Proceedings of the American Mathematical Society, ISSN 0002-9939, 08/1999, Volume 127, Issue 8, pp. 2259 - 2264

This paper investigates the fixed points for self-maps of a closed set in a space of abstract continuous functions...

Mathematical theorems | Abstract spaces | Differential equations | Abstracting | Banach space | Cauchy problem | Continuous functions | Self-maps of a closed set | Fixed point | Iterative sequence | MATHEMATICS | MATHEMATICS, APPLIED | self-maps of a closed set | iterative sequence | fixed point

Mathematical theorems | Abstract spaces | Differential equations | Abstracting | Banach space | Cauchy problem | Continuous functions | Self-maps of a closed set | Fixed point | Iterative sequence | MATHEMATICS | MATHEMATICS, APPLIED | self-maps of a closed set | iterative sequence | fixed point

Journal Article

Abstract and applied analysis, ISSN 1687-0409, 2013, Volume 2013, pp. 1 - 4

Recently, the concept of -ward continuity was introduced and studied. In this paper, we prove that the uniform limit of -ward continuous functions is -ward...

Sequences (Mathematics) | Functions, Continuous | Research | Mathematical research | Cauchy problem

Sequences (Mathematics) | Functions, Continuous | Research | Mathematical research | Cauchy problem

Journal Article

Mathematics, ISSN 2227-7390, 03/2017, Volume 5, Issue 1, p. 12

.... The use of the transfer function in Laplace and Fourier spaces in connection with Sinc convolutions allow to find exponentially converging computing schemes...

Riesz-Feller derivative | Approximation | Computation | Integral equations | Caputo derivative | Sinc methods | Fractional Fokker Planck equation | approximation | CONVOLUTION QUADRATURE | sinc methods | computation | MATHEMATICS | integral equations | fractional Fokker Planck equation | CONTINUOUS-TIME FINANCE | DIFFUSION | DISCRETIZED OPERATIONAL CALCULUS | FUNDAMENTAL SOLUTION | Convolution | Initial conditions | Mathematical analysis | Numerical methods | Transfer functions | Fokker-Planck equation | Cauchy problem

Riesz-Feller derivative | Approximation | Computation | Integral equations | Caputo derivative | Sinc methods | Fractional Fokker Planck equation | approximation | CONVOLUTION QUADRATURE | sinc methods | computation | MATHEMATICS | integral equations | fractional Fokker Planck equation | CONTINUOUS-TIME FINANCE | DIFFUSION | DISCRETIZED OPERATIONAL CALCULUS | FUNDAMENTAL SOLUTION | Convolution | Initial conditions | Mathematical analysis | Numerical methods | Transfer functions | Fokker-Planck equation | Cauchy problem

Journal Article

Taiwanese Journal of Mathematics, ISSN 1027-5487, 3/2005, Volume 9, Issue 1, pp. 95 - 109

Some inequalities and approximations for the finite Hilbert transform by the use of Taylor's formula with the integral remainder are given.

Numerical quadratures | Approximation | Numerical integration | Mathematical integrals | Error bounds | Mathematical inequalities | Cauchy mean value theorem | Gaussian quadratures | Analytic inequalities | Hilbert transform | Taylor's formula | MATHEMATICS | PRINCIPAL VALUE INTEGRALS | QUASI-INTERPOLATING SPLINES | APPROXIMATING SPLINES | VALUES | NUMERICAL EVALUATION | UNIFORM-CONVERGENCE | DERIVATIVES | analytic inequalities | PRODUCT RULE

Numerical quadratures | Approximation | Numerical integration | Mathematical integrals | Error bounds | Mathematical inequalities | Cauchy mean value theorem | Gaussian quadratures | Analytic inequalities | Hilbert transform | Taylor's formula | MATHEMATICS | PRINCIPAL VALUE INTEGRALS | QUASI-INTERPOLATING SPLINES | APPROXIMATING SPLINES | VALUES | NUMERICAL EVALUATION | UNIFORM-CONVERGENCE | DERIVATIVES | analytic inequalities | PRODUCT RULE

Journal Article

Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 05/2011, Volume 80, Issue 275, pp. 1431 - 1458

We give sufficient conditions under which the convergence of finite difference approximations in the space variable of possibly degenerate second order...

