On a Functional Integral Equation

Abstract

In this paper, we establish some results for a Volterra–Hammerstein integral equation with modified arguments: existence and uniqueness, integral inequalities, monotony and Ulam-Hyers-Rassias stability. We emphasize that many problems from the domain of symmetry are modeled by differential and integral equations and those are approached in the stability point of view. In the literature, Fredholm, Volterra and Hammerstein integrals equations with symmetric kernels are studied. Our results can be applied as particular cases to these equations.

Semi-Hyers–Ulam–Rassias Stability of Some Volterra Integro-Differential Equations via Laplace Transform

“…Hyers-Ulam stability of integral equations was also studied, by various methods, in numerous papers among which we mention [19][20][21][22][23][24][25][26][27][28][29].…”

Numerical Treatments of Functional Fredholm Integral Equation in 2D with Discontinuous Kernels

“…Jafar and others, in [12], studied the functional integral equa- tions numerically. The authors in [13], studied the Volterra-Hammerstein integral equation. In [14], the authors applied a numerical method for obtaining numerical solutions of Fredholm two-dimensional functional linear integral equations based on the radial basis function.…”

Semi-Hyers–Ulam–Rassias Stability of a Volterra Integro-Differential Equation of Order I with a Convolution Type Kernel via Laplace Transform

“…Several results for the Hyers-Ulam stability of integral equations were obtained in [11][12][13][14]. In [11], a class of nonlinear integral equations was studied; in [12], an integral equation with supremum; in [13], a class of fractional integro-differential equations; and in [14], a class of Volterra-Hammerstein integral equations with modified arguments.…”