## Abstract and Applied Analysis

### Complex Convexity of Musielak-Orlicz Function Spaces Equipped with the $p$-Amemiya Norm

#### Abstract

The complex convexity of Musielak-Orlicz function spaces equipped with the $p$-Amemiya norm is mainly discussed. It is obtained that, for any Musielak-Orlicz function space equipped with the $p$-Amemiya norm when $1\le p<\infty$, complex strongly extreme points of the unit ball coincide with complex extreme points of the unit ball. Moreover, criteria for them in above spaces are given. Criteria for complex strict convexity and complex midpoint locally uniform convexity of above spaces are also deduced.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 190203, 6 pages.

Dates
First available in Project Euclid: 2 October 2014

https://projecteuclid.org/euclid.aaa/1412276978

Digital Object Identifier
doi:10.1155/2014/190203

Mathematical Reviews number (MathSciNet)
MR3208518

Zentralblatt MATH identifier
1340.46018

#### Citation

Chen, Lili; Cui, Yunan; Zhao, Yanfeng. Complex Convexity of Musielak-Orlicz Function Spaces Equipped with the $p$ -Amemiya Norm. Abstr. Appl. Anal. 2014 (2014), Article ID 190203, 6 pages. doi:10.1155/2014/190203. https://projecteuclid.org/euclid.aaa/1412276978

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