The purpose of this paper is to obtain univalence of a certain nonlinear integral transform of functions belonging to a subclass of analytic functions. We also give several interesting geometric properties of the integral transform.

The p-adic q-integral (= Iq-integral) was defined by author in the previous paper [1, 3]. In this paper, we consider Iq-Fourier transform and investigate some properties which are related to this transform. §

1. The Classical Problems 1 2. Roth’s Orthogonal Function Method 5 3. Halász’s Modification of Roth’s Method 7 4. The Method of van der Corput 10 5. The Method of Davenport 12 6. Generalizations of the Problem 16 7. Beck’s Probabilistic Method 23 8. A Combinatorial and Geometric Approach 27 9. A Fourier Transform Approach 37 10. An Integral Geometric Approach 46 11. The Davenport-Roth Method Re...

There are various numerical methods to solve nonlinear integral equations. Most of them transform the integral equation into a system of nonlinear algebraic equations. It is cumbersome to solve these systems, or the solution may be unreliable. In this paper, we study the application of the fixed point method to solve Volterra-Hammerstein integral equations. This method does not lead to a nonlin...

Fractal dimension spectra have been used to characterize the complexity of dynamical time series since the 1980s. Calculation of these spectra are traditionally based on fixed-size methods that are grid-based, such as the histogram technique, or sample-based, such as the correlation-integral method. This paper extends the Chhabra and Jensen direct approach on histogrambinned data by deriving th...

This paper presents an extension of McKean’s (1965) incomplete Fourier transform method to solve the two-factor partial differential equation for the price and early exercise surface of an American call option, in the case where the volatility of the underlying evolves randomly. The Heston (1993) square-root process is used for the volatility dynamics. The price is given by an integral equation...

In this study, we present a direct method to solve nonlinear two-dimensional VolterraHammerestein integral equations in terms of twodimensional piecewise constant block-pulse functions (2D-PCBFs). Properties of these functions and operational matrix of integration together with the product operational matrix are presented and used to transform the integral equation to a matrix equation which co...

‎the main purpose of this paper is to study the numerical solution of nonlinear volterra integral equations with constant delays, based on the multistep collocation method. these methods for approximating the solution in each subinterval are obtained by fixed number of previous steps and fixed number of collocation points in current and next subintervals. also, we analyze the convergence of the...

This paper presents a volume integral equation method for an electromagnetic scattering problem for three-dimensional Maxwell’s equations in the presence of a biperiodic, anisotropic, and possibly discontinuous dielectric scatterer. Such scattering problem can be reformulated as a strongly singular volume integral equation (i.e., integral operators that fail to be weakly singular). In this pape...