INEQUALITIES FOR THE RIEMANN-STIELTJES INTEGRAL OF (p; q)-H-DOMINATED INTEGRATORS WITH APPLICATIONS
نویسنده
چکیده
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 f gdh Z b a jf j p du 1=p Z b a jgj q dv 1=q for any continuous functions f; g : [a; b] ! C. Applications for the trapezoidal and midpoint inequalities are also given.
منابع مشابه
Inequalities for the Riemann-stieltjes Integral of S-dominated Integrators with Applications (i)
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