An inclusion properties of generalized Orlicz sequence spaces

• Main Authors: Dasep, Fatimah, Siti, Kustiawan, Cece, Sumiaty, Encum, Masta, Al Azhary
• Format: Conference Proceeding
• Language: English
• ISSN: 0094-243X; 1551-7616
• DOI: 10.1063/5.0191919

The Orlicz spaces are an extension of the Lebesgue spaces, which in 1931 were first introduced by W. Orlicz and Z. W. Birnbaum. There are two types of Orlicz spaces, namely continuous Orlicz spaces and sequenced Orlicz spaces. One of the interesting things studied by many researchers is the inclusion properties in the Orlicz spaces. Research on the inclusion properties in the Orlicz spaces was first carried out by Welland in 1966 by giving sufficient conditions to the Orlicz spaces. The aim of this study is to obtain the sufficient and necessary conditions for inclusion properties of generalized Orlicz sequence spaces. The method used in this study is to use the generalized Young function to define the generalized Orlicz sequence spaces and to use the quasi norm on the Orlicz sequence spaces to obtain inclusion properties. The results obtained in this study are the generalized definition of the Orlicz sequence spaces and the sufficient and necessary conditions for inclusion properties.