New Developments on Ostrowski Type Inequalities via <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mi>q</a:mi> </a:math>-Fractional Integrals Involving <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M2"> <c:mi>s</c:mi> </c:math>-Convex Functions

Abstract

In the present paper, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M3"> <a:mi>q</a:mi> </a:math> -fractional integral operators are used to construct quantum analogue of Ostrowski type inequalities for the class of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M4"> <c:mi>s</c:mi> </c:math> -convex functions. The limiting cases include the nonfractional existing cases from literature. Specially, Ostrowski type inequalities for <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" id="M5"> <e:mi>q</e:mi> </e:math> -integrals and Ostrowski type inequalities for convex functions are deduced.