 
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 LeggettWilliams fixed point theorem which is void
of any invariance like conditions. The underlying sets in the LeggettWilliams
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
LeggettWilliams fixed point theorem are replaced by sets that are defined using
operators.
Key words: Multiple fixedpoint theorems, LeggettWilliams, expansion, compres
sion.
Mathematics Subject Classifications: 47H10
1 Introduction
Mavridis [8] attempted to generalize the LeggettWilliams [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
