Some different types of parameterized inequalities pertaining to generalized (m, h₁, h₂) -preinvex functions via generalized fractional integral operators and their applications

Abstract

A new identity, with two parameters for differentiable function with respect to another functions via generalized integral operators, is first obtained. By applying the established identity, the trapezium, midpoint and Simpson type integral inequalities pertaining to generalized (m, h₁, h₂) -preinvex functions are deduced. It is pointed out that the results of this research provide integral inequalities for almost all fractional integrals discovered in recent past decades. Various special cases have been identified. Some applications of the our results to special means and new error estimates for the trapezium and midpoint quadrature formula have been presented. The ideas and techniques of this paper may stimulate further research in the field of integral inequalities.

Subject Classification: (2010):

• Primary: 26A51
• Secondary: 26A33
• 26D07
• 26D10
• 26D15

Keywords:

• Trapezium inequality
• Simpson inequality
• Preinvexity
• General fractional integrals