Existence of solutions for some nonlinear integral equations

On the solutions of a class of nonlinear functional integral equations in space C [0,a]

“…x(t) = g(t, x(t)) + f t, t 0 u(t, s, x(s))ds, x (β(t)) , and κ > 1−λ 2+2an in condition (H4), the result in [8] is inapplicable to integral Eq. (11) .…”

“…K. Maleknejad et al in [7] and [8] studied the existence of the solutions of the following equations x(t) = f (t, x(α(t))) t 0 u(t, s, x(s))ds, t ∈ [0, 1] 106İ.Özdemir,Ü. Ç akan and x(t) = g(t, x(t)) + f t, t 0 u(t, s, x(s))ds, x (α(t)) , t ∈ [0, a] , respectively.…”

“…The main tool used in our study is associated with the technique of measures of noncompactness. We give also some examples satisfying the conditions of our main theorem but not satisfying the conditions in [8]. …”

On existence theorems for some generalized nonlinear functional-integral equations with applications

“…for t ∈ [0, a]. Maleknejad et al [23,24] investigated the existence of solutions for the nonlinear functional…”

Convergence analysis for numerical solution of Fredholm integral equation by Sinc approximation

“…Numerical and theoretical methods for solving integro-differential and integral equations have been studied by many authors so far [1][2][3][4][5][6][7][8][9]. Some of them usually use techniques based on an expansion in terms of some basis functions or use some quadrature formulas, and the convergence rate of these methods are usually of polynomial order with respect to N where N represents the number of terms of the expansion or the number of points of the quadrature formula.…”