On new general versions of Hermite–Hadamard type integral inequalities via fractional integral operators with Mittag-Leffler kernel View Full Text


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Article Info

DATE

2021-11-18

AUTHORS

Havva Kavurmacı Önalan, Ahmet Ocak Akdemir, Merve Avcı Ardıç, Dumitru Baleanu

ABSTRACT

The main motivation of this study is to bring together the field of inequalities with fractional integral operators, which are the focus of attention among fractional integral operators with their features and frequency of use. For this purpose, after introducing some basic concepts, a new variant of Hermite–Hadamard (HH-) inequality is obtained for s-convex functions in the second sense. Then, an integral equation, which is important for the main findings, is proved. With the help of this integral equation that includes fractional integral operators with Mittag-Leffler kernel, many HH-type integral inequalities are derived for the functions whose absolute values of the second derivatives are s-convex and s-concave. Some classical inequalities and hypothesis conditions, such as Hölder’s inequality and Young’s inequality, are taken into account in the proof of the findings. More... »

PAGES

186

References to SciGraph publications

  • 2012-03-08. A multivariate extension of an inequality of Brenner–Alzer in ARCHIV DER MATHEMATIK
  • 2013-06-07. Necessary and sufficient conditions for the validity of Jensen’s inequality in ARCHIV DER MATHEMATIK
  • 2011-10-13. New inequalities of hermite-hadamard type for convex functions with applications in JOURNAL OF INEQUALITIES AND APPLICATIONS
  • 2008. Two Korovkin-type theorems in multivariate approximation in BANACH JOURNAL OF MATHEMATICAL ANALYSIS
  • 2020-09-17. Hermite–Jensen–Mercer type inequalities for conformable integrals and related results in ADVANCES IN CONTINUOUS AND DISCRETE MODELS
  • 2011-09-23. A class of nonlinear four-point subdivision schemes in ADVANCES IN COMPUTATIONAL MATHEMATICS
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    http://scigraph.springernature.com/pub.10.1186/s13660-021-02721-9

    DOI

    http://dx.doi.org/10.1186/s13660-021-02721-9

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