Let c be a linear functional defined by its moments c(x) = ci for i = 0, 1, . . .. We proved that the nonlinear functional equations P (t) = c(P (x)P (x + t)) and P (t) = c(P (x)P (xt)) admit polynomial solutions which are the polynomials belonging to the family of formal orthogonal polynomials with respect to a linear functional related to c. Other types of nonlinear functional equations whose...

We prove an existence theorem for a quadratic functional-integral equation of mixed type. The functional-integral equation studied below contains as special cases numerous integral equations encountered in nonlinear analysis. With help of a suitable measure of noncompactness, we show that the functional integral equation of mixed type has solutions being continuous and bounded on the interval [...

in this paper, the numerical technique based on hybrid bernoulli and block-pulse functions has been developed to approximate the solution of system of linear volterra integral equations. system of volterra integral equations arose in many physical problems such as elastodynamic, quasi-static visco-elasticity and magneto-electro-elastic dynamic problems. these functions are formed by the hybridi...

in this paper, we use the parametric form of fuzzy numbers, and aniterative approach for obtaining approximate solution for a classof fuzzy nonlinear fredholm integral equations of the second kindis proposed. this paper presents a method based on newton-cotesmethods with positive coefficient. then we obtain approximatesolution of the fuzzy nonlinear integral equations by an iterativeapproach.

in this paper, we apply the local fractional adomian decomposition and variational iteration methods to obtain the analytic approximate solutions of fredholm integral equations of the second kind within local fractional derivative operators. the iteration procedure is based on local fractional derivative. the obtained results reveal that the proposed methods are very efficient and simple tools ...

in this paper, an effective and simple numerical method is proposed for solving systems of integral equations using radial basis functions (rbfs). we present an algorithm based on interpolation by radial basis functions including multiquadratics (mqs), using legendre-gauss-lobatto nodes and weights. also a theorem is proved for convergence of the algorithm. some numerical examples are presented...

‎We study dual integral equations which appear in formulation of the‎ ‎potential distribution of an electrified plate with mixed boundary‎ ‎conditions‎. ‎These equations will be converted to a system of‎ ‎singular integral equations with Cauchy type kernels‎. ‎Using‎ ‎Chebyshev polynomials‎, ‎we propose a method to approximate the‎ ‎solution of Cauchy type singular integral equation which will ...

Some new nonlinear integral inequalities of Gronwall type for retarded functions are established, which extend the results Lipovan 2003 and Pachpatte 2004 . These inequalities can be used as basic tools in the study of certain classes of functional differential equations as well as integral equations. A existence and a uniqueness on the solution of the functional differential equation involving...