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Fuzzy Sets and Systems, ISSN 0165-0114, 02/2017, Volume 309, pp. 145 - 164
In the present paper, using fuzzy Haar wavelets, we introduce an iterative method for numerical solving two-dimensional nonlinear Urysohn fuzzy integral... 
Iterative method | Fuzzy Haar wavelets | Two-dimensional nonlinear Urysohn fuzzy integral equations (2DNUFIEs) | Numerical stability | EXISTENCE | MATHEMATICS, APPLIED | QUADRATURE FORMULA | NUMBER-VALUED FUNCTIONS | STATISTICS & PROBABILITY | COMPUTER SCIENCE, THEORY & METHODS | RULES | UNIQUENESS
Journal Article
International Journal of Computer Mathematics, ISSN 0020-7160, 03/2018, Volume 95, Issue 3, pp. 465 - 489
In this paper, we consider the discrete Legendre spectral Galerkin method to approximate the solution of Urysohn integral equation with smooth kernel. The... 
spectral method | 45G10 | Urysohn integral equations | 45B05 | 65R20 | discrete Galerkin method | Legendre polynomials | superconvergence | MATHEMATICS, APPLIED | CONVERGENCE ANALYSIS | HYPERINTERPOLATION | PROJECTION METHODS | Spectra | Galerkin method | Integral equations | Convergence
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 01/2016, Volume 273, pp. 562 - 569
A very general nonlinear singular integral equation is introduced, namely > 0 and 0 < < 1. The above equation is called Erdélyi–Kober fractional... 
Erdélyi–Kober | Darbo fixed point theorem | Urysohn–Volterra | Generalized fractional | Erdélyi-Kober | Urysohn-Volterra | EXISTENCE | MATHEMATICS, APPLIED | LINEAR MODIFICATION | ARGUMENT | DIFFERENTIAL-EQUATIONS | TRANSPORT-THEORY | Erdelyi-Kober
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 06/2014, Volume 263, Issue 1, pp. 88 - 102
In this paper, we consider the Legendre spectral Galerkin and Legendre spectral collocation methods to approximate the solution of Urysohn integral equation.... 
Urysohn integral equations | Galerkin method | Collocation method | Legendre polynomials | Smooth kernels | Superconvergence rates | MATHEMATICS, APPLIED
Journal Article
BIT Numerical Mathematics, ISSN 0006-3835, 3/2017, Volume 57, Issue 1, pp. 3 - 20
Journal Article
Applied Numerical Mathematics, ISSN 0168-9274, 04/2018, Volume 126, pp. 180 - 198
Approximate solutions of linear and nonlinear integral equations using methods related to an interpolatory projection involve many integrals which need to be... 
Nyström approximation | Interpolatory projection | Urysohn integral operator | Gauss points | MATHEMATICS, APPLIED | COLLOCATION | Nystrom approximation
Journal Article
Studies in Computational Intelligence, ISSN 1860-949X, 2019, Volume 793, pp. 147 - 161
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 03/2016, Volume 294, pp. 309 - 322
Consider a nonlinear operator equation , where is a Urysohn integral operator with a Green’s function type kernel. Using the orthogonal projection onto a space... 
Collocation method | Galerkin method | Urysohn integral operator | MATHEMATICS, APPLIED | COMPACT OPERATOR-EQUATIONS | Operators (mathematics) | Kernels | Approximation | Mathematical analysis | Projection | Mathematical models | Galerkin methods | Convergence | Numerical Analysis | Mathematics
Journal Article
Journal of Applied Mathematics and Computing, ISSN 1598-5865, 2/2018, Volume 56, Issue 1, pp. 1 - 24
Journal Article
Numerical Functional Analysis and Optimization, ISSN 0163-0563, 05/2017, Volume 38, Issue 5, pp. 549 - 574
In this paper, polynomially-based discrete M-Galerkin and M-collocation methods are proposed to solve nonlinear Fredholm integral equation with a smooth... 
multi-projection methods | 45G10 | 45B05 | 65R20 | urysohn integral equations | Legendre polynomials | smooth kernel | MATHEMATICS, APPLIED | CONVERGENCE ANALYSIS | HYPERINTERPOLATION | Error analysis | Approximation | Infinity | Integral equations | Collocation methods | Projection | Galerkin method | Kernels | Nonlinearity | Mathematical models | Approximation methods | Optimization
Journal Article
Rocky Mountain Journal of Mathematics, ISSN 0035-7596, 12/2018, Volume 48, Issue 6, pp. 1743 - 1762
Journal Article
Journal of Applied Analysis, ISSN 1425-6908, 12/2016, Volume 22, Issue 2, pp. 153 - 161
A version of the Arzelà–Ascoli theorem for being a σ-locally compact Hausdorff space is proved. The result is used in proving compactness of Fredholm,... 
Hammerstein | 46E15 | 47H10 | compact operators | Arzelà–Ascoli theorem | 47G10 | Fredholm | Urysohn | Arzelà-Ascoli theorem | Studies | Integral equations | Mathematics
Journal Article
Journal of Integral Equations and Applications, ISSN 0897-3962, 2016, Volume 28, Issue 2, pp. 221 - 261
Consider a nonlinear operator equation x - K(x) = f , where K is a Urysohn integral operator with a kernal of the type of Green's function and defined on... 
Collocation method | Gauss points | Urysohn integral operator | collocation method | MATHEMATICS | MATHEMATICS, APPLIED | MODIFIED PROJECTION METHODS | COMPACT OPERATOR-EQUATIONS
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 05/2012, Volume 218, Issue 17, pp. 8800 - 8805
We study the existence of monotonic solutions for a perturbed functional integral equation of Urysohn type in the space of Lebesgue integrable functions on an... 
Functional integral equation | Compact in measure | Monotonic solutions | Existence | Urysohn | SUPERPOSITION OPERATOR | MATHEMATICS, APPLIED | WEAK NONCOMPACTNESS | Intervals | Tools | Mathematical models | Computation | Integral equations | Mathematical analysis
Journal Article
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, ISSN 0035-7596, 2018, Volume 48, Issue 6, pp. 1743 - 1762
Using a Krasnoselskii-type fixed point theorem due to Burton [7], we discuss the existence of integrable solutions of general quadratic-Urysohn integral... 
MATHEMATICS | integrable solutions | Quadratic-Urysohn integral equations | Krasnoselskii's fixed point theorem | uniqueness of the solution
Journal Article
Siberian Advances in Mathematics, ISSN 1055-1344, 7/2018, Volume 28, Issue 3, pp. 166 - 174
We study one class of nonlinear Urysohn integral equations in a quadrant of the plane. It is assumed that, for the corresponding two-dimensional Urysohn... 
Carathéodory condition | Urysohn equation | Mathematics, general | iteration | Mathematics | monotonicity | power nonlinearity | Operators (mathematics) | Nonlinearity | Nonlinear equations | Mathematical analysis | Integral equations
Journal Article
Electronic Journal of Differential Equations, ISSN 1072-6691, 10/2016, Volume 2016, Issue 271, pp. 1 - 15
The goal in this paper is to prove an existence theorem for the solutions of a class of functional integral equations which contain a number of classical... 
Nonlinear integral equation | Fixed-point theorem | Measure of noncompactness | MATHEMATICS | fixed-point theorem | MATHEMATICS, APPLIED | URYSOHN TYPE | measure of noncompactness
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 2010, Volume 60, Issue 7, pp. 2058 - 2065
Journal Article
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