Some inequalities using s-preinvexity via quantum calculus

Abstract

Utilizing mappings whose first derivatives absolute values are s-preinvex, we present a unified approach to investigating some different types of quantum integral inequalities such as midpoint-type, Simpson-type, averaged midpoint-trapezoid-type and trapezoid-type inequality. Also, we give an upper bound for quantum integral inequalities via product of two s-preinvex functions.

Subject Classification: (2010):

• 26A51
• 26D15
• 05A30
• 41A55

Keywords:

• Quantum integrals
• S-preinvex functions
• Hermite–Hadamard’s inequality
• Simpson’s inequality