Displaying similar documents to “New integral inequalities for iterated integrals with applications.”

Inequalities for the Riemann–Stieltjes Integral of under the Chord Functions with Applications

Silvestru S. Dragomir (2014)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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We say that the function f : [ a , b ] → ℝ is under the chord if b - t f ( a ) + t - a f ( b ) b - a ≥ f ( t ) for any t ∈ [ a , b ] . In this paper we proved amongst other that ∫ a b u ( t ) d f ( t ) ≥ f ( b ) - f ( a ) b - a ∫ a b u ( t ) d t provided that u : [ a , b ] → ℝ is monotonic nondecreasing and f : [ a , b ] → ℝ is continuous and under the chord. Some particular cases for the weighted integrals in connection with the Fejér inequalities are provided. Applications for continuous functions of selfadjoint operators on Hilbert spaces are also given.