Some New Hermite-Hadamard-Fejér Fractional Type Inequalities for h -Convex and Harmonically h -Convex Interval-Valued Functions

Humaira Kalsoom, Muhammad Amer Latif, Zareen A. Khan and Miguel Vivas-Cortez
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Humaira Kalsoom: Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
Muhammad Amer Latif: Department of Basic Sciences, King Faisal University, Hofuf 31982, Al-Hasa, Saudi Arabia
Zareen A. Khan: Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
Miguel Vivas-Cortez: Escuela de Ciencias Físicas y Matemáticas, Facultad de Ciencias Naturales y Exactas, Pontificia Universidad Católica del Ecuador, Sede Quito 17-01-2184, Ecuador

Mathematics, 2021, vol. 10, issue 1, 1-22

Abstract: In this article, firstly, we establish a novel definition of weighted interval-valued fractional integrals of a function ? ? using an another function ? ( ? ? ) . As an additional observation, it is noted that the new class of weighted interval-valued fractional integrals of a function ? ? by employing an additional function ? ( ? ? ) characterizes a variety of new classes as special cases, which is a generalization of the previous class. Secondly, we prove a new version of the Hermite-Hadamard-Fejér type inequality for h -convex interval-valued functions using weighted interval-valued fractional integrals of a function ? ? according to another function ? ( ? ? ) . Finally, by using weighted interval-valued fractional integrals of a function ? ? according to another function ? ( ? ? ) , we are establishing a new Hermite-Hadamard-Fejér type inequality for harmonically h -convex interval-valued functions that is not previously known. Moreover, some examples are provided to demonstrate our results.

Keywords: weighted interval-valued fractional operators; h -convex interval-valued functions; h -harmonically convex interval-valued functions; weighted interval-valued Hermite-Hadamard type inequality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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