Abstract
In this paper, using a generalized integral operator, of the Riemann-Liouville type, defined and studied in a previous work by the authors, we obtain various integral inequalities for positive functions, which contains several reported in the literature. Various remarks carried out throughout the work and pointed out in the Conclusions, show the scope and strength of our results, in particular, it is shown that under particular cases of the considered kernel, several known fractional integral operators are obtained.
Highlights
Calculus, using di¤erent notions of derivatives and integrals of arbitrary order, has become in recent years one of the centers of attention of mathematical researchers, both pure and applied.By other hand, one of the most developed mathematical areas in the last 20 years is that of Integral Inequalities, associated with di¤erent functional notions: convex, synchronous functions within the framework of Riemann, fractional and generalized integral operators.Throughout the work we use the functionsand k: 2020 Mathematics Subject Classi...cation
The main purpose of this paper, using the generalized fractional integral operator of the Riemann-Liouville type, from De...nition 1, is to establish several integral inequalities, which contain as particular cases, several of those reported in the literature
In this work we have obtained various inequalities of the Hermite-Hadamard type, in the case of di¤erent notions of convexity, and using a generalized fractional operator, which allows obtaining as particular cases, several of those reported in the literature
Summary
Calculus, using di¤erent notions of derivatives and integrals of arbitrary order, has become in recent years one of the centers of attention of mathematical researchers, both pure and applied.By other hand, one of the most developed mathematical areas in the last 20 years is that of Integral Inequalities, associated with di¤erent functional notions: convex, synchronous functions within the framework of Riemann, fractional and generalized integral operators.Throughout the work we use the functions (see [8,9,10,11])and k (cf. de...ned by [2]): 2020 Mathematics Subject Classi...cation. In this paper, using a generalized integral operator, of the RiemannLiouville type, de...ned and studied in a previous work by the authors, we obtain various integral inequalities for positive functions, which contains several reported in the literature. Various remarks carried out throughout the work and pointed out in the Conclusions, show the scope and strength of our results, in particular, it is shown that under particular cases of the considered kernel, several known fractional integral operators are obtained.
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