Chebyshev and Grüss type inequalities involving two linear functionals and applications

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...

Some extended Simpson-type inequalities and applications

‎In this paper‎, ‎we shall establish some extended Simpson-type inequalities‎ ‎for differentiable convex functions and differentiable concave functions‎ ‎which are connected with Hermite-Hadamard inequality‎. ‎Some error estimates‎ ‎for the midpoint‎, ‎trapezoidal and Simpson formula are also given‎.

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.

Some generalized Ostrowski-Grüss type integral inequalities

Grüss type inequalities for double integrals on time scales

We prove some weighted Grüss type inequalities for double integrals on time scales and unify the corresponding continuous and discrete versions, which are the generalizations of the results proved earlier in the literature