We generalize the Bourbaki, Dunkl–Williams, Hudzick–Landes, and Maligranda2 inequalities in normed linear spaces for various p-angular distances. Then we obtain3 several equality conditions of these generalized inequalities, mainly, in strictly con-4 vex spaces. In addition, corresponding to some p-angular distance, we compare the5 achieved upper bounds with each other. Furthermore, we present several examples and6 counterexamples illustrate our results.

Keywords