Common φ-Fixed Point Results for S-Operator Pair in Symmetric M-Metric Spaces

In this article, we define a new class of noncommuting self mappings known as the S-operator pair. Also, we provide the existence and uniqueness of common fixed point results involving the S-operator pair satisfying the (Formula presented.) -contractive condition in m-metric spaces, which unifies and generalizes most of the existing relevant fixed point theorems. Furthermore, the variables in the m-metric space are symmetric, which is significant for solving nonlinear problems in operator theory. In addition, examples are provided in order to illustrate the concepts and results presented herein. It has been demonstrated that the results can be applied to prove the existence of a solution to a system of integral equations, a nonlinear fractional differential equation and an ordinary differential equation for damped forced oscillations. Also, in the end, the satellite web coupling problem is solved.