scholarly journals Approximation of Analytic Functions by Chebyshev Functions

2011 ◽  
Vol 2011 ◽  
pp. 1-10
Author(s):  
Soon-Mo Jung ◽  
Themistocles M. Rassias
Keyword(s):  
Differential Equation ◽  
Analytic Functions ◽  
Chebyshev Functions

We solve the inhomogeneous Chebyshev's differential equation and apply this result for approximating analytic functions by the Chebyshev functions.

scholarly journals The Lagrangian Stability for a Class of Second-Order Quasi-Periodic Reversible Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
Yanling Shi ◽  
Jia Li
Keyword(s):  
Differential Equation ◽  
Analytic Functions ◽  
Order Differential Equation ◽  
Reversible Systems ◽  
Invariant Curves ◽  
Real Analytic Functions ◽  
All Solutions ◽  
Small Twist Theorem ◽  
Real Analytic ◽  
Twist Theorem

We study the following two-order differential equation,(Φp(x'))'+f(x,t)Φp(x')+g(x,t)=0,whereΦp(s)=|s|(p-2)s,p>0.f(x,t)andg(x,t)are real analytic functions inxandt,2aπp-periodic inx, and quasi-periodic intwith frequencies(ω1,…,ωm). Under some odd-even property off(x,t)andg(x,t), we obtain the existence of invariant curves for the above equations by a variant of small twist theorem. Then all solutions for the above equations are bounded in the sense ofsupt∈R|x′(t)|<+∞.

scholarly journals Solvability of a New q-Differential Equation Related to q-Differential Inequality of a Special Type of Analytic Functions

2021 ◽  
Vol 5 (4) ◽  
pp. 228
Author(s):  
Ibtisam Aldawish ◽  
Rabha W. Ibrahim
Keyword(s):  
Differential Equation ◽  
Differential Operator ◽  
Analytic Functions ◽  
Differential Inequality ◽  
Laguerre Polynomial ◽  
Analytic Solutions ◽  
Confluent Hypergeometric Function ◽  
Differential Inequalities ◽  
Quantum Calculus

The current study acts on the notion of quantum calculus together with a symmetric differential operator joining a special class of meromorphic multivalent functions in the puncher unit disk. We formulate a quantum symmetric differential operator and employ it to investigate the geometric properties of a class of meromorphic multivalent functions. We illustrate a set of differential inequalities based on the theory of subordination and superordination. In this real case study, we found the analytic solutions of q-differential equations. We indicate that the solutions are given in terms of confluent hypergeometric function of the second type and Laguerre polynomial.

scholarly journals Inclusion and neighborhood properties of a certain subclasses of p-valent functions with negative coefficients

Filomat ◽  
2009 ◽  
Vol 23 (3) ◽  
pp. 1-13 ◽  
Author(s):  
R.M. El-Ashwah
Keyword(s):  
Differential Equation ◽  
Analytic Functions ◽  
Function Class ◽  
Derivative Operator ◽  
Coefficient Bounds ◽  
Ruscheweyh Derivative Operator ◽  
Ruscheweyh Derivative ◽  
Inclusion Relations

By means of Ruscheweyh derivative operator, we introduced and investigated two new subclasses of p-valent analytic functions. The various results obtained here for each of these function class include coefficient bounds and distortion inequalities, associated inclusion relations for the (n, ?)-neighborhoods of subclasses of analytic and multivalent functions with negative coefficients, which are defined by means of non-homogenous differential equation.

Solutions of a singular integro-differential equation related to the adhesive contact problems of elasticity theory

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Nugzar Shavlakadze ◽  
Otar Jokhadze
Keyword(s):  
Differential Equation ◽  
Analytic Functions ◽  
Contact Problems ◽  
Approximate Solutions ◽  
Integral Transforms ◽  
Algebraic Equations ◽  
Adhesive Interaction ◽  
Normal Contact ◽  
Integro Differential Equation ◽  
Linear Algebraic Equations

Abstract Exact and approximate solutions of a some type singular integro-differential equation related to problems of adhesive interaction between elastic thin half-infinite or finite homogeneous patch and elastic plate are investigated. For the patch loaded with vertical forces, there holds a standard model in which vertical elastic displacements are assumed to be constant. Using the theory of analytic functions, integral transforms and orthogonal polynomials, the singular integro-differential equation is reduced to a different boundary value problem of the theory of analytic functions or to an infinite system of linear algebraic equations. Exact or approximate solutions of such problems and asymptotic estimates of normal contact stresses are obtained.

scholarly journals Approximation of Analytic Functions by Bessel's Functions of Fractional Order

2011 ◽  
Vol 2011 ◽  
pp. 1-13
Author(s):  
Soon-Mo Jung
Keyword(s):  
Differential Equation ◽  
Fractional Order ◽  
Analytic Functions ◽  
Bessel Functions

We will solve the inhomogeneous Bessel's differential equationx2y″(x)+xy′(x)+(x2-ν2)y(x)=∑m=0∞amxm, whereνis a positive nonintegral number and apply this result for approximating analytic functions of a special type by the Bessel functions of fractional order.

scholarly journals CORDIAL VOLTERRA INTEGRAL EQUATIONS AND SINGULAR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS IN SPACES OF ANALYTIC FUNCTIONS∗

2017 ◽  
Vol 22 (4) ◽  
pp. 548-567 ◽  
Author(s):  
Urve Kangro
Keyword(s):  
Differential Equation ◽  
Integral Equations ◽  
Analytic Functions ◽  
Analytic Solution ◽  
Exponential Convergence ◽  
Approximate Solutions ◽  
Volterra Integral Equations ◽  
Volterra Integral Operator ◽  
Convergence Of Approximate Solutions ◽  
Spaces Of Analytic Functions

We study general cordial Volterra integral equations of the second kind and certain singular fractional integro-differential equation in spaces of analytic functions. We characterize properties of the cordial Volterra integral operator in these spaces, including compactness and describe its spectrum. This enables us to obtain conditions under which these equations have a unique analytic solution. We also consider approximate solution of these equations and prove exponential convergence of approximate solutions to the exact solution.

Linear directional differential equations in the unit ball: solutions of bounded L-index

2019 ◽  
Vol 69 (5) ◽  
pp. 1089-1098 ◽  
Author(s):  
Andriy Bandura ◽  
Oleh Skaskiv
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Differential Equations ◽  
Unit Ball ◽  
Analytic Functions ◽  
Entire Functions ◽  
Sufficient Conditions ◽  
Analytic Solutions ◽  
Directional Derivatives ◽  
Several Variables

Abstract We study sufficient conditions of boundedness of L-index in a direction b ∈ ℂn ∖ {0} for analytic solutions in the unit ball of a linear higher order non-homogeneous differential equation with directional derivatives. These conditions are restrictions by the analytic coefficients in the unit ball of the equation. Also we investigate asymptotic behavior of analytic functions of bounded L-index in the direction and estimate its growth. The results are generalizations of known propositions for entire functions of several variables.

scholarly journals Generalized Briot-Bouquet differential equation based on new differential operator with complex connections

2020 ◽  
Vol 28 (1) ◽  
pp. 105-114
Author(s):  
Rabha W. Ibrahim
Keyword(s):  
Differential Equation ◽  
Differential Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Difference Operator ◽  
Open Unit ◽  
Open Unit Disk ◽  
New Class ◽  
Generalized Operator ◽  
Generalized Differential

AbstractInequality study is a magnificent field for investigating the geometric behaviors of analytic functions in the open unit disk calling the subordination and superordination. In this work, we aim to formulate a generalized differential-difference operator. We introduce a new class of analytic functions having the generalized operator. Some subordination results are included in the sequel.

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