On some new midpoint inequalities for the functions of two variables via quantum calculus

Abstract

Abstract In this paper, first we obtain a new identity for quantum integrals, the result is then used to prove midpoint type inequalities for differentiable coordinated convex mappings. The outcomes provided in this article are an extension of the comparable consequences in the literature on the midpoint inequalities for differentiable coordinated convex mappings.

Keywords

• Hermite–Hadamard inequality
• q 1 q 2 $q_{1}q_{2}$ -integrals
• Quantum calculus
• Co-ordinated convexity
• q 1 q 2 $q_{1}q_{2}$ -derivatives