New Grüss Type Inequalities for Riemann--Stieltjes Integral With Monotonic Integrators and Applications

New Grüss Type Inequalities for Riemann–stieltjes Integral with Monotonic Integrators and Applications

In this paper several new inequalities of Grüss’ type for Riemann– Stieltjes integral with monotonic nondecreasing integrators under various assumptions for integrands are proved. Applications for functions of selfadjoint operators on complex Hilbert spaces are provided as well. Department of Mathematics, Faculty of Science, Jerash University, 26150 Jerash, Jordan. E-mail address: mwomath@gmail...

Some Grüss Type Inequalities for Riemann-stieltjes Integral and Applications

Inequalities for the Riemann-stieltjes Integral of S-dominated Integrators with Applications (i)

Assume that u; v : [a; b] ! R are monotonic nondecreasing on the interval [a; b] : We say that the complex-valued function h : [a; b] ! C is S-dominated by the pair (u; v) if jh (y) h (x)j 2 [u (y) u (x)] [v (y) v (x)] for any x; y 2 [a; b] : In this paper we show amongst other that Z b a f (t) dh (t) 2 Z b a jf (t)j du (t) Z b a jf (t)j dv (t) ; for any continuous function f : [a; b] ! C. Appl...

INEQUALITIES FOR THE RIEMANN-STIELTJES INTEGRAL OF (p; q)-H-DOMINATED INTEGRATORS WITH APPLICATIONS

Assume that u; v : [a; b] ! R are monotonic nondecreasing on the interval [a; b] : For p; q > 1 with 1 p + 1 q = 1; we say that the complex-valued function h : [a; b] ! C is (p; q)-H-dominated by the pair (u; v) if jh (y) h (x)j [u (y) u (x)] 1=p [v (y) v (x)] 1=q for any x; y 2 [a; b] with y x: In this paper we show amongst other that Z b a f dh Z b a jf j du 1=p Z b a jf j dv 1=q ; and Z b a ...

New Jensen and Ostrowski Type Inequalities for General Lebesgue Integral with Applications

Some new inequalities related to Jensen and Ostrowski inequalities for general Lebesgue integral are obtained. Applications for $f$-divergence measure are provided as well.