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Fixed Point Theorem Utilizing Operators and Functionals
 

Summary: Fixed Point Theorem Utilizing
Operators and Functionals
Douglas R. Anderson, Richard I. Avery,
Johnny Henderson and Xueyan Liu
Abstract
This paper presents a fixed point theorem utilizing operators and functionals
in the spirit of the original Leggett-Williams fixed point theorem which is void
of any invariance like conditions. The underlying sets in the Leggett-Williams
fixed point theorem that were defined using the total order of the real numbers
are replaced by sets that are defined using an ordering generated by a border
symmetric set, that is, the sets that were defined using functionals in the original
Leggett-Williams fixed point theorem are replaced by sets that are defined using
operators.
Key words: Multiple fixed-point theorems, Leggett-Williams, expansion, compres-
sion.
Mathematics Subject Classifications: 47H10
1 Introduction
Mavridis [8] attempted to generalize the Leggett-Williams [7] fixed point theorem by
replacing arguments that involved concave and convex functionals with arguments
that involved concave and convex operators. Some of the arguments went through

  

Source: Anderson, Douglas R. - Department of Mathematics and Computer Science, Concordia College

 

Collections: Mathematics