Integers | Approximation | Mathematical theorems | Difference equations | Uniqueness | Mathematical functions | Coefficients | Continuous functions | Induction assumption | Richardson's method | Finite differences | Extrapolation to the limit | Cauchy problem | EXTRAPOLATION | MATHEMATICS, APPLIED | finite differences | extrapolation to the limit

Integers | Approximation | Mathematical theorems | Difference equations | Uniqueness | Mathematical functions | Coefficients | Continuous functions | Induction assumption | Richardson's method | Finite differences | Extrapolation to the limit | Cauchy problem | EXTRAPOLATION | MATHEMATICS, APPLIED | finite differences | extrapolation to the limit

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 02/2003, Volume 131, Issue 2, pp. 487 - 499

...(t)) eqnarray where the set-valued function F is locally Lipschitz and takes values which are nonempty and closed. The relaxation considered is the inclusion eqnarray DI...

Integers | Mathematical intervals | Approximation | Mathematical theorems | Topological theorems | Differentials | Trajectories | Mathematical functions | Cauchy problem | Continuous functions | MATHEMATICS | MATHEMATICS, APPLIED

Integers | Mathematical intervals | Approximation | Mathematical theorems | Topological theorems | Differentials | Trajectories | Mathematical functions | Cauchy problem | Continuous functions | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

The Journal of Integral Equations and Applications, ISSN 0897-3962, 7/2012, Volume 24, Issue 2, pp. 283 - 319

.... A general version of Gronwall's inequality is also established. A recurring theme throughout the work is the incorporation of desirable qualities of the classical Mittag-Leffler function...

Approximation | Differential equations | Uniqueness | Ordinary differential equations | Mathematical inequalities | Mathematical functions | Cauchy problem | Continuous functions | Perceptron convergence procedure | Cauchy-peano method | Existence and uniqueness of solutions | Initial value problem | Nonlinear fractional differential equations of arbitrary order | Gronwall inequality | Successive approximations | Topological degree | topological degree | MATHEMATICS | MATHEMATICS, APPLIED | successive approximations | initial value problem | nonlinear fractional differential equations of arbitrary order | Cauchy-Peano method | 34A12 | 34A08

Approximation | Differential equations | Uniqueness | Ordinary differential equations | Mathematical inequalities | Mathematical functions | Cauchy problem | Continuous functions | Perceptron convergence procedure | Cauchy-peano method | Existence and uniqueness of solutions | Initial value problem | Nonlinear fractional differential equations of arbitrary order | Gronwall inequality | Successive approximations | Topological degree | topological degree | MATHEMATICS | MATHEMATICS, APPLIED | successive approximations | initial value problem | nonlinear fractional differential equations of arbitrary order | Cauchy-Peano method | 34A12 | 34A08

Journal Article

Indiana University Mathematics Journal, ISSN 0022-2518, 1/2013, Volume 62, Issue 1, pp. 333 - 354

... of T. We allow the corresponding characteristic operator function of T to be non-inner. We relate the unitary dilation of such a contraction to its rank n unitary perturbations...

