Hermite–Hadamard-type inequalities for interval-valued preinvex functions via Riemann–Liouville fractional integrals
Nidhi Sharma, Sanjeev Kumar Singh, Shashi Kant Mishra, Abdelouahed Hamdi
Abstract
Abstract In this paper, we introduce $(h_{1},h_{2})$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>h</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>h</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo>)</mml:mo> </mml:math> -preinvex interval-valued function and establish the Hermite–Hadamard inequality for preinvex interval-valued functions by using interval-valued Riemann–Liouville fractional integrals. We obtain Hermite–Hadamard-type inequalities for the product of two interval-valued functions. Further, some examples are given to confirm our theoretical results.
Topics & Concepts
Hermite polynomialsMathematicsInterval (graph theory)Hadamard transformType (biology)AlgorithmMathematical analysisCombinatoricsEcologyBiologyMathematical Inequalities and ApplicationsFunctional Equations Stability ResultsOptimization and Variational Analysis