Generalized fractional Hermite-Hadamard type inequalities for m-convex and (α, m)-convex functions

Fractional analysis, as a rapidly developing area, is a tool to bring new derivatives and integrals into the literature with the effort put forward by many researchers in recent years. The theory of inequalities is a subject of many mathematicians’ work in the last century and has contributed to other areas with its applications. Especially in recent years, these two fields, fractional analysis and inequality theory, have shown a synchronous development. Inequality studies have been carried out by using new operators revealed in the fractional analysis. In this paper, by combining two important concepts of these two areas we obtain new inequalities of Chebyshev–Polya–Szegö type by means of generalized fractional integral operators. Our results are concerned with the integral of the product of two functions and the product of two integrals. They improve the results in the paper (J. Math. Inequal. 10(2):491–504, 2016).

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Hermite–Hadamard-Type Inequalities for Convex Functions via the Fractional Integrals with Exponential Kernel

Wang

Zhang

2019

Mathematics

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In this paper, we establish three fundamental integral identities by the first- and second-order derivatives for a given function via the fractional integrals with exponential kernel. With the help of these new fractional integral identities, we introduce a few interesting Hermite–Hadamard-type inequalities involving left-sided and right-sided fractional integrals with exponential kernels for convex functions. Finally, some applications to special means of real number are presented.

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Generalized fractional Hermite-Hadamard type inequalities for m-convex and (α, m)-convex functions

Cited by 4 publications

References 8 publications

Generalized fractional integral inequalities for some classes of symmetrized convex functions

Generalized fractional integral inequalities for some classes of symmetrized convex functions

New refinements of Chebyshev–Pólya–Szegö-type inequalities via generalized fractional integral operators

Hermite–Hadamard-Type Inequalities for Convex Functions via the Fractional Integrals with Exponential Kernel

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