Generalized Fixed Point Theorems in G-Cone Metric Spaces Involving Φ-Contractions and Auxiliary Perturbations

In this work, we provide a set of enhanced fixed-point theorems over Banach spaces with normal cones in the context of G-cone metric spaces. Our results extend and generalize existing theorems by incorporating φ-contractive mappings and perturbation functions within the contractive conditions. Specifically, we propose new fixed-point theorems using φ-difference type conditions, auxiliary control functions, and jointly lower semi-continuous metrics. We present illustrative instances to confirm that the theorems are applicable. The results obtained improve classical fixed-point theorems and offer broader applicability in nonlinear analysis. We also demonstrate the applicability of the developed theorems to fractional differential equations.