Abstract
In this work the authors establish a new generalized version of Montgomery’s identity in the setting of quantum calculus. From this result, some new estimates of Ostrowski type inequalities are given using preinvex functions. Given the generality of preinvex functions, particular q —integral inequalities are established with appropriate choice of the parametric bifunction. Some new special cases from the main results are obtained and some known results are recaptured as well. At the end, a briefly conclusion is given.
Highlights
Quantum calculus, or q−calculus, has had an important development in recent decades, both in pure mathematics and its applicability, for example in Physics [1]
The convexity of a function has played an important role as a tool in the development of inequalities
Motivated by the above literatures, the main objective of this article is to obtain a generalization of the Montgomery identity given in (4) using the concepts of q-calculus
Summary
Q−calculus, has had an important development in recent decades, both in pure mathematics and its applicability, for example in Physics [1]. The convexity of a function has played an important role as a tool in the development of inequalities. Some fields of Mathematics have used this property: harmonic analysis, interpolation theory, and control theory, as can be seen in the works of C.P. Niculescu [2], C. Trenţă [5,6]
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