Some Generalizations of Different Types of Quantum Integral Inequalities for Differentiable Convex Functions with Applications

Abstract

In this paper, we prove a new quantum integral equality involving a parameter, left and right quantum derivatives. Then, we use the newly established equality and prove some new estimates of quantum Ostrowski, quantum midpoint, quantum trapezoidal and quantum Simpson’s type inequalities for q-differentiable convex functions. It is also shown that the newly established inequalities are the refinements of the existing inequalities inside the literature. Finally, some examples and applications are given to illustrate the investigated results.

Keywords

• midpoint inequalities
• trapezoidal inequalities
• Ostrowski’s inequalities
• Simpson’s inequalities
• quantum calculus
• convex functions