Related papers: A note on comparison between Birkhoff and McShane-…
In this work we discuss the connection between Feynman integrals and Fox functions. Illustrative examples are given.
Multiple-integral representations of the (skew-)Macdonald symmetric functions are obtained. Some bosonization schemes for the integral representations are also constructed.
In this research, Minkowski type functions which are constructed on certain probability distributions, are introduced. There are investigated differential, integral, and other properties of these functions.
By using some basic calculus of multiple integration, we provide an alternative expression of the integral $$ \int_{]a,b[^n} f(\mathbf{x},\min x_i,\max x_i) d\mathbf{x}, $$ in which the minimum and the maximum are replaced with two single…
The q-Bessel-Macdonald functions of kinds 1, 2 and 3 are considered. Their representations by classical integral are constructed.
In this article, we investigate partial integrals and partial derivatives of bivariate fractal interpolation functions. We prove also that the mixed Riemann-Liouville fractional integral and derivative of order $\gamma = (p, q); p > 0,q >…
In this paper we investigate multifractal decompositions based on values of Birkhoff averages of functions from a class of symbolically continuous functions. This will be done for an expanding interval map with infinitely many branches and…
In this paper, we establish new an inequality of weighted Ostrowski-type for double integrals involving functions of two independent variables by using fairly elementary analysis.
In this paper, we obtain some Simpson type inequalities for functions whose second derivatives absolute value or q-th power of them are Q-class functions. Also we give applications to numerical integration.
In this study, we obtain some new integral inequalities for different classes of convex functions by using some elementary inequalities and classical inequalities like general Cauchy inequality and Minkowski inequality.
We explore the properties of an interesting new example of a function which is Lebesgue integrable but not Riemann integrable.
In this paper, the author establishes some Hadamard-type and Bullen-type inequalities for Lipschitzian functions via Riemann Liouville fractional integral. These results have some relationships with [K.-L. Tseng, S.-R. Hwang and K.-C. Hsu,…
The aim of this paper is to study relationships among "gauge integrals" (Henstock, Mc Shane, Birkhoff) and Pettis integral of multifunctions whose values are weakly compact and convex subsets of a general Banach space, not necessarily…
An integral for a scalar function with respect to a multimeasure $N$ taking its values in a locally convex space is introduced. The definition is independent of the selections of $N$ and is related to a functional version of the…
Some integration techniques for real-valued functions with respect to vector measures with values in Banach spaces (and viceversa) are investigated in order to establish abstract versions of classical theorems of Probability and Stochastic…
We supplement the result of the first part of the work with estimates of the integrals of the difference of subharmonic functions in measure with some deterioration of the absolute constants, but these estimates have the form of a…
In the paper we prove several inequalities involving two isotonic linear functionals. We consider inequalities for functions with variable bounds, for Lipschitz and H\" older type functions etc. These results give us an elegant method for…
We study several types of multivalued functions in digital topology.
In this paper we prove a criterion for plurisubharmonic functions in terms of integral mean by complex ellipsoids. Moreover, by using the criterion we prove an analogue of Blaschke-Privalov theorem for plurisubharmonic functions.
An example of constructive (in A.A.Markov's sense) real-valued function, which is integrable by Riemann, but is not integrable by Darboux, is constructed.