On a functional equation with asymptotically unique continuous solutions.
On a functional inequality arising in the construction of the product of several metric spaces.
On a functional inequality of Kemperman
On a further generalization of Steffensen's inequality.
On a generalisation of the Hahn-Jordan decomposition for real càdlàg functions
For a real càdlàg function f and a positive constant c we find another càdlàg function which has the smallest total variation among all functions uniformly approximating f with accuracy c/2. The solution is expressed in terms of truncated variation, upward truncated variation and downward truncated variation introduced in earlier work of the author. They are always finite even if the total variation of f is infinite, and they may be viewed as a generalisation of the Hahn-Jordan decomposition for...
On a generalization of Henstock-Kurzweil integrals
We study a scale of integrals on the real line motivated by the integral by Ball and Preiss and some recent multidimensional constructions of integral. These integrals are non-absolutely convergent and contain the Henstock-Kurzweil integral. Most of the results are of comparison nature. Further, we show that our indefinite integrals are a.e. approximately differentiable. An example of approximate discontinuity of an indefinite integral is also presented.
On a generalization of Hilbert-type integral inequality.
On a generalization of smooth and symmetric functions
On a generalization of the Darboux theorem to the multidimensional case.
On a generalization of the Hermite-Hadamard inequality. II.
On a generalization of the Lebesgue integral in
On a generalization of the Perron integral on one-dimensional intervals
On a generalization of -means.
On a generalized Carleson inequality
On a generalized Dhombres functional equation. II.
We consider the functional equation where is a given increasing homeomorphism of an open interval and is an unknown continuous function. In a previous paper we proved that no continuous solution can cross the line where is a fixed point of , with a possible exception for . The range of any non-constant continuous solution is an interval whose end-points are fixed by and which contains in its interior no fixed point except for . We also gave a characterization of the class of continuous...
On a generalized Minkowski inequality and its relation to dominates for t-norms.
On a generalized -inner product and the corresponding Cauchy-Schwarz inequality.
On a generalized retarded integral inequality with two variables.
On a geometric property of positive definite matrices cone.
On a Hilbert-type integral inequality in the subinterval and its operator expression.