Displaying similar documents to “Some nonlinear weakly singular integral inequalities with two variables and 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.

Periodic solutions for second order Hamiltonian systems

Qiongfen Zhang, X. H. Tang (2012)

Applications of Mathematics

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By using the least action principle and minimax methods in critical point theory, some existence theorems for periodic solutions of second order Hamiltonian systems are obtained.