Aral, AliOzsarac, FiratYilmaz, Basar2025-01-212025-01-2120221385-12921572-9281https://doi.org/10.1007/s11117-022-00926-whttps://hdl.handle.net/20.500.12587/25350In this work, we introduce a new modulus of continuity for locally integrable function spaces which is influenced by the natural structure of the L-p space. After basic properties of it are given, we obtain a quantitative type theorem for the rate of convergence of convolution type integral operators and iterates of them. Their global smoothness preservation property involving the new modulus of continuity is presented. Finally, the obtained results are applied to Gauss-Weierstrass operators.eninfo:eu-repo/semantics/closedAccessQuantitative theorems; Locally integrable function space; Weighted modulus of continuityArticle26310.1007/s11117-022-00926-w2-s2.0-85132993561Q2WOS:000815636100001Q2