Integrable functions of fuzzy cone and ξ - fuzzy cone and their application in the fixed point theorem

Abstract

The purpose of this study is to present the idea of an f-partition for a closed interval. Additionally, we introduce a new notion for fuzzy cone metric spaces called a fuzzy cone integrable function and prove fundamental fixed-point theorems. Moreover, we develop the concept of a ξ -fuzzy cone integrable function. Finally, we present new results of the fixed- point theorem for ξ -fuzzy cone integrable functions.

Subject Classification: (2010):

• 54A40
• 54E35
• 54E15

Keywords:

• Fuzzy cone metric space
• f-partition for [u, υ]
• Fuzzy cone Integrable function
• ξ - function
• ξ -h function
• ξ -f cone integrable and fixed point theorems