scholarly journals Majorization problems and integral transforms for a Class of Univalent Functions with missing coefficients

2014 ◽  
Vol 33 (2) ◽  
pp. 217 ◽  
Author(s):  
Som P. Goyal ◽  
Rakesh Kumar ◽  
Teodor Bulboaca
Keyword(s):  
Integral Transform ◽  
Univalent Functions ◽  
Integral Transforms ◽  
Geometrical Properties ◽  
Important Concept ◽  
Special Integral

In 2005, Ponnusamy and Sahoo have introduced a special subclass of univalent functions Un(\lambda) (n 2 N, > 0) and obtained some geometrical properties, including strongly starlikeness and convexity, for the functions of this subclass Un(). Moreover, they have studied some important properties of an integral transform connected with these subclasses. The aim of the present paper is to investigate another important concept of majorization for the functions belonging to the class Un(\lambda) (0 <\lambda=< 1). We shall also discuss a majorization problem for some special integral transforms.

INTEGRAL TRANSFORM OF K4-FUNCTION

2021 ◽  
Vol 21 (2) ◽  
pp. 429-436
Author(s):  
SEEMA KABRA ◽  
HARISH NAGAR
Keyword(s):  
Laplace Transform ◽  
Hypergeometric Function ◽  
Integral Transform ◽  
Integral Transforms ◽  
Gauss Hypergeometric Function ◽  
Wright Function ◽  
Generalized Wright Function ◽  
Special Cases ◽  
Euler Transform

In this present work we derived integral transforms such as Euler transform, Laplace transform, and Whittaker transform of K4-function. The results are given in generalized Wright function. Some special cases of the main result are also presented here with new and interesting results. We further extended integral transforms derived here in terms of Gauss Hypergeometric function.

Generalized Mellin Convolutions and their Asymptotic Expansions

1984 ◽  
Vol 36 (5) ◽  
pp. 924-960 ◽  
Author(s):  
R. Wong ◽  
J. P. Mcclure
Keyword(s):  
Asymptotic Expansions ◽  
Fractional Integral ◽  
Integral Transform ◽  
Integral Transforms ◽  
Generalized Function ◽  
Positive Parameter ◽  
Ordinary Sense ◽  
Integrable Functions ◽  
Classical Integral ◽  
Image Position

A large number of important integral transforms, such as Laplace, Fourier sine and cosine, Hankel, Stieltjes, and Riemann- Liouville fractional integral transforms, can be put in the form1.1where f(t) and the kernel, h(t), are locally integrable functions on (0,∞), and x is a positive parameter. Recently, two important techniques have been developed to give asymptotic expansions of I(x) as x → + ∞ or x → 0+. One method relies heavily on the theory of Mellin transforms [8] and the other is based on the use of distributions [24]. Here, of course, the integral I(x) is assumed to exist in some ordinary sense.If the above integral does not exist in any ordinary sense, then it may be regarded as an integral transform of a distribution (generalized function). There are mainly two approaches to extend the classical integral transforms to distributions.

scholarly journals Some Schemata for Applications of the Integral Transforms of Mathematical Physics

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 254 ◽  
Author(s):  
Yuri Luchko
Keyword(s):  
Differential Equations ◽  
Integral Transform ◽  
First Integral ◽  
Integral Transforms ◽  
Mathematical Physics ◽  
Basic Properties ◽  
Survey Article ◽  
Laplace Integral ◽  
Generating Operators

In this survey article, some schemata for applications of the integral transforms of mathematical physics are presented. First, integral transforms of mathematical physics are defined by using the notions of the inverse transforms and generating operators. The convolutions and generating operators of the integral transforms of mathematical physics are closely connected with the integral, differential, and integro-differential equations that can be solved by means of the corresponding integral transforms. Another important technique for applications of the integral transforms is the Mikusinski-type operational calculi that are also discussed in the article. The general schemata for applications of the integral transforms of mathematical physics are illustrated on an example of the Laplace integral transform. Finally, the Mellin integral transform and its basic properties and applications are briefly discussed.

