New inequalities on generalized \(m\)-convexity on fractal sets. (English) Zbl 1515.26028
Summary: In this research, we study some algebraic and topological properties of generalized \(m\)-convex functions on fractal sets and establish a new Jensen type inequality. Also, we obtain some new Hermite-Hadamard type inequalities for local fractional integrals of this class of functions. As applications, we present some inequalities with generalized special means and generalized probability density functions.
MSC:
| 26D15 | Inequalities for sums, series and integrals |
| 26A33 | Fractional derivatives and integrals |
| 26A51 | Convexity of real functions in one variable, generalizations |
| 28A80 | Fractals |
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