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.
A new simple proof for an inequality of Chebyshev type.
A new theorem on exponential stability of periodic evolution families on Banach spaces.
A new type of stable generalized convex functions.
A new upper bound of the logarithmic mean.
A non absolutely convergent integral which admits transformation and can be used for integration on manifolds
A non-absolutely convergent integral in and the theorem of Gauss
A non-absolutely convergent integral which admits -transformations
A non-archimedean “curve integral” and its application to the construction of potentials and solutions of differential equations
A non-commutative sewing lemma.
A nonexistence result for the Kurzweil integral
It is shown that there exist a continuous function and a regulated function defined on the interval such that vanishes everywhere except for a countable set, and the -integral of with respect to does not exist. The problem was motivated by extensions of evolution variational inequalities to the space of regulated functions.
A nonlinear Banach-Steinhaus theorem and some meager sets in Banach spaces
We establish a Banach-Steinhaus type theorem for nonlinear functionals of several variables. As an application, we obtain extensions of the recent results of Balcerzak and Wachowicz on some meager subsets of L¹(μ) × L¹(μ) and c₀ × c₀. As another consequence, we get a Banach-Mazurkiewicz type theorem on some residual subset of C[0,1] involving Kharazishvili's notion of Φ-derivative.
A nonlinear inequality arising in geometry and Calabi-Bernstein type problems.
A nonstandard analysis characterization of Arzela's quasi-uniform convergence for sequences of real functions