Operator type expansion-compression fixed point theorem

Abstract

This article presents an alternative to the compression and expansion fixed point theorems of functional type by using operators and functions to replace the functionals and constants that are used in functional compression and expansion fixed point theorems. Only portions of the boundaries are required to be mapped outward or inward in the spirit of the original work of Leggett-Williams. We conclude with an application verifying the existence of a positive solution to a second-order boundary-value problem.

Keywords

• Fixed-point theorems
• Leggett-Williams
• expansion
• compression
• positive solutions