Ostrowski’s inequality on time scales Original Research Article

A time scale version of Ostrowski’s inequality is given as follows: Let View the MathML sourcef,g∈Crd([a,b],R) be two linearly independent functions, then for any α∈[−1,1]α∈[−1,1] and any arbitrary x∈Crd([a,b],R)x∈Crd([a,b],R) with equation(C1) View the MathML source∫abf(t)x(t)Δt=0,∫abg(t)x(t)Δt=1, Turn MathJax on the function View the MathML sourceαx(t)+(1−α)y(t),t∈[a,b] Turn MathJax on satisfies condition (C1) and View the MathML source∫abx2(t)Δt≥∫ab[αx(t)+(1−α)y(t)]2Δt≥AAB−C2, Turn MathJax on where View the MathML sourceA=∫abf2(t)Δt,B=∫abg2(t)Δt,C=∫abf(t)g(t)Δt Turn MathJax on and View the MathML source