Quantum Ostrowski-type inequalities for twice quantum differentiable functions in quantum calculus
Quantum Ostrowski-type inequalities for twice quantum differentiable functions in quantum calculus
Abstract In this paper, we first prove an identity for twice quantum differentiable functions. Then, by utilizing the convexity of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo stretchy="false">∣</m:mo> <m:mrow> <m:mmultiscripts> <m:mrow> <m:mi>D</m:mi> </m:mrow> <m:mrow> <m:mi>q</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> <m:mprescripts /> <m:none /> <m:mrow> <m:mi>b</m:mi> </m:mrow> </m:mmultiscripts> <m:mspace width="0.08em" /> <m:mi>f</m:mi> </m:mrow> <m:mo …