Modeling climate smart agriculture in G-metric spaces

Abstract

The aim of climate-smart agriculture (CSA) is to simultaneously enhance agricultural productivity, sustainability, and carbon sequestration. These three objectives are interdependent and the conventional metric spaces, which involve only pair-wise distances, cannot model this. Our approach is a mathematical theory of G-metric spaces, in which the distance function takes three arguments. We present climate-dependent contractive mappings with time-varying contractivity modulators. Our results are: (i) a G-contraction theorem with non-constant modulators, (ii) a coupled fixed-point theorem for bidirectional canopy–soil interactions, and (iii) a stability estimate for policy changes. Our findings are used to evaluate threshold irrigation efficiencies in semi-arid lands and to plan crop rotations for carbon sequestration.