Related papers: The Hausdorff-integral and its applications
New index transforms, involving the real part of the modified Bessel function of the first kind as the kernel are considered. Mapping properties such as the boundedness and invertibility are investigated for these operators in the Lebesgue…
In the paper, the authors introduce a new concept "extended $s$-convex functions", establish some new integral inequalities of Hermite-Hadamard type for this kind of functions, and apply these inequalities to derive some inequalities of…
Two kinds of novel generalizations of Nesbitt's inequality are explored in various cases regarding dimensions and parameters in this article. Some other cases are also discussed elaborately by using the semiconcave-semiconvex theorem. The…
L\"uroth series, like regular continued fractions, provide an interesting identification of real numbers with infinite sequences of integers. These sequences give deep arithmetic and measure-theoretic properties of subsets of numbers…
The purpose of this note is to compare various approximation methods as applied to the inverse of the Bessel function of the first kind, in a given domain of the complex plane.
In this paper, a fractional version of the Clifford-Fourier transform is introduced, depending on two numerical parameters. A series expansion for the kernel of the resulting integral transform is derived. In the case of even dimension,…
We use the Laplace transform and the Gamma function to introduce a new integral transform and name it the Laplace-type transform possessing the property of mapping a function to a functional sequence, which cannot be achieved by the Laplace…
The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.
We have recently established some integral inequalities for convex functions via the Hermite-Hadamard's inequalities. In continuation here, we also establish some interesting new integral inequalities for convex functions via the…
This paper develops a new integrated ball (pseudo)metric which provides an intermediary between a chosen starting (pseudo)metric d and the L_p distance in general function spaces. Selecting d as the Hausdorff or Fr\'echet distances, we…
In this paper, some new integral inequalities of Hermite-Hadamard type related to the s-geometrically convex functions are established and some applications to special means of positive real numbers are also given.
We present in this survey some results regarding Riemann_Lebesgue integrability with respect to arbitrary non-additive set functions.
We define a non-absolutely convergent integration on integral currents of dimension 1 in Euclidean space. This integral is closely related to the Henstock-Kurzweil and Pfeffer Integrals. Using it, we prove a generalized Fundamental Theorem…
Several concepts of approximate reasoning in uncertainty processing are linked to the processing of distribution functions. In this paper we make use of probabilistic framework of approximate reasoning by proposing a Lebesgue-type approach…
In this paper, we establish several new inequalities for some differantiable mappings that are connected with the celebrated Hermite-Hadamard integral inequality. Some applications for special means of real numbers are also provided.
We study various measure theories using the classical approach and then compute the Hausdorff dimension of some simple objects and self-similar fractals. We then develop a nonstandard approach to these measure theories and examine the…
New index transforms with Weber type kernels, consisting of products of Bessel functions of the first and second kind are investigated. Mapping properties and inversion formulas are established for these transforms in Lebesgue spaces. The…
This paper shows how the Lebesgue integral can be obtained as a Riemann sum and provides an extension of the Morse Covering Theorem to open sets. Let $X$ be a finite dimensional normed space; let $\mu$ be a Radon measure on $X$ and let…
We aim to introduce a new extension of Mittag-Leffler function via q-analogue and obtained their significant properties including integral representation, q-differentiation, q-Laplace transform, image formula under q-derivative operators.…
We find a generalization of the Mordell integral and we also establish a set of properties for a generalization of the Mordell integral similar to those in the third author's PhD thesis.