doi:10.1186/s13660-016-1078-0engAdell Pascual, José AntonioLekuona Amiano, AlbertoTowards the best constant in front of the Ditzian-Totik modulus of smoothnessART-2016-95195We give accurate estimates for the constants (Formula presented.), where I = R or I = 0, 8), Ln is a positive linear operator acting on real functions f defined on the interval I, A(I) is a certain subset of such function, and ¿s 2(f; ·) is the Ditzian-Totik modulus of smoothness of f with weight function s. This is done under the assumption that s is concave and satisfies some simple boundary conditions at the endpoint of I, if any. Two illustrative examples closely connected are discussed, namely, Weierstrass and Szàsz-Mirakyan operators. In the first case, which involves the usual second modulus, we obtain the exact constants when A(R) is the set of convex functions or a suitable set of continuous piecewise linear functions.2016http://zaguan.unizar.es/record/5629010.1186/s13660-016-1078-0http://zaguan.unizar.es/record/56290oai:zaguan.unizar.es:56290info:eu-repo/grantAgreement/ES/DGA/E64info:eu-repo/grantAgreement/ES/MINECO/MTM2015-67006-PJOURNAL OF INEQUALITIES AND APPLICATIONS 2016, 137 (2016), [17 pp.]byhttp://creativecommons.org/licenses/by/3.0/es/info:eu-repo/semantics/openAccess