Exponential type p–convex function with some related inequalities and their applications

Abstract

In this paper, the idea of exponential type p–convex function and its algebraic properties have been investigated.The authors proved new trapezium type inequality for this new class of functions and derived many refinements of the trapezium type inequality for functions whose first derivative in absolute value at certain power is exponential type p–convex. Finally, some new bounds for special means of different positive real numbers are provided as well. The findings show some generalizations of the known results.