New fixed point results for (ω,t0)-Taylor-Lagrange distance function

We study fixed point problems for mappings that are not contractions in the classical sense. Using the (ω,t0)-Taylor-Lagrange distance function and nonlinear control functions (subhomogeneous and superhomogeneous), we extend previous fixed point results such as those of Banach and Reich. Our method allows handling mappings with nonlinear behavior where earlier approaches fail. The main results include existence and uniqueness theorems supported by examples where classical theorems are not applicable. This work solves an open problem by Jleli and Samet and introduces a flexible framework combining differential structure and nonlinear control, offering new tools in fixed point theory.