A new Hilbert-type integral inequality and the equivalent form.
A new Hilbert-type linear operator with a composite kernel and its applications.
A new inequality similar to Hilbert's inequality.
A new kind of error bounds for some quadrature rules.
A new look at Newton's inequalities.
A new method to obtain decay rate estimates for dissipative systems
We consider the wave equation damped with a boundary nonlinear velocity feedback p(u'). Under some geometrical conditions, we prove that the energy of the system decays to zero with an explicit decay rate estimate even if the function ρ has not a polynomial behavior in zero. This work extends some results of Nakao, Haraux, Zuazua and Komornik, who studied the case where the feedback has a polynomial behavior in zero and completes a result of Lasiecka and Tataru. The proof is based on the construction...
A new method to prove and find analytic inequalities.
A new method to study analytic inequalities.
A new nonlinear retarded integral inequality and its application.
A new part-metric-related inequality chain and an application.
A new proof of a theorem about generalized orthogonal polynomials.
A new proof of inequality for continuous linear functionals.
A new proof of Kelley's Theorem
Kelley's Theorem is a purely combinatorial characterization of measure algebras. We first apply linear programming to exhibit the duality between measures and this characterization for finite algebras. Then we give a new proof of the Theorem using methods from nonstandard analysis.
A new proof of monotonicity for extended mean values.
A new proof of some inequality connected with quadratures.
A new proof of the monotonicity of power means.
A new proof of the monotonicity property of power means.
A new refinement of the Hermite-Hadamard inequality for convex functions.
A new series of conjectures and open questions in optimization and matrix analysis
We present below a new series of conjectures and open problems in the fields of (global) Optimization and Matrix analysis, in the same spirit as our recently published paper [J.-B. Hiriart-Urruty, Potpourri of conjectures and open questions in Nonlinear analysis and Optimization. SIAM Review 49 (2007) 255–273]. With each problem come a succinct presentation, a list of specific references, and a view on the state of the art of the subject.
A new series of conjectures and open questions in optimization and matrix analysis
We present below a new series of conjectures and open problems in the fields of (global) Optimization and Matrix analysis, in the same spirit as our recently published paper [J.-B. Hiriart-Urruty, Potpourri of conjectures and open questions in Nonlinear analysis and Optimization. SIAM Review49 (2007) 255–273]. With each problem come a succinct presentation, a list of specific references, and a view on the state of the art of the subject.