Quantum Ostrowski inequalities for q-differentiable convex functions

Quantum calculus or q -calculus is sometimes called as calculus without limits. In this, we obtain q -analogues of mathematical objects that can be recaptured as q → 1. There are two types of q -addition, the Nalli-Ward-Al-Salam q -addition (NWA) and the Jackson-Hahn-Cigler q -addition (JHC). The first one is commutative and associative, while the second one is neither. That is why sometimes more than one q -analogue exists. These two operators form the basis of the method which unities hypergeometric series and q -hypergeometric series and which gives many formulas of q -calculus a natural form. The history of quantum calculus can be traced back to Euler (1707– 1783), who first introduced the q in the tracks of Newton’s infinite series. In recent years many researchers have shown keen interest in studying and investigating quantum calculus thus it emerges as interdisciplinary subject. This is of course due to the fact that quantum analysis is very helpful numerous fields and has large applications in various areas of pure and applied sciences such as computer science and particle physics, and also acts as an important tool for researchers working with analytic number theory or in theoretical physics. The quantum calculus can be viewed as bridge between Mathematics and Physics. Many scientists who are using quantum calculus are physicists, as quantum calculus has many applications in quantum group theory. For some recent developments in quantum calculus interested readers are referred to [3, 4, 5, 6, 7, 8, 10, 11, 12]. In recent decades theory of convex functions has been extensively studied due to its great importance in various fields of pure and applied sciences. Theory of inequalities and theory of convex functions are closely related to each other, thus various inequalities can be found in the literature which are proved for convex functions and