Fixed point theorems for multivalued mappings in G- and G-cone metric spaces using G-Hausdorff contractions

This paper establishes two general fixed-point theorems for multivalued contractive-type maps in G-metric and G-cone metric spaces. A G-Hausdorff contraction condition is generalized to extend the classical results. Nadler’s theorem in the setting of an advanced metric space endowed with higher-order and cone-valued metrics. The framework merges previous findings from the more general extended b-metric and G-metric space theory by considering explicit cone-based inequalities combined with rigorous data-based convergence. From this study, one can see that the fixed-point theorem in the G-cone metric context generalizes the corresponding one in the G-metric space, which shows the more powerful ability of cone-valued analysis. Furthermore, the compactness and upper semi-continuity conditions for multivalued mappings are characterized in this general setting, which allows the results to be applied to more general nonlinear systems. In general, the results provide a more general, analytically solid platform for the fixed point theory in abstract metric-like setting and they promote the development of functional and nonlinear analysis.