New integral inequalities involving p-convex and s-p-convex functions

Abstract

In this study, new lemmas on $p-$convex and $s-p-$convex functions were derived utilizing the integral $\int_{j}^{k} \frac{\left(x^p - j^p\right)^f \left(k^p - x^p\right)^g m(x)}{x^{(f+g)p}} \,dx$. Through this equality, new integral inequalities were established, and novel upper bounds were obtained with the aid of Euler's beta and hypergeometric functions. The results provided new inequalities for the class of classical convex functions and the class of harmonic convex functions.

Keywords

• $P-$convex function
• $s-p-$convex function
• harmonically convex function
• hypergeometric function

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