GENERALIZED n-POLYNOMIAL P-FUNCTIONS WITH SOME RELATED INEQUALITIES AND THEIR APPLICATIONS

Abstract. In this paper, we introduce the notion of generalized n-polynomial P-function. We explore some algebraic properties of this function class. Additionally, we establish a new trapezium type inequality for this generalized class of functions and derive several refinements of the trapezium type inequality for functions whose first derivative in absolute value at a certain power is generalized n-polynomial P-function. Finally, we conclude our paper by exploring some applications of the results we have obtained in the context of special means. Our novel findings generalize previously known results in the literature.