Boundary value problems | Mathematical theorems | Model theory | Separable spaces | Eigenfunctions | Hilbert spaces | Mathematical independent variables | Mathematics | Mathematical functions | Continuous spectra | Dilation theory | Finite rank perturbations | Normalized Cauchy transform | Rank one perturbations | MATHEMATICS | finite rank perturbations | rank one perturbations | normalized Cauchy transform | dilation theory | CONTRACTIVE PERTURBATIONS | Mathematics - Functional Analysis

Boundary value problems | Mathematical theorems | Model theory | Separable spaces | Eigenfunctions | Hilbert spaces | Mathematical independent variables | Mathematics | Mathematical functions | Continuous spectra | Dilation theory | Finite rank perturbations | Normalized Cauchy transform | Rank one perturbations | MATHEMATICS | finite rank perturbations | rank one perturbations | normalized Cauchy transform | dilation theory | CONTRACTIVE PERTURBATIONS | Mathematics - Functional Analysis

Journal Article

Complex Variables and Elliptic Equations, ISSN 1747-6933, 04/2014, Volume 59, Issue 4, pp. 462 - 483

In this paper, in the terms of the Cauchy transform, the continuous linear functionals on the spaces of functions holomorphic in the polydisc are described...

Cauchy transform | analytic functions | anisotropic weighted spaces | polydisc | mixed norm | continuous linear functionals | MATHEMATICS | 46E15 | 47B38 | 32A10 | 32C37 | Functionals | Analytic functions | Mathematical analysis | Transforms | Images | Norms | Complex variables | Representations

Cauchy transform | analytic functions | anisotropic weighted spaces | polydisc | mixed norm | continuous linear functionals | MATHEMATICS | 46E15 | 47B38 | 32A10 | 32C37 | Functionals | Analytic functions | Mathematical analysis | Transforms | Images | Norms | Complex variables | Representations

Journal Article

Decisions in economics and finance, ISSN 1593-8883, 2017, Volume 40, Issue 1-2, pp. 301 - 315

Quasilinear utility functions are often met in various economic applications. We provide an axiomatization of preferences that are representable by a continuous quasilinear utility function...

Economics | Public Finance | D11 | Economic Theory/Quantitative Economics/Mathematical Methods | Quasilinear utility | Preferences representation | Management | Finance, general | Cauchy’s functional equation | Operations Research/Decision Theory | Connectedness | Econometrics | D81 | D61 | Axioms | Utility functions | Continuity (mathematics)

Economics | Public Finance | D11 | Economic Theory/Quantitative Economics/Mathematical Methods | Quasilinear utility | Preferences representation | Management | Finance, general | Cauchy’s functional equation | Operations Research/Decision Theory | Connectedness | Econometrics | D81 | D61 | Axioms | Utility functions | Continuity (mathematics)

Journal Article

71.
Full Text
Multigrid Waveform Relaxation on Spatial Finite Element Meshes: The Continuous-Time Case

SIAM Journal on Numerical Analysis, ISSN 0036-1429, 4/1996, Volume 33, Issue 2, pp. 456 - 474

... parabolic initial boundary value problem. The convergence properties of the continuous-time algorithm are theoretically investigated on finite-length and infinite-length time-intervals...

Approximation | Heat equation | Spectral theory | Odes | Waveforms | Eigenvalues | Mathematical relaxation method | Boundary conditions | Mathematical functions | Cauchy problem | Dynamic iteration | Finite elements | Waveform relaxation | Multigrid | Parabolic partial differential equations | MATHEMATICS, APPLIED | dynamic iteration | waveform relaxation | multigrid | DYNAMIC ITERATION METHODS | DIFFERENTIAL-EQUATIONS | parabolic partial differential equations | finite elements

Approximation | Heat equation | Spectral theory | Odes | Waveforms | Eigenvalues | Mathematical relaxation method | Boundary conditions | Mathematical functions | Cauchy problem | Dynamic iteration | Finite elements | Waveform relaxation | Multigrid | Parabolic partial differential equations | MATHEMATICS, APPLIED | dynamic iteration | waveform relaxation | multigrid | DYNAMIC ITERATION METHODS | DIFFERENTIAL-EQUATIONS | parabolic partial differential equations | finite elements

Journal Article

Iranian Journal of Mathematical Sciences and Informatics, ISSN 1735-4463, 05/2018, Volume 13, Issue 1, pp. 97 - 102

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2009, Volume 349, Issue 2, pp. 420 - 435

... , χ ∈ H , and h : [ 0 , T ) × H → H is a uniformly Lipschitz function, is studied in order to establish continuous dependence results for solutions to approximate well-posed problems...

