Fejér-Type Midpoint and Trapezoidal Inequalities for the Operator ω 1 , ω 2 -Preinvex Functions.

In this work, we obtain some new integral inequalities of the Hermite–Hadamard–Fejér type for operator ω 1 , ω 2 -preinvex functions. The bounds for both left-hand and right-hand sides of the integral inequality are established for operator ω 1 , ω 2 -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. [ABSTRACT FROM AUTHOR]