scholarly journals Integral transforms, convolution products, and first variations

2004 ◽  
Vol 2004 (11) ◽  
pp. 579-598 ◽  
Author(s):  
Bong Jin Kim ◽  
Byoung Soo Kim ◽  
David Skoug
Keyword(s):  
Integral Transform ◽  
Integral Transforms ◽  
Continuous Functions ◽  
Convolution Product ◽  
First Variation ◽  
Alpha Beta ◽  
Convolution Products ◽  
The First Variation ◽  
Complex Valued

We establish the various relationships that exist among the integral transformℱα,βF, the convolution product(F∗G)α, and the first variationδFfor a class of functionals defined onK[0,T], the space of complex-valued continuous functions on[0,T]which vanish at zero.

scholarly journals On Integral Transforms

1956 ◽  
Vol 10 (3) ◽  
pp. 125-128
Author(s):  
B. W. Conolly
Keyword(s):  
Integral Transform ◽  
Integral Transforms ◽  
Mellin Transforms ◽  
Image Position

Titchmarsh and others [4] havo studied integral transform pairs of tho typeshowing how such pairs may be generated as a consequence of the relation which holds between the Mellin transforms of the kernels.

scholarly journals Extended Stokes' Problems for Relatively Moving Porous Half-Planes

2009 ◽  
Vol 2009 ◽  
pp. 1-10 ◽  
Author(s):  
Chi-Min Liu
Keyword(s):  
Exact Solutions ◽  
Integral Transform ◽  
Initial Conditions ◽  
Integral Transforms ◽  
Momentum Equation ◽  
Transform Method ◽  
Stokes Problems ◽  
Flow Phenomena ◽  
Mass Influx ◽  
Mathematical Techniques

A shear flow motivated by relatively moving half-planes is theoretically studied in this paper. Either the mass influx or the mass efflux is allowed on the boundary. This flow is called the extended Stokes' problems. Traditionally, exact solutions to the Stokes' problems can be readily obtained by directly applying the integral transforms to the momentum equation and the associated boundary and initial conditions. However, it fails to solve the extended Stokes' problems by using the integral-transform method only. The reason for this difficulty is that the inverse transform cannot be reduced to a simpler form. To this end, several crucial mathematical techniques have to be involved together with the integral transforms to acquire the exact solutions. Moreover, new dimensionless parameters are defined to describe the flow phenomena more clearly. On the basis of the exact solutions derived in this paper, it is found that the mass influx on the boundary hastens the development of the flow, and the mass efflux retards the energy transferred from the plate to the far-field fluid.

scholarly journals Certain Integral Transform and Fractional Integral Formulas for the Generalized Gauss Hypergeometric Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Junesang Choi ◽  
Praveen Agarwal
Keyword(s):  
Hypergeometric Functions ◽  
Fractional Integral ◽  
Integral Transform ◽  
Special Functions ◽  
Integral Transforms ◽  
Integral Formulas ◽  
Special Cases

A remarkably large number of integral transforms and fractional integral formulas involving various special functions have been investigated by many authors. Very recently, Agarwal gave some integral transforms and fractional integral formulas involving theFp(α,β)(·). In this sequel, using the same technique, we establish certain integral transforms and fractional integral formulas for the generalized Gauss hypergeometric functionsFp(α,β,m)(·). Some interesting special cases of our main results are also considered.

