Cauchy and Pólya-Szegö type inequalities involving two linear isotonic functionals

Ostrowski Type Inequalities for Isotonic Linear Functionals

Some inequalities of Ostrowski type for isotonic linear functionals defined on a linear class of function L := {f : [a, b] → R} are established. Applications for integral and discrete inequalities are also given.

Chebyshev and Grüss Type Inequalities Involving Two Linear Functionals and Applications

In the present paper we prove the Chebyshev inequality involving two isotonic linear functionals. Namely, if A and B are isotonic linear functionals, then A(p f g)B(q)+A(p)B(q f g) A(p f )B(qg) + A(pg)B(q f ) , where p,q are non-negative weights and f ,g are similarly ordered functions such that the above-mentioned terms are well-defined. If functionals are equal, i.e. A = B and if p = q , then...

Integral Inequalities on Time Scales via the Theory of Isotonic Linear Functionals

and Applied Analysis 3 Theorem 2.3 Jensen’s inequality 5, Theorem 2.2 . Let a, b ∈ T with a < b, and suppose I ⊂ R is an interval. Assume h ∈ Crd a, b ,R satisfies ∫b a |h t |Δt > 0. If Φ ∈ C I,R is convex and f ∈ Crd a, b , I , then Φ ⎛ ⎝ ∫b a |h t |f t Δt ∫b a |h t |Δt ⎞ ⎠ ≤ ∫b a |h t |Φ ( f t ) Δt ∫b a |h t |Δt . 2.3 In 6 , Özkan et al. proved that Theorem 2.3 is also true if we use the nabl...

The Cauchy problem for linear growth functionals

On a Reverse of Jessen’s Inequality for Isotonic Linear Functionals

A reverse of Jessen’s inequality and its version for m − Ψ−convex and M − Ψ−convex functions are obtained. Some applications for particular cases are also pointed out.