Fixed point theorems for Maia α-ψ contractive type mappings with applications

We introduce the concept of Maia α-ψ contractive type mappings and establish new fixed point theorems. We derive some results for comparable mappings in partially ordered metric spaces, which extend and generalize various known theorems on the topic. As applications, we study the existence and uniqueness of solutions to inhomogeneous Fredholm integral equations of the second kind, and we apply this study to a nonlinear third order two–point boundary value problem.