Inequalities for the Riemann-stieltjes Integral of S-dominated Integrators with Applications (i)
نویسنده
چکیده
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. Applications for the trapezoidal and midpoint inequalities are given. New inequalities for some µ Cebyšev and (CBS)-type functionals are presented. Natural applications for continuous functions of selfadjoint and unitary operators on Hilbert spaces are provided as well.
منابع مشابه
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...
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