Unified Integral Transform Approach in the Hybrid Solution of Multidimensional Nonlinear Convection-Diffusion Problems

2010 ◽  
Author(s):  
Renato M. Cotta ◽  
Joa˜o N. N. Quaresma ◽  
Leandro A. Sphaier ◽  
Carolina P. Naveira-Cotta
Keyword(s):  
Open Source ◽  
Integral Transform ◽  
Nonlinear Partial Differential Equations ◽  
Integral Transforms ◽  
Analytical Methodology ◽  
Convection Diffusion ◽  
Development Platform ◽  
Unit Code ◽  
Nonlinear Transient ◽  
Diffusion Problems

The present work summarizes the theory and describes the algorithm related to the construction of an open source mixed symbolic-numerical computational code named UNIT — Unified Integral Transforms, that provides a development platform for finding solutions of linear and nonlinear partial differential equations via integral transforms. The reported research was performed by making use of the symbolic computational system Mathematica v.7.0 and the hybrid numerical-analytical methodology Generalized Integral Transform Technique — GITT. The aim here is to illustrate the robust and precision controlled simulation of multidimensional nonlinear transient convection-diffusion problems, while providing a brief introduction of this open source code. Test cases are selected based on nonlinear multi-dimensional formulations of the Burgers equations, with the establishment of reference results for specific numerical values of the governing parameters. Special aspects and computational behaviors of the algorithm are then discussed, demonstrating the implemented possibilities within the present version of the UNIT code.

scholarly journals Generalized integral transforms with the translation operator on function space

Filomat ◽  
2019 ◽  
Vol 33 (3) ◽  
pp. 869-880
Author(s):  
Seung Chang ◽  
Jae Choi ◽  
Hyun Chung
Keyword(s):  
Integral Transform ◽  
Integral Transforms ◽  
Translation Operator ◽  
Convolution Product ◽  
Generalized Convolution ◽  
Brownian Motion Process ◽  
Motion Process ◽  
Generalized Brownian Motion Process ◽  
Nonzero Mean ◽  
Mean Function

Main goal of this paper is to establish various basic formulas for the generalized integral transform involving the generalized convolution product. In order to establish these formulas, we use the translation operator which was introduced in [9]. It was not easy to establish basic formulas for the generalized integral transforms because the generalized Brownian motion process used in this paper has the nonzero mean function. In this paper, we can easily establish various basic formulas for the generalized integral transform involving the generalized convolution product via the translation operator.

scholarly journals Geometric properties of some linear operators defined by convolution

2008 ◽  
Vol 39 (4) ◽  
pp. 325-334 ◽  
Author(s):  
R. Aghalary ◽  
A. Ebadian ◽  
S. Shams
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Integral Transform ◽  
Integral Transforms ◽  
Linear Operators ◽  
Geometric Properties ◽  
Special Cases ◽  
Classical Integral ◽  
Alpha Beta

Let $\mathcal{A}$ denote the class of normalized analytic functions in the unit disc $ U $ and $ P_{\gamma} (\alpha, \beta) $ consists of $ f \in \mathcal{A} $ so that$ \exists ~\eta \in \mathbb{R}, \quad \Re \bigg \{e^{i\eta} \bigg [(1-\gamma) \Big (\frac{f(z)}{z}\Big )^{\alpha}+ \gamma \frac{zf'(z)}{f(z)} \Big (\frac{f(z)}{z}\Big )^{\alpha} - \beta\bigg ]\bigg \} > 0. $ In the present paper we shall investigate the integral transform$ V_{\lambda, \alpha}(f)(z) = \bigg \{\int_{0}^{1} \lambda(t) \Big (\frac{f(tz)}{t}\Big )^{\alpha}dt\bigg \}^{\frac{1}{\alpha}}, $ where $ \lambda $ is a non-negative real valued function normalized by $ \int_{0}^{1}\lambda(t) dt=1 $. Actually we aim to find conditions on the parameters $ \alpha, \beta, \gamma, \beta_{1}, \gamma_{1} $ such that $ V_{\lambda, \alpha}(f) $ maps $ P_{\gamma}(\alpha, \beta) $ into $ P_{\gamma_{1}}(\alpha, \beta_{1}) $. As special cases, we study various choices of $ \lambda(t) $, related to classical integral transforms.

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