On Geometrical Characteristics and Inequalities of New Bicomplex Lebesgue Spaces With Hyperbolic-Valued Norm

Abstract

In this work, it is assumed that the norm over bicomplex numbers is the hyperbolic ( D -valued) norm. In this paper, we provide an overview of bicomplex Lebesgue spaces and investigate some of their geometric properties, including BC-convexity, BC -strict convexity, and BC -uniform convexity. Moreover, the basic inequalities such as D-Holder's inequality and D -Minkowski inequality for bicomplex Lebesgue spaces are presented, used to show geometric properties.