‎the subject of this paper is the solution of the fredholm integral equation with toeplitz, hankel and the toeplitz plus hankel kernel. the mean value theorem for integrals is applied and then extended for solving high dimensional problems and finally, some example and graph of error function are presented to show the ability and simplicity of the ‎method.

A factorization theory is proposed for Wiener-Hopf plus Hankel operators with almost periodic Fourier symbols. We introduce a factorization concept for the almost periodic Fourier symbols such that the properties of the factors will allow corresponding operator factorizations. Conditions for left, right, or both-sided invertibility of the Wiener-Hopf plus Hankel operators are therefore obtained...

In this paper we consider a class of weighted integral operators on L2(0,∞) and show that they are unitarily equivalent to little Hankel operators between weighted Bergman spaces of the right half plane. We use two parameters α, β ∈ (−1,∞) and involve two weights to define Bergman spaces of the domain and range of the little Hankel operators. We obtained conditions for the Hankel integral opera...

The method of realizing certain self-reciprocal transforms as (absolute) scattering, previously presented in summarized form in the case of the Fourier cosine and sine transforms, is here applied to the self-reciprocal transform f(y) 7→ H(f)(x) = ∫∞ 0 J0(2 √ xy)f(y) dy, which is isometrically equivalent to the Hankel transform of order zero and is related to the functional equations of the Dede...

In this article we define a class of starlike functions with respect to symmetric points in the domain sine function. Also, investigate coefficients bounds and upper for third order Hankel determinant defined class. We also evaluate Zalcman functional \(|a_{3}^{2}-a_{5}|\). Specializing parameters, improve functions.

Abstract In the present paper, we found sharp bounds of second Hankel determinant logarithmic coefficients starlike and convex functions order $$\alpha $$ ? .

In this presentation we establish new bounds on functions, which have their n-th order Hankel Transform bandlimited. This class of functions is proved to be also Fourier Transform bandlimited. N-th order Hankel Transforms and the consequent bounds are important for the reconstruction in CAT, MRI (Magnetic Resonance Imaging) etc. Indeed many algorithms of modern tomography use the appropriate fo...

In the theory for continuous-time linear systems, the system Hankel operator plays an important role in a number of realization problems ranging from providing an abstract notion of state to yielding tests for state space minimality and algorithms for model reduction. But in the case of continuous-time nonlinear systems, Hankel theory is considerably less developed beyond a well known Hankel ma...

In recent years, the study of Hankel determinants for various subclasses normalised univalent functions f∈S given by f(z)=z+∑n=2∞anzn D={z∈C:|z|<1} has produced many interesting results. The main focus interest been estimating second determinant form H2,2(f)=a2a4−a32. A non-sharp bound H2,2(f) when f∈K(α), α∈[0,1) consisting convex order α was found Krishna and Ramreddy (Hankel starlike alpha. ...