Journal of Prime Research in Mathematics

# Fuzzy L$$^P$$ -Spaces

Marzieh Shams Yousef$$^{a,*}$$, Forouzan Farahrooz$$^b$$

$$^a$$Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran.
$$^b$$Department of Mathematics, Payame Noor University, Tehran, Iran.

Correspondence should be addressed to: mmaths@gmail.com

### Abstract

The purpose of this paper is to introduce the fuzzy L$$^P$$-Spaces. We give some basic definitions and main properties of fuzzy spaces. The fuzzy Holder’s inequality will be proved. Also we show that the dual offuzzy L$$^P$$-spaces is fuzzy L$$^q$$-spaces, where the scalars p and q are conjugate exponents.

#### Keywords:

α-cut, Fuzzy functions, Hausdorff distance, Fuzzy L$$^P$$-Spaces.