Continuous dependence on modeling | Nonlinear ill-posed problem | Abstract Cauchy problem | MATHEMATICS | MATHEMATICS, APPLIED | EQUATIONS | BANACH-SPACE

Continuous dependence on modeling | Nonlinear ill-posed problem | Abstract Cauchy problem | MATHEMATICS | MATHEMATICS, APPLIED | EQUATIONS | BANACH-SPACE

Journal Article

Materials and Manufacturing Processes: Special Issue on Genetic Algorithms, ISSN 1042-6914, 04/2015, Volume 30, Issue 4, pp. 414 - 424

The inverse modeling of heat transfer is a useful tool in analyzing contact heat transfer at the ingot surfaces during the continuous casting process...

Inverse heat transfer | Continuous casting | Mathematical modeling | Evolutionary algorithms | Evolutionaryalgorithms | Inverseheattransfer | Mathematicalmodeling | Continuouscasting | NATURE-INSPIRED TOOL | MATERIALS SCIENCE, MULTIDISCIPLINARY | SOLIDIFICATION | MATERIALS SCIENCE | PARAMETERS | MODEL | MECHANICAL-PROPERTIES | GENETIC ALGORITHMS | OPTIMIZATION | ENGINEERING, MANUFACTURING | HEURISTIC-SEARCH TECHNIQUE | MICROSTRUCTURE

Inverse heat transfer | Continuous casting | Mathematical modeling | Evolutionary algorithms | Evolutionaryalgorithms | Inverseheattransfer | Mathematicalmodeling | Continuouscasting | NATURE-INSPIRED TOOL | MATERIALS SCIENCE, MULTIDISCIPLINARY | SOLIDIFICATION | MATERIALS SCIENCE | PARAMETERS | MODEL | MECHANICAL-PROPERTIES | GENETIC ALGORITHMS | OPTIMIZATION | ENGINEERING, MANUFACTURING | HEURISTIC-SEARCH TECHNIQUE | MICROSTRUCTURE

Journal Article

Journal of computational and applied mathematics, ISSN 0377-0427, 2020, Volume 368, p. 112526

.... Convergence of the numerical method is demonstrated in weighted uniform normed spaces of continuous functions...

Weighted spaces of continuous functions | Cauchy singular integro-differential equations | Polynomial collocation methods and convergence | MATHEMATICS, APPLIED | INTEGRAL-EQUATIONS | UNIFORM-CONVERGENCE

Weighted spaces of continuous functions | Cauchy singular integro-differential equations | Polynomial collocation methods and convergence | MATHEMATICS, APPLIED | INTEGRAL-EQUATIONS | UNIFORM-CONVERGENCE

Journal Article

Filomat, ISSN 0354-5180, 1/2015, Volume 29, Issue 1, pp. 159 - 178

In this paper the author considers the various types of completeness for di-uniform texture spaces and especially for complemented ones. Following that, the...

Morphisms | Topological theorems | Mathematical completeness | Functors | Complementation | Topology | Algebraic topology | Uniformity | Topological spaces | Continuous functions | Di-Uniformity | Quotient Category | Bicomplete | Dicomplete | C-space | Ditopology | Realcompact | Jointly Complete | Texture | B-Complete | Cauchy filter pair | Real Dicompact | Difilter | Plain Dicompletion | Quasi-Uniformity | MATHEMATICS, APPLIED | FUZZY TOPOLOGY | SPACES | MATHEMATICS | REAL DICOMPACTNESS

Morphisms | Topological theorems | Mathematical completeness | Functors | Complementation | Topology | Algebraic topology | Uniformity | Topological spaces | Continuous functions | Di-Uniformity | Quotient Category | Bicomplete | Dicomplete | C-space | Ditopology | Realcompact | Jointly Complete | Texture | B-Complete | Cauchy filter pair | Real Dicompact | Difilter | Plain Dicompletion | Quasi-Uniformity | MATHEMATICS, APPLIED | FUZZY TOPOLOGY | SPACES | MATHEMATICS | REAL DICOMPACTNESS

Journal Article

Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 07/2004, Volume 73, Issue 247, pp. 1235 - 1259

We study a relaxation scheme of the Jin and Xin type for conservation laws with a flux function that depends discontinuously on the spatial location through a coefficient k(x). If k...

Conservation laws | Mathematical discontinuity | Approximation | Function discontinuity | Scalars | Mathematical functions | Entropy | Coefficients | Cauchy problem | Relaxation scheme | Discontinuous coefficient | Conservation law | Convergence compensated compactness | Numerical example | MATHEMATICS, APPLIED | DIFFERENCE SCHEME | CONTINUOUS SEDIMENTATION | GODUNOVS METHOD | TRAFFIC FLOW | CAUCHY-PROBLEM | ZERO RELAXATION | FLUX FUNCTION | convergence compensated compactness | conservation law | POINT-SOURCE | SYSTEMS | numerical example | relaxation scheme | discontinuous coefficient | CONVERGENCE-RATES

Conservation laws | Mathematical discontinuity | Approximation | Function discontinuity | Scalars | Mathematical functions | Entropy | Coefficients | Cauchy problem | Relaxation scheme | Discontinuous coefficient | Conservation law | Convergence compensated compactness | Numerical example | MATHEMATICS, APPLIED | DIFFERENCE SCHEME | CONTINUOUS SEDIMENTATION | GODUNOVS METHOD | TRAFFIC FLOW | CAUCHY-PROBLEM | ZERO RELAXATION | FLUX FUNCTION | convergence compensated compactness | conservation law | POINT-SOURCE | SYSTEMS | numerical example | relaxation scheme | discontinuous coefficient | CONVERGENCE-RATES

Journal Article

Journal of King Saud University - Science, ISSN 1018-3647, 10/2010, Volume 22, Issue 4, pp. 217 - 221

In this paper the notion of contraction mappings on probabilistic metric spaces and probabilistic 2-metric spaces are applied. Several fixed point theorems for...

Probabilistic metric spaces | Menger space | Continuous t-norm | Distribution function | Cauchy sequence | 2-Metric spaces | Fixed point

Probabilistic metric spaces | Menger space | Continuous t-norm | Distribution function | Cauchy sequence | 2-Metric spaces | Fixed point

Journal Article

79.
Full Text
Adaptive radial basis function–generated finite differences method for contact problems

International journal for numerical methods in engineering, ISSN 1097-0207, 2019, Volume 119, Issue 7, pp. 661 - 686

...–based algorithm from a given continuous density function, which is altered during the refinement process based on the error indicator...

meshfree methods | linear elasticity | adaptive h‐refinement | Cauchy‐Navier equations | radial basis functions | contact problems | Cauchy-Navier equations | adaptive h-refinement | INTERPOLATION | REFINEMENT | POLYNOMIALS | SCHEME | NUMERICAL-SOLUTION | TRANSPORT | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | FUNCTION COLLOCATION METHOD | ERROR ESTIMATOR | Finite element method | Fatigue tests | Radial basis function | Algorithms | Boussinesq equations | Stress distribution | Meshless methods | Contact pressure | Fatigue failure | Ultrasonic testing | Continuity (mathematics)

meshfree methods | linear elasticity | adaptive h‐refinement | Cauchy‐Navier equations | radial basis functions | contact problems | Cauchy-Navier equations | adaptive h-refinement | INTERPOLATION | REFINEMENT | POLYNOMIALS | SCHEME | NUMERICAL-SOLUTION | TRANSPORT | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | FUNCTION COLLOCATION METHOD | ERROR ