Quantum Integral Inequalities on Finite Intervals

The Integral Inequalities can be used for the study of qualitative and quantitative properties of integrals and they perform an important role in the theory of differential equations. The study of the fractional q-integral inequalities is also of great importance. The purpose of this thesis is to study q-calculus analogs of some classical integral inequalities. In particular, some of the greatest significant integral inequalities of analysis are extended to Quantum calculus. We will work on the q-generalization of the Hölder, Hermite-Hadamard, Trapezoid, Ostrowski, Cauchy-BunyakovskySchwarz, Grüss, and Grüss-Chebysev integral inequalities. The analysis is based on the notions of q-derivative and q-integral on finite intervals presented recently by the author in [9]. Keywords: Quantum Integral Inequalities; Hölder’s inequality, Hermite-Hadamard’s inequality, Ostrowski's Inequality, Grüss-Chebysev integral inequality