Existence of solutions for boundary value problems and nonlinear matrix equations via F-contraction mappings in b-metric spaces

The purpose of this paper is to present some sufficient conditions for the existence of solutions for nonlinear matrix equations and the second-order two-point boundary value problems for nonlinear ordinary differential equations via fixed point theorem. To do this, we introduce two classes of mappings called the Suzuki-Geraghty-(alpha, beta)-F-contraction mappings and generalize Suzuki-type (alpha, beta)-F-contraction mappings and establish some fixed point results for these classes of mappings. The results obtained in this work complements, extends, generalizes, and improves some known results in the literature.