Çanak, İbrahim2024-07-122024-07-122021Çanak, İ. (2021). A revisited Tauberian theorem for which slow decrease with respect to a weight function is a tauberian condition for the weighted mean summability of integrals over R+. Fourth International Conference of Mathematical Sciences, Maltepe Üniversitesi. s. 1-2.978-0-7354-4078-4https://aip.scitation.org/doi/10.1063/5.0042366https://hdl.handle.net/20.500.12415/1931. In this extended abstract, we present an alternative proof of a Tauberian theorem of slowly decreasing type with respect to the weight function due to Karamata [5] for the weighted mean summable real-valued integrals over R+ := [0, ?). Some particular choices of weight functions provide alternative proofs of some well-known Tauberian theorems given for several important summability methods.enCC0 1.0 Universalinfo:eu-repo/semantics/openAccessWeighted mean method of summabilityTauberian conditions and theoremsslow decrease with respect to a weight functionConference Object21