In the present paper, we are defining a subclass of harmonic univalent functions with positive coefficients in unit disc U by using fractional calculus operator. Further we obtain distortion bounds, extreme points and radii of convexity for functions belonging to this class and discuss a class preserving integral operator. Here we also determine that the class studied in this paper is closed un...

This paper aims to provide sufficient conditions for starlikeness and convexity of Hadamard product (convolution) certain multivalent analytic functions with positive real parts. Moreover, the a integral operator other convolution results are also considered.

The X s,b spaces, as used by Beals, Bourgain, Kenig-Ponce-Vega, Klainerman-Machedon and others, are fundamental tools to study the low-regularity behaviour of non-linear dispersive equations. It is of particular interest to obtain bilinear or multilinear estimates involving these spaces. By Plancherel's theorem and duality, these estimates reduce to estimating a weighted convolution integral in...

We introduce an algebraic theory of integration on quantum planes and other braided spaces. In the one dimensional case we obtain a novel picture of the Jackson q-integral as indefinite integration on the braided group of functions in one variable x. Here x is treated with braid statistics q rather than the usual bosonic or Grassmann ones. We show that the definite integral ∫ x∞ −x∞ can also be...

The paper is concerned with the evaluation of the convolution integral R R d 1 x−y f (y)dy in d dimensions (usually d = 3), when f is given as piecewise polynomial of possibly large degree, i.e., f may be considered as an hp-finite element function. The underlying grid is locally refined using various levels of dyadically organised grids. The result of the convolution is approximated in the sam...

The Line Integral Convolution (LIC) method, which blurs white noise textures along a vector field, is an effective way to visualize overall flow patterns in a 2D domain [Cabral & Leedom '93]. The method produces a flow texture image based on the input velocity field defined in the domain. Because of the nature of the algorithm, the texture image tends to be blurry. This sometimes makes it diffi...

UFLIC (Unsteady Flow Line Integral Convolution) is an effective texture synthesis technique to visualize unsteady flow with enhanced temporal coherence, but it is time-consuming to generate. This paper presents an accelerated algorithm, called AUFLIC (Accelerated UFLIC), to speed up the UFLIC generation. Our algorithm saves, re-uses, and updates pathlines in the value scattering processes. A fl...

Recommended by Brigitte Forster-Heinlein For λ > −1 and μ ≥ 0, we consider a liner operator I μ λ on the class A of analytic functions in the unit disk defined by the convolution f μ −1 * fz, where f μ 1 − μz 2 F 1 a, b, c; z μzz 2 F 1 a, b, c; z , and introduce a certain new subclass of A using this operator. Several interesting properties of these classes are obtained.

Because of their causal structure, (convolution) Volterra integral equations arise as models in a variety of real-world situations including rheological stress-strain analysis, population dynamics and insurance risk prediction. In such practical situations, often only an approximation for the kernel is available. Consequently, a key aspect in the analysis of such equations is estimating the eff...