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Volume 50 Number 2
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Research articles

ScienceAsia 49 (2023): 212-223 |doi: 10.2306/scienceasia1513-1874.2022.147

Inequalities for m-polynomial exponentially s-type convex functions in fractional calculus

Pshtiwan Othman Mohammeda, Artion Kashurib, Bahaaeldin Abdallac,*, Y. S. Hamedd, Khadijah M. Abualnajad

ABSTRACT:     In this article, we introduce a new class of functions named the m-polynomial exponentially s-type convex and we study some of its algebraic properties. We investigate a new integral inequality of Hermite-Hadamard (H-H) type by using the new introduced definition. Also, we prove a new midpoint identity. By examining this identity we can deduce some integral inequalities of midpoint type for the new introduced definition. Several special cases are discussed in details which emphasize that the results accounted in this paper unify and extend various results in this field of study. Finally, we provide some applications on the Bessel functions and special means of distinct positive real numbers to demonstrate the applicability of the new results.

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a Department of Mathematics, College of Education, University of Sulaimani, Sulaimani, Kurdistan Region, Iraq
b Department of Mathematics, Faculty of Technical and Natural Sciences, University ?Ismail Qemali?, Vlora, Albania
c Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586 Saudi Arabia
d Department of Mathematics and Statistics, College of Science, Taif University, Taif 21944 Saudi Arabia

* Corresponding author, E-mail: babdallah@psu.edu.sa

Received 29 Mar 2021, Accepted 26 Aug 2022