Abstract
The aim of this study is to investigate the existence of solutions for the following Fredholm integral inclusion phi(t)is an element of f(t)+integral 01K(t,s,phi(s))rho s for 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]xR -> Kcv(R) a given multivalued operator, where Kcv represents the family of non-empty compact and convex subsets of R, phi is an element of C[0,1] is the unknown function and rho is a metric defined on C[0,1]. To attain this target, we take advantage of fixed point theorems for alpha-fuzzy mappings satisfying a new class of contractive conditions in the context of complete metric spaces. We derive new fixed point results which extend and improve the well-known results of Banach, Kannan, Chatterjea, Reich, Hardy-Rogers, Berinde and Ciric by means of this new class of contractions. We also give a significantly non-trivial example to support our new results.