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

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

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

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

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

Integral equations occur naturally in many fields of mechanics and mathematical physics. In this paper a superconvergent Nyström method has been used for...

45G10 | Nyström method | Computational Mathematics and Numerical Analysis | 65R20 | Numeric Computing | Mathematics, general | Superconvergence | Mathematics | 65D15 | Urysohn equations | Gauss points | Nystrom method | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | DEGENERATE KERNEL METHODS | 2ND KIND | PROJECTION METHODS | Nonlinear equations | Estimating techniques | Iterative methods | Mathematical analysis | Integral equations | Nonlinear systems

45G10 | Nyström method | Computational Mathematics and Numerical Analysis | 65R20 | Numeric Computing | Mathematics, general | Superconvergence | Mathematics | 65D15 | Urysohn equations | Gauss points | Nystrom method | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | DEGENERATE KERNEL METHODS | 2ND KIND | PROJECTION METHODS | Nonlinear equations | Estimating techniques | Iterative methods | Mathematical analysis | Integral equations | Nonlinear systems

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

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

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

In this paper, we consider the multi-Galerkin and multi-collocation methods for solving the Urysohn integral equation with a smooth kernel, using Legendre...

Computational Mathematics and Numerical Analysis | 65R20 | Urysohn integral equation | Mathematics | Theory of Computation | Superconvergence | Smooth kernel | 45G10 | 45B05 | Multi-projection method | Mathematics of Computing | Mathematical and Computational Engineering | Legendre polynomials | Nonlinear equations | Error analysis | Approximation | Basis functions | Integral equations | Collocation methods | Galerkin method | Polynomials

Computational Mathematics and Numerical Analysis | 65R20 | Urysohn integral equation | Mathematics | Theory of Computation | Superconvergence | Smooth kernel | 45G10 | 45B05 | Multi-projection method | Mathematics of Computing | Mathematical and Computational Engineering | Legendre polynomials | Nonlinear equations | Error analysis | Approximation | Basis functions | Integral equations | Collocation methods | Galerkin method | Polynomials

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

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

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

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

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

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

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

Nonlinear integral equation | Fixed-point theorem | Measure of noncompactness | MATHEMATICS | fixed-point theorem | MATHEMATICS, APPLIED | URYSOHN TYPE | measure of noncompactness

Journal Article

Rocky Mountain Journal of Mathematics, ISSN 0035-7596, 2018, Volume 48, Issue 6, pp. 1743 - 1762

Journal Article

19.
Full Text
Urysohn integral equations approach by common fixed points in complex-valued metric spaces

Advances in Difference Equations, ISSN 1687-1839, 12/2013, Volume 2013, Issue 1, pp. 1 - 14

Recently, the complex-valued metric spaces which are more general than the metric spaces were first introduced by Azam et al. (Numer. Funct. Anal. Optim....

Urysohn integral equations | Ordinary Differential Equations | Functional Analysis | Analysis | complex-valued metric spaces | Difference and Functional Equations | Mathematics, general | Mathematics | common fixed points | weakly compatible | Partial Differential Equations | Common fixed points | Complex-valued metric spaces | Weakly compatible | MATHEMATICS | MATHEMATICS, APPLIED | COMPATIBLE MAPS | THEOREMS | MAPPINGS | Technology application | Usage | Differential equations | Inequalities (Mathematics) | Functions, Entire | Fixed point theory

Urysohn integral equations | Ordinary Differential Equations | Functional Analysis | Analysis | complex-valued metric spaces | Difference and Functional Equations | Mathematics, general | Mathematics | common fixed points | weakly compatible | Partial Differential Equations | Common fixed points | Complex-valued metric spaces | Weakly compatible | MATHEMATICS | MATHEMATICS, APPLIED | COMPATIBLE MAPS | THEOREMS | MAPPINGS | Technology application | Usage | Differential equations | Inequalities (Mathematics) | Functions, Entire | Fixed point theory

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 2010, Volume 60, Issue 7, pp. 2058 - 2065

The Newton–Kantorovich method is a well-known method for solving nonlinear integral equations. This method attempts to solve a sequence of linear integral...

Nonlinear integral equation | Quadrature | Newton–Kantorovich method | Urysohn integral equation | Newton-Kantorovich method | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Approximation | Computer simulation | Integral equations | Mathematical analysis | Exact solutions | Nonlinearity | Mathematical models | Quadratures

Nonlinear integral equation | Quadrature | Newton–Kantorovich method | Urysohn integral equation | Newton-Kantorovich method | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Approximation | Computer simulation | Integral equations | Mathematical analysis | Exact solutions | Nonlinearity | Mathematical models | Quadratures

Journal Article

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