scholarly journals Beta type integral formula associated with the generalized Lommel-Wright function

2019 ◽  
Vol 2019 (1) ◽  
pp. 39-44
Author(s):  
Kottakkaran Sooppy Nisar ◽  
Sirazul Haq ◽  
Abdul Hakim Khan
Keyword(s):  
Integral Formula ◽  
Wright Function ◽  
Type Integral

scholarly journals Fractional Integral Inequalities for Exponentially Nonconvex Functions and Their Applications

2021 ◽  
Vol 5 (3) ◽  
pp. 80
Author(s):  
Hari Mohan Srivastava ◽  
Artion Kashuri ◽  
Pshtiwan Othman Mohammed ◽  
Dumitru Baleanu ◽  
Y. S. Hamed
Keyword(s):  
Integral Inequalities ◽  
Fractional Integrals ◽  
Auxiliary Result ◽  
Wright Function ◽  
Nonconvex Functions ◽  
Special Cases ◽  
Type Integral ◽  
Generic Class ◽  
Two Parameters ◽  
Class Of Functions

In this paper, the authors define a new generic class of functions involving a certain modified Fox–Wright function. A useful identity using fractional integrals and this modified Fox–Wright function with two parameters is also found. Applying this as an auxiliary result, we establish some Hermite–Hadamard-type integral inequalities by using the above-mentioned class of functions. Some special cases are derived with relevant details. Moreover, in order to show the efficiency of our main results, an application for error estimation is obtained as well.

scholarly journals BAKER–AKHIEZER FUNCTION AS ITERATED RESIDUE AND SELBERG-TYPE INTEGRAL

2009 ◽  
Vol 51 (A) ◽  
pp. 59-73 ◽  
Author(s):  
GIOVANNI FELDER ◽  
ALEXANDER P. VESELOV
Keyword(s):  
Root System ◽  
Integral Formula ◽  
Explicit Evaluation ◽  
Type Integral

AbstractA simple integral formula as an iterated residue is presented for the Baker–Akhiezer function related toAn-type root system in both the rational and trigonometric cases. We present also a formula for the Baker–Akhiezer function as a Selberg-type integral and generalise it to the deformedAn,1-case. These formulas can be interpreted as new cases of explicit evaluation of Selberg-type integrals.

scholarly journals On regularization of the Cauchy problem for elliptic systems in weighted Sobolev spaces

2019 ◽  
Vol 27 (6) ◽  
pp. 815-834
Author(s):  
Yulia Shefer ◽  
Alexander Shlapunov
Keyword(s):  
Cauchy Problem ◽  
Sobolev Spaces ◽  
Integral Formula ◽  
Weighted Sobolev Spaces ◽  
Elliptic Systems ◽  
Fundamental Solutions ◽  
Type Integral ◽  
The Cauchy Problem ◽  
Ill Posed ◽  
Neumann Type

AbstractWe consider the ill-posed Cauchy problem in a bounded domain{\mathcal{D}}of{\mathbb{R}^{n}}for an elliptic differential operator{\mathcal{A}(x,\partial)}with data on a relatively open subsetSof the boundary{\partial\mathcal{D}}. We do it in weighted Sobolev spaces{H^{s,\gamma}(\mathcal{D})}containing the elements with prescribed smoothness{s\in\mathbb{N}}and growth near{\partial S}in{\mathcal{D}}, controlled by a real number γ. More precisely, using proper (left) fundamental solutions of{\mathcal{A}(x,\partial)}, we obtain a Green-type integral formula for functions from{H^{s,\gamma}(\mathcal{D})}. Then a Neumann-type series, constructed with the use of iterations of the (bounded) integral operators applied to the data, gives a solution to the Cauchy problem in{H^{s,\gamma}(\mathcal{D})}whenever this solution exists.

scholarly journals Gap Phenomenon of an Abstract Willmore Type Functional of Hypersurface in Unit Sphere

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Yanqi Zhu ◽  
Jin Liu ◽  
Guohua Wu
Keyword(s):  
Critical Point ◽  
Unit Sphere ◽  
Variational Equation ◽  
Integral Formula ◽  
Willmore Functional ◽  
Type Integral

For ann-dimensional hypersurface in unit sphere, we introduce an abstract Willmore type calledWn,F-Willmore functional, which generalizes the well-known classic Willmore functional. Its critical point is called theWn,F-Willmore hypersurface, for which the variational equation and Simons’ type integral equalities are obtained. Moreover, we construct a few examples ofWn,F-Willmore hypersurface and give a gap phenomenon characterization by use of our integral formula.

scholarly journals Integral formulas with weight factors

1992 ◽  
Vol 52 (1) ◽  
pp. 26-39
Author(s):  
Telemachos Hatziafratis
Keyword(s):  
Complete Intersection ◽  
Integral Formula ◽  
Integral Formulas ◽  
Weight Factors ◽  
Type Integral

AbstractA Bochner-Martinelli-Koppelman type integral formula with weight factors is derived on complete intersection submanifolds of domains of Cn.

scholarly journals An explicit Koppelman type integral formula on analytic varieties.

1986 ◽  
Vol 33 (3) ◽  
pp. 335-341 ◽  
Author(s):  
Telemachos E. Hatziafratis
Keyword(s):  
Integral Formula ◽  
Type Integral ◽  
Analytic Varieties
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