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

Canak I.2021-05-032021-05-03202197807354407840094-243X0094-243Xhttps://doi.org/10.1063/5.0042366https://hdl.handle.net/11454/714614th International Conference of Mathematical Sciences, ICMS 2020 -- 17 June 2020 through 21 June 2020 -- -- 167553In 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. © 2021 American Institute of Physics Inc.. All rights reserved.en10.1063/5.0042366info:eu-repo/semantics/openAccessSlow decrease with respect to a weight functionTauberian conditions and theoremsWeighted mean method of summabilityRevisited tauberian theorem for which slow decrease with respect to a weight function is a tauberian condition for the weighted mean summability of integrals over rConference Object23342-s2.0-85102307914N/A