On Hilbert-Pachpatte multiple integral inequalities.
On Hilbert's inequality for double series and its applications.
On homeomorphic and diffeomorphic solutions of the Abel equation on the plane
We consider the Abel equation φ[f(x)] = φ(x) + a on the plane ℝ², where f is a free mapping (i.e. f is an orientation preserving homeomorphism of the plane onto itself with no fixed points). We find all its homeomorphic and diffeomorphic solutions φ having positive Jacobian. Moreover, we give some conditions which are equivalent to f being conjugate to a translation.
On homogeneous quasideviation menas.
On ideal equal convergence
We consider ideal equal convergence of a sequence of functions. This is a generalization of equal convergence introduced by Császár and Laczkovich [Császár Á., Laczkovich M., Discrete and equal convergence, Studia Sci. Math. Hungar., 1975, 10(3–4), 463–472]. Our definition of ideal equal convergence encompasses two different kinds of ideal equal convergence introduced in [Das P., Dutta S., Pal S.K., On and *-equal convergence and an Egoroff-type theorem, Mat. Vesnik, 2014, 66(2), 165–177]_and [Filipów...
On indefinite BV-integrals
We present an example of a locally BV-integrable function in the real line whose indefinite integral is not the sum of a locally absolutely continuous function and a function that is Lipschitz at all but countably many points.
On inequalities for hypergeometric analogues of the arithmetic-geometric mean.
On Inequalities for Products of Power Sums.
On inequalities of Hardy-Sobolev type.
On infinite composition of affine mappings
Let be affine mappings of . It is well known that if there exists j ≤ 1 such that for every the composition (1) is a contraction, then for any infinite sequence and any , the sequence (2) is convergent and the limit is independent of z. We prove the following converse result: If (2) is convergent for any and any belonging to some subshift Σ of N symbols (and the limit is independent of z), then there exists j ≥ 1 such that for every the composition (1) is a contraction. This result...
On integrability in F-spaces
Some usual and unusual properties of the Riemann integral for functions x : [a,b] → X where X is an F-space are investigated. In particular, a continuous integrable -valued function (0 < p < 1) with non-differentiable integral function is constructed. For some class of quasi-Banach spaces X it is proved that the set of all X-valued functions with zero derivative is dense in the space of all continuous functions, and for any two continuous functions x and y there is a sequence of differentiable...
On integrability of functions defined by trigonometric series.
On integral forms of generalised Mathieu series.
On integral inequalities for functions of several independent variables.
On integral inequalities of Gronwall-Bellman-Bihari type in several variables.
On integral inequalities of the Sobolev type.
On inverse Hilbert-type inequalities.
On iterative roots of a homeomorphism of the circle with an irrational rotation number.
On Itô-Kurzweil-Henstock integral and integration-by-part formula
In this paper we derive the Integration-by-Parts Formula using the generalized Riemann approach to stochastic integrals, which is called the Itô-Kurzweil-Henstock integral.
On jensen type inequalities with ordered variables.