Lipschitz (q,p)-Summing Maps from C(K)-Spaces to G-Metric Spaces

Abstract

We introduce and study variants of Lipschitz (q,p)-summing operators in the framework of G-metric spaces, extending classical results from metric spaces to this broader setting. G-metric spaces, introduced by Mustafa and Sims, provide a natural generalization of metric spaces where the distance function takes three arguments instead of two. We establish fundamental properties of Lipschitz (q,p)-summing maps from C(K)-spaces to G-metric spaces, prove domination theorems analogous to Pietsch's classical results, and develop a theory of G-metric concave operators. Our main result extends Pisier's theorem to the G-metric setting, providing integral domination estimates for certain classes of these operators. Applications to fixed point theory, approximation theory, and geometric analysis in G-metric spaces are discussed.