A generalized inequality in non-Newtonian calculus using a multiplicative absolute value for twice-differentiable functions

Abstract

The present paper introduces a novel general inequality derived from functions that are twice differentiable in a multiplicative sense, according to the Riemann integral. By employing the multiplicative absolute value and presuming that the function demonstrates multiplicative $h$-convexity, we can derive further inequality principles. We also present these results for multiplicatively $s$-convex functions and $P$-functions. The final section discusses specific cases, including trapezoids, midpoints, Bullen, Milne, and Simpson multiplicative inequalities.

Keywords

• generalized inequalities
• multiplicative integrals
• multiplicative absolute value
• multiplicative h-convex functions

References

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