A generalization of Simpson’s inequality via differentiable mapping using extended \((s,m)\)-convex functions. (English) Zbl 1411.26020

Du, Tingsong; Li, Yujiao; Yang, Zhiqiao

Appl. Math. Comput. 293, 358-369 (2017).

Summary: The authors deduce a differentiable mapping integral identity with two parameters. Using this integral identity, this paper establishes new inequalities of Simpson type for extended \((s,m)\)-convex functions under certain conditions. This contributes to new better estimates than the earlier results. Finally, these inequalities are applied to special means.

MSC:

26D15	Inequalities for sums, series and integrals
26A51	Convexity of real functions in one variable, generalizations
39B62	Functional inequalities, including subadditivity, convexity, etc.

Keywords:

Simpson inequality; Hölder inequality; \((s,m)\)-convex function

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