Fuzzy Rate Analysis of Operators and its Applications in Linear Spaces

TL;DR

This paper introduces the fuzzy rate of operators in linear spaces, explores its properties, and applies it to establish a new fixed point theorem, advancing the understanding of operator behavior in fuzzy contexts.

Contribution

It proposes the novel concept of fuzzy rate for operators in linear spaces and demonstrates its utility through a fixed point existence theorem.

Findings

Fuzzy rate of an operator is defined and its properties are studied.

A fixed point existence theorem using fuzzy rate is proved.

Application to operators in a plane is discussed.

Abstract

In this paper, a new concept, the fuzzy rate of an operator in linear spaces is proposed for the very first time. Some properties and basic principles of it are studied. Fuzzy rate of an operator $B$ which is specific in a plane is discussed. As its application, a new fixed point existence theorem is proved.