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

Sikander Mehmood; Hari Mohan Srivastava; Pshtiwan Othman Mohammed; Eman Al-Sarairah; Fiza Zafar; Kamsing Nonlaopon

doi:10.3390/axioms12010016

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

Sikander Mehmood, Hari Mohan Srivastava, Pshtiwan Othman Mohammed, Eman Al-Sarairah, Fiza Zafar, Kamsing Nonlaopon

Mathematics

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1 Scopus citations

Abstract

In this work, we obtain some new integral inequalities of the Hermite–Hadamard–Fejér type for operator (Formula presented.) -preinvex functions. The bounds for both left-hand and right-hand sides of the integral inequality are established for operator (Formula presented.) -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.

Original language	British English
Article number	16
Journal	Axioms
Volume	12
Issue number	1
DOIs	https://doi.org/10.3390/axioms12010016
State	Published - Jan 2023

Keywords

functions of self-adjoint operators
Hermite–Hadamard inequalities
Hermite–Hadamard–Fejér inequalities
Hölder inequality
positive operators
self-adjoint operators
synchronous (asynchronous) functions
ω,ω-preinvexity

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10.3390/axioms12010016

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title = "Fej{\'e}r-Type Midpoint and Trapezoidal Inequalities for the Operator ω1,ω2-Preinvex Functions",

abstract = "In this work, we obtain some new integral inequalities of the Hermite–Hadamard–Fej{\'e}r type for operator (Formula presented.) -preinvex functions. The bounds for both left-hand and right-hand sides of the integral inequality are established for operator (Formula presented.) -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 = "functions of self-adjoint operators, Hermite–Hadamard inequalities, Hermite–Hadamard–Fej{\'e}r inequalities, H{\"o}lder inequality, positive operators, self-adjoint operators, synchronous (asynchronous) functions, ω,ω-preinvexity",

author = "Sikander Mehmood and Srivastava, {Hari Mohan} and Mohammed, {Pshtiwan Othman} and Eman Al-Sarairah and Fiza Zafar and Kamsing Nonlaopon",

note = "Funding Information: This work was supported by the National Science, Research, and Innovation Fund (NSRF), Thailand. Publisher Copyright: {\textcopyright} 2022 by the authors.",

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AU - Mehmood, Sikander

AU - Srivastava, Hari Mohan

AU - Mohammed, Pshtiwan Othman

AU - Al-Sarairah, Eman

AU - Zafar, Fiza

AU - Nonlaopon, Kamsing

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N2 - In this work, we obtain some new integral inequalities of the Hermite–Hadamard–Fejér type for operator (Formula presented.) -preinvex functions. The bounds for both left-hand and right-hand sides of the integral inequality are established for operator (Formula presented.) -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.

AB - In this work, we obtain some new integral inequalities of the Hermite–Hadamard–Fejér type for operator (Formula presented.) -preinvex functions. The bounds for both left-hand and right-hand sides of the integral inequality are established for operator (Formula presented.) -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.

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KW - Hermite–Hadamard inequalities

KW - Hermite–Hadamard–Fejér inequalities

KW - Hölder inequality

KW - positive operators

KW - self-adjoint operators

KW - synchronous (asynchronous) functions

KW - ω,ω-preinvexity

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

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