A Loeb Measure Approach To The Riesz Representation Theorem
A lower bound for ratio of power means.
A method for constructing orthonormal bases for non-archimedean Banach spaces of continuous functions
A method for solving fuzzy Fredholm integral equations of the second kind.
A monotonicity property of power means.
A monotonicity property of ratios of symmetric homogeneous means.
A New Approach to Fuzzy Arithmetic
This work shows an application of a generalized approach for constructing dilation-erosion adjunctions on fuzzy sets. More precisely, operations on fuzzy quantities and fuzzy numbers are considered. By the generalized approach an analogy with the well known interval computations could be drawn and thus we can define outer and inner operations on fuzzy objects. These operations are found to be useful in the control of bioprocesses, ecology and other domains where data uncertainties exist.* This work...
A new approach to Ky Fan-type inequalities.
A new generalization of Ostrowski type inequality on time scales.
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 the monotonicity of power means.
A new proof of the monotonicity property of power means.
A new upper bound of the logarithmic mean.
A nonstandard analysis characterization of Arzela's quasi-uniform convergence for sequences of real functions
A nonstandard characterization of regular surfaces.
A nonstandard-analysis characterization of submanifolds in Euclidean space.
A note on Bierstone-Milman-Pawłucki's paper "Composite differentiable functions"
We demonstrate that the composite function theorems of Bierstone-Milman-Pawłucki and of Glaeser carry over to any polynomially bounded, o-minimal structure which admits smooth cell decomposition. Moreover, the assumptions of the o-minimal versions can be considerably relaxed compared with the classical analytic ones.
A note on composition operators on spaces of real analytic functions
We characterize composition operators on spaces of real analytic functions which are open onto their images. We give an example of a semiproper map φ such that the associated composition operator is not open onto its image.
A note on differences of Power means