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Hadamard and Fejér–Hadamard Inequalities for <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mfenced open="(" close=")" separators="|"> <a:mrow> <a:mi>α</a:mi> <a:mo>,</a:mo> <a:mi>h</a:mi> <a:mo>−</a:mo> <a:mi>m</a:mi> </a:mrow> </a:mfenced> <a:mo>−</a:mo> <a:mi>p</a:mi> </a:math>-Convex Functions via Riemann–Liouville Fractional Integrals

Wenyan Jia, Muhammad Yussouf, Ghulam Farid, Khuram Ali Khan

2021Mathematical Problems in Engineering14 citationsDOIOpen Access PDF

Abstract

In this paper, we introduce <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M2"> <a:mfenced open="(" close=")" separators="|"> <a:mrow> <a:mi>α</a:mi> <a:mo>,</a:mo> <a:mi>h</a:mi> <a:mo>−</a:mo> <a:mi>m</a:mi> </a:mrow> </a:mfenced> <a:mo>−</a:mo> <a:mi>p</a:mi> </a:math> -convex function and some related functions. By applying this generalized definition, new versions of Hadamard and Fejér–Hadamard fractional integral inequalities for Riemann–Liouville fractional integrals are given. The presented results hold at the same time for different types of convexities.

Topics & Concepts

Hadamard transformMathematicsConvex functionHadamard three-lines theoremRegular polygonPure mathematicsDiscrete mathematicsMathematical analysisHadamard matrixGeometryMathematical Inequalities and ApplicationsFunctional Equations Stability Results
Hadamard and Fejér–Hadamard Inequalities for <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mfenced open="(" close=")" separators="|"> <a:mrow> <a:mi>α</a:mi> <a:mo>,</a:mo> <a:mi>h</a:mi> <a:mo>−</a:mo> <a:mi>m</a:mi> </a:mrow> </a:mfenced> <a:mo>−</a:mo> <a:mi>p</a:mi> </a:math>-Convex Functions via Riemann–Liouville Fractional Integrals | Litcius