Fejér-Type Midpoint and Trapezoidal Inequalities for the Operator <i>ω</i>₁,<i>ω</i>₂-Preinvex Functions

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
• <i>ω</i>₁,<i>ω</i>₂-preinvexity
• self-adjoint operators
• positive operators
• functions of self-adjoint operators