Aral, AliGat, Sorin G.2020-06-252020-06-252008closedAccess1027-54872224-6851https://hdl.handle.net/20.500.12587/4055Introducing a higher order modulus of smoothness based on q-integers, in this paper first we obtain Jackson-type estimates in approximation by Jackson-type generalizations of the q-Picard and q-Gauss-Weierstrass singular integrals and give their global smoothness preservation property with respect to the uniform norm. Then, we study approximation and geometric properties of the complex variants for these q -singular integrals attached to analytic functions in compact disks. Finally, we prove approximation properties of these q-singular integrals attached to vector-valued functions.eninfo:eu-repo/semantics/closedAccessq-Picard singular integralq-Gauss-Weierstrass singular integralJackson-type estimateModulus of continuityComplex q-singular integralsStarlikeConvex and spirallike functionsVector valued functionsArticle129250125152-s2.0-74049103064Q3WOS:000262237400016Q2