Hermite-Hadamard inequalities for generalized convex functions in interval-valued calculus

Jorge E. Macías-Díaz; Muhammad Bilal Khan; Muhammad Aslam Noor; Abd Allah A. Mousa; Safar M Alghamdi; Jorge E. Macías-Díaz; Muhammad Bilal Khan; Muhammad Aslam Noor; Abd Allah A. Mousa; Safar M Alghamdi

doi:10.3934/math.2022236

AIMS Mathematics

2022, Volume 7, Issue 3: 4266-4292. doi: 10.3934/math.2022236

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Hermite-Hadamard inequalities for generalized convex functions in interval-valued calculus

1.
Departamento de Matemáticas y Física, Universidad Autónoma de Aguascalientes, Avenida Universidad 940, Ciudad Universitaria, Aguascalientes 20131, Mexico
2.
Department of Mathematics, School of Digital Technologies, TallinnUniversity, Narva Rd. 25, 10120 Tallinn, Estonia
3.
Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, Pakistan
4.
Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia

Received: 06 November 2021 Revised: 14 December 2021 Accepted: 14 December 2021 Published: 20 December 2021
MSC : 26A33, 26A51, 26D10

The importance of convex and non-convex functions in the study of optimization is widely established. The concept of convexity also plays a key part in the subject of inequalities due to the behavior of its definition. 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 study, first, Hermite-Hadamard type inequalities for LR-$ p $-convex interval-valued functions (LR-$ p $-convex-I-V-F) are constructed in this study. Second, for the product of p-convex various Hermite-Hadamard (HH) type integral inequalities are established. Similarly, we also obtain Hermite-Hadamard-Fejér (HH-Fejér) type integral inequality for LR-$ p $-convex-I-V-F. Finally, for LR-$ p $-convex-I-V-F, various discrete Schur's and Jensen's type inequalities are presented. Moreover, the results presented in this study are verified by useful nontrivial examples. Some of the results reported here for be LR-$ p $-convex-I-V-F are generalizations of prior results for convex and harmonically convex functions, as well as $ p $-convex functions.
Citation: Jorge E. Macías-Díaz, Muhammad Bilal Khan, Muhammad Aslam Noor, Abd Allah A. Mousa, Safar M Alghamdi. Hermite-Hadamard inequalities for generalized convex functions in interval-valued calculus[J]. AIMS Mathematics, 2022, 7(3): 4266-4292. doi: 10.3934/math.2022236

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Abstract

The importance of convex and non-convex functions in the study of optimization is widely established. The concept of convexity also plays a key part in the subject of inequalities due to the behavior of its definition. 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 study, first, Hermite-Hadamard type inequalities for LR-$ p $-convex interval-valued functions (LR-$ p $-convex-I-V-F) are constructed in this study. Second, for the product of p-convex various Hermite-Hadamard (HH) type integral inequalities are established. Similarly, we also obtain Hermite-Hadamard-Fejér (HH-Fejér) type integral inequality for LR-$ p $-convex-I-V-F. Finally, for LR-$ p $-convex-I-V-F, various discrete Schur's and Jensen's type inequalities are presented. Moreover, the results presented in this study are verified by useful nontrivial examples. Some of the results reported here for be LR-$ p $-convex-I-V-F are generalizations of prior results for convex and harmonically convex functions, as well as $ p $-convex functions.

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