On Hammerstein Integral Equations and Engineering Models via Paired Contractions in Partial Metric Spaces

This paper presents a novel class of paired contractions to establish fixed point results for multivalued mappings within the framework of partial metric spaces. Requirements for the existence of fixed points are investigated, and a few nontrivial instances are given to illustrate the usefulness and relevance of the proposed notions. The findings herein improve, expand upon, and harmonize some of the most significant results in the literature. To show how, under certain assumptions, the new class of contractions reduces to classical situations, corollaries are inferred. Sufficient conditions for the existence of solutions for a class of nonlinear Hammerstein integral equations and the solvability of a boundary value problem of Bessel-type differential equations subject to integral boundary conditions pertaining to the ascending motion of a rocket, as an engineering model, are formulated in order to illustrate the effectiveness of the idea herein.