Generalized Hukuhara-Clarke Derivative of Interval-valued Functions and its Properties

This paper is devoted to the study of gH - Clarke derivative for interval-valued functions. To find properties of the gH -Clarke derivative, the concepts of limit superior, limit inferior, and sublinear interval-valued functions are studied in the sequel. It is proved that the upper gH -Clarke derivative of a gH -Lipschitz continuous interval-valued function (IVF) always exists. For a convex and gH -Lipschitz IVF, the upper gH -Clarke derivative is found to be identical with the gH -directional derivative. It is observed that the upper gH -Clarke derivative is a sublinear IVF. Several numerical examples are provided to support the entire study.