关键词: 正定理, 逆定理, K-泛函, Orlicz空间, Szász-Mirakjan-Durrmeyer算子

Abstract: This paper investigates approximation problems in Orlicz spaces generated by Young functions. Utilizing Jensen's inequality and the equivalence between the $K$-functional and the modulus of smoothness, we establish both direct and inverse theorems for approximation by linear combinations of Szász-Mirakjan-Durrmeyer operators in these spaces.

Key words: Direct theorem, Inverse theorem, K-functional, Orlicz space, Szász-Mirakjan-Durrmeyer operator