Gupta, VijayAral, AliÖzsaraç, Firat2025-01-212025-01-2120221664-2368https://doi.org/10.1007/s13324-022-00723-4https://hdl.handle.net/20.500.12587/23495The paper deals with the semi-exponential type Gauss–Weierstrass operators. The central moments of these operators are constant functions. We estimate some direct results. We also provide a modification of such operators so as the preserve two exponential functions, we estimate weighted approximation, quantitative asymptotic formula for the modified form of operators. Later, a comparison is stated, that shows that in a certain sense and for certain family of illustrative functions the modified form of the semi-exponential Gauss–Weierstrass operators approximates better than the classical ones. Finally, we give some numerical results, which help us better understand the theoretical results obtained in the previous sections. © 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.eninfo:eu-repo/semantics/closedAccessGauss–Weierstrass operators; Moment generating function; Moments; Quantitative asymptotic formula; Semi-exponential Gauss–Weierstrass operators; Weighted approximationArticle12510.1007/s13324-022-00723-42-s2.0-85136533486Q1