New Extensions of the Parameterized Inequalities Based on Riemann–Liouville Fractional Integrals

Hasan Kara, Hüseyin Budak () and Fatih Hezenci
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Hasan Kara: Department of Mathematics, Faculty of Science and Arts, Duzce University, Düzce 81620, Türkiye
Hüseyin Budak: Department of Mathematics, Faculty of Science and Arts, Duzce University, Düzce 81620, Türkiye
Fatih Hezenci: Department of Mathematics, Faculty of Science and Arts, Duzce University, Düzce 81620, Türkiye

Mathematics, 2022, vol. 10, issue 18, 1-12

Abstract: In this article, we derive the above and below bounds for parameterized-type inequalities using the Riemann–Liouville fractional integral operators and limited second derivative mappings. These established inequalities generalized the midpoint-type, trapezoid-type, Simpson-type, and Bullen-type inequalities according to the specific choices of the parameter. Thus, a generalization of many inequalities and new results were obtained. Moreover, some examples of obtained inequalities are given for better understanding by the reader. Furthermore, the theoretical results are supported by graphs in order to illustrate the accuracy of each of the inequalities obtained according to the specific choices of the parameter.

Keywords: bounded functions; Hermite–Hadamard type inequality; trapezoid inequalities; midpoint-type inequalities; Simpson-type inequalities; Bullen-type inequalities (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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