Introduce Gateaux and Frechet Derivatives in Riesz Spaces - Aydin, Abdullah; Korkmaz, Erdal (Prairie View A & M Univ, Dept Mathematics, 2020)
In this paper, the Gateaux and Frechet differentiations of functions on Riesz space are introduced without topological structure. Thus, we aim to study Gateaux and Frechet differentiability functions in vector lattice by developing topology-free techniques, and also, we give some relations with other kinds of operators.
Keywords: Gateaux differentiable; Frechet differentiable; Riesz space; Order bounded operator