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Article

Fejér-Type Midpoint and Trapezoidal Inequalities for the Operator ω1,ω2-Preinvex Functions

by
Sikander Mehmood
1,
Hari Mohan Srivastava
2,3,4,5,
Pshtiwan Othman Mohammed
6,
Eman Al-Sarairah
7,8,
Fiza Zafar
1 and
Kamsing Nonlaopon
9,*
1
Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan 60800, Pakistan
2
Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
3
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
4
Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ1007 Baku, Azerbaijan
5
Center for Converging Humanities, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Republic of Korea
6
Department of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, Iraq
7
Department of Mathematics, Khalifa University, Abu Dhabi P.O. Box 127788, United Arab Emirates
8
Department of Mathematics, Al-Hussein Bin Talal University, Ma’an P.O. Box 33011, Jordan
9
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
*
Author to whom correspondence should be addressed.
Axioms 2023, 12(1), 16; https://doi.org/10.3390/axioms12010016
Submission received: 17 November 2022 / Revised: 20 December 2022 / Accepted: 21 December 2022 / Published: 24 December 2022
(This article belongs to the Section Mathematical Analysis)
Versions Notes

Abstract

In this work, we obtain some new integral inequalities of the Hermite–Hadamard–Fejér type for operator ω1,ω2-preinvex functions. The bounds for both left-hand and right-hand sides of the integral inequality are established for operator ω1,ω2-preinvex functions of the positive self-adjoint operator in the complex Hilbert spaces. We give the special cases to our results; thus, the established results are generalizations of earlier work. In the last section, we give applications for synchronous (asynchronous) functions.
Keywords: Hermite–Hadamard inequalities; Hermite–Hadamard–Fejér inequalities; ω1,ω2-preinvexity; self-adjoint operators; positive operators; functions of self-adjoint operators; Hölder inequality; synchronous (asynchronous) functions Hermite–Hadamard inequalities; Hermite–Hadamard–Fejér inequalities; ω1,ω2-preinvexity; self-adjoint operators; positive operators; functions of self-adjoint operators; Hölder inequality; synchronous (asynchronous) functions

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MDPI and ACS Style

Mehmood, S.; Srivastava, H.M.; Mohammed, P.O.; Al-Sarairah, E.; Zafar, F.; Nonlaopon, K. Fejér-Type Midpoint and Trapezoidal Inequalities for the Operator ω1,ω2-Preinvex Functions. Axioms 2023, 12, 16. https://doi.org/10.3390/axioms12010016

AMA Style

Mehmood S, Srivastava HM, Mohammed PO, Al-Sarairah E, Zafar F, Nonlaopon K. Fejér-Type Midpoint and Trapezoidal Inequalities for the Operator ω1,ω2-Preinvex Functions. Axioms. 2023; 12(1):16. https://doi.org/10.3390/axioms12010016

Chicago/Turabian Style

Mehmood, Sikander, Hari Mohan Srivastava, Pshtiwan Othman Mohammed, Eman Al-Sarairah, Fiza Zafar, and Kamsing Nonlaopon. 2023. "Fejér-Type Midpoint and Trapezoidal Inequalities for the Operator ω1,ω2-Preinvex Functions" Axioms 12, no. 1: 16. https://doi.org/10.3390/axioms12010016

APA Style

Mehmood, S., Srivastava, H. M., Mohammed, P. O., Al-Sarairah, E., Zafar, F., & Nonlaopon, K. (2023). Fejér-Type Midpoint and Trapezoidal Inequalities for the Operator ω1,ω2-Preinvex Functions. Axioms, 12(1), 16. https://doi.org/10.3390/axioms12010016

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