Some New Versions of Integral Inequalities for Left and Right Preinvex Functions in the Interval-Valued Settings

Muhammad Bilal Khan, Savin Treanțǎ, Mohamed S. Soliman, Kamsing Nonlaopon and Hatim Ghazi Zaini
Additional contact information
Muhammad Bilal Khan: Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, Pakistan
Savin Treanțǎ: Department of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, Romania
Mohamed S. Soliman: Department of Electrical Engineering, College of Engineering, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
Kamsing Nonlaopon: Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
Hatim Ghazi Zaini: Department of Computer Science, College of Computers and Information Technology, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia

Mathematics, 2022, vol. 10, issue 4, 1-15

Abstract: The principles of convexity and symmetry are inextricably linked. Because of the considerable association that has emerged between the two in recent years, we may apply what we learn from one to the other. In this paper, our aim is to establish the relation between integral inequalities and interval-valued functions ( IV-Fs ) based upon the pseudo-order relation. Firstly, we discuss the properties of left and right preinvex interval-valued functions (left and right preinvex IV-Fs ). Then, we obtain Hermite–Hadamard (𝓗-𝓗) and Hermite–Hadamard–Fejér (𝓗-𝓗-Fejér) type inequality and some related integral inequalities with the support of left and right preinvex IV-Fs via pseudo-order relation and interval Riemann integral. Moreover, some exceptional special cases are also discussed. Some useful examples are also given to prove the validity of our main results.

Keywords: left and right preinvex interval-valued function; interval Riemann integral; Hermite–Hadamard type inequality; Hermite–Hadamard–Fejér type inequality (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 (4)

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