación Operativa
000046556 773__ $$g2015 (2015), 915358 [11 pp]$$pAbstract and Applied Analysis$$tAbstract and Applied Analysis$$x1085-3375
000046556 8564_ $$s2020622$$uhttp://zaguan.unizar.es/record/46556/files/texto_completo.pdf$$yVersión publicada
000046556 8564_ $$s71596$$uhttp://zaguan.unizar.es/record/46556/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000046556 909CO $$ooai:zaguan.unizar.es:46556$$particulos$$pdriver
000046556 951__ $$a2017-05-04-09:46:26
000046556 980__ $$aARTICLE