Generalized Hölder^s Inequality on Generalized Sequence Orlicz Spaces
Dasep1,a), Al Azhary Masta2, Encum Sumiaty3, Siti Fatimah4, Cece Kustiawan5, Endang Cahya Mulyaning6, Sofihara Al Hazmy7

1,2,3,4,5,6Mathematics Study Program, Universitas Pendidikan Indonesia, Jl. Dr. Setiabudi 229, Bandung 40154, Indonesia

7Fakultas Matematika dan Ilmu Pengetahuan Alam Militer, Universitas Pertahanan Republik Indonesia, Kawasan IPSC Sentul, Sukahati, Bogor, Jawa Barat 16810

Abstract

The Orlicz space was first introduced by Z. W. Birnbaum and W. Orlicz as an extension of the Labesgue space. There are two types of Orlicz spaces, namely continuous Orlicz spaces and sequence Orlicz spaces. Some of the properties that apply to continuous Orlicz spaces are known, as are the properties of sequence Orlicz spaces. The purpose of this study is to discuss the properties that apply to the sequence Orlicz space that also apply to the generalized sequence Orlicz space, especially generalized Holder^s inequlity in sequencer Orlicz spaces. The method in this study uses the properties that apply to the sequence Orlicz space and the s-Young function. Meanwhile, the results of this study show that the properties that apply to the sequence Orlicz space also apply to the generalized sequence Orlicz space by adding other conditions.

Keywords: s-convex function, s-Young function, sequence Orlicz space, generalized Holder^s inequality.

Topic: Mathematic