Ozsarac, FiratAcu, Ana MariaAral, AliRasa, Ioan2025-01-212025-01-2120230163-05631532-2467https://doi.org/10.1080/01630563.2023.2239326https://hdl.handle.net/20.500.12587/25211In this paper, we define a new generalization of Mellin-Gauss-Weierstrass operators that preserve logarithmic functions. We compute logarithmic moments of the new operators and describe the behavior of the modified operators in some weighted spaces. The weighted approximation properties of operators including weighted approximation and weighted quantitative type approximation properties, using weighted logarithmic modulus of continuity, are presented. Using the Mellin-Gauss-Weierstrass kernel p(., .) as a logarithmic probability density, we study the associated information potential, the expected value E[log p(., .)] and the variance Var[log p(., .)].eninfo:eu-repo/semantics/closedAccessInformation potential; logarithmic moments; Mellin-Gauss-Weierstrass operators; weighted logarithmic modulus of continuityArticle44111194120810.1080/01630563.2023.22393262-s2.0-85166020691Q2WOS:001038805100001Q2