Abstract

Convex functions play an important role in finding the inequalities, those help in finding the solutions of different types of equations and equations involving functions. In this article, we have considered convex functions in a normed linear space. We have established some results on composite convex sets and composite convex functions. We have considered quasi-arithmetic mean, that unifies efficiently all types of power means. On applying the principles of composite convex functions, we have established a Hermite-Hadamard like inequality. The functions considered are composite convex functions with respect to a strictly monotonic continuous composite function. The composite convex functions serve as a comprehensive generalization of composite convex functions. As an application, we have established some inequalities on integrable composite convex functions. The results are deferred mean type inequalities. The results on inequalities can be applied for further investigations as well as for application in finding the solutions in different areas of research.

Keywords and Phrases

Integral inequality; Convex function; Composite function.

A.M.S. subject classification

26A51, 26B25, 26D15, 90C26.

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