Abstract
The purpose of this article is to define almost (alpha, F-sigma)-contractions and establish some generalized fixed-point results for a new class of contractive conditions in the setting of complete metric spaces. In application, we apply our fixed-point theorem to prove the existence theorem for Fredholm integral inclusions omega(t) is an element of [f(t) + integral K-1 (0)(t, s, chi(s))theta s] , t is an element of [0, 1] where f is an element of C [0, 1] is a given real valued function and K : [0, 1] x [0, 1] x R -> K-cv(R) is a given multivalued operator, where K-cv represents the family of nonempty compact and convex subsets of R and omega is an element of C [0, 1] is the unknown function. We also provide a non-trivial example to show the significance of our main result.