In this brief note,  using the technique of measures of noncompactness, we give some extensions of Darbo fixed point theorem. Also we prove  an existence result for a quadratic  integral equation of Hammerstein type on an unbounded interval in two variables  which includes several classes of nonlinear integral equations of Hammerstein type. Furthermore, an example is presented to show the effic...

In this paper, interval Legendre wavelet method is investigated to approximated the solution of the interval Volterra-Fredholm-Hammerstein integral equation. The shifted interval Legendre polynomials are introduced and based on interval Legendre wavelet method is defined. The existence and uniqueness theorem for the interval Volterra-Fredholm-Hammerstein integral equations is proved. Some examp...

in this study a numerical method is developed to solve the hammerstein integral equations. to this end the kernel has been approximated using the leastsquares approximation schemes based on legender-bernstein basis. the legender polynomials are orthogonal and these properties improve the accuracy of the approximations. also the nonlinear unknown function has been approximated by using the berns...

in this work, a new iterative method is proposed for obtaining the approximate solution of a class of hammerstein type integral equations system. the main structure of this method is based on the richardson iterative method for solving an algebraic linear system of equations. some conditions for existence and unique solution of this type equations are imposed. convergence analysis and error bou...

In this study a numerical method is developed to solve the Hammerstein integral equations. To this end the kernel has been approximated using the leastsquares approximation schemes based on Legender-Bernstein basis. The Legender polynomials are orthogonal and these properties improve the accuracy of the approximations. Also the nonlinear unknown function has been approximated by using the Berns...

An approximation method based on operational matrices of Bernstein polynomials used for the solution of Hammerstein integral equations. The operational matrices of these functions are utilized to reduce a nonlinear Hammerstein and Volterra Hammerstein integral equation to a system of nonlinear algebraic equations. The method is computationally very simple and attractive, and applications are de...

An ecient method, based on the Legendre wavelets, is proposed to solve thesecond kind Fredholm and Volterra integral equations of Hammerstein type.The properties of Legendre wavelet family are utilized to reduce a nonlinearintegral equation to a system of nonlinear algebraic equations, which is easilyhandled with the well-known Newton's method. Examples assuring eciencyof the method and its sup...

The Volterra delay integral equations have numerous applications in various branches of science, including biology, ecology, physics and modeling of engineering and natural sciences. In many cases, it is difficult to obtain analytical solutions of these equations. So, numerical methods as an efficient approximation method for solving Volterra delay integral equations are of interest to many res...

In this article, we study the exact controllability of an abstract model described by the controlled generalized Hammerstein type integral equation