Vector Fixed Point Theorem with Application to Systems of Nonlinear Elastic Beams Equations (Journal of Nonlinear Modeling and Analysis, 2025)
In this work, we establish a new existence and uniqueness of vectorfixed point for a class of sum-type vector operators with some mixed monotoneproperty in partially ordered product Banach spaces. The technique used isThompson’s part metric, and our goal is to extend and improve existing worksin the scalar case vector case. As an application, we study the existence anduniqueness of solutions for systems of nonlinear singular fourth-order elasticbeam equations with nonlinear boundary conditions.
Keywords: Mixed monotone vector operators; Meir-Keeler type; systems of nonlinear elastic beams equations; Thompson metric; $ε$-chainable metric space.