JOURNAL OF INEQUALITIES AND SPECIAL FUNCTIONS, vol.8, no.3, pp.15-24, 2017 (ESCI)
By using the Bernstein basis functions and Bernstein operator with their integral, we derive some combinatorial sums and identities including the Bernoulli numbers and polynomials, the Stirling numbers of the second kind and also some relations. Moreover, we give some inequalities involving combinatorial numbers and binomial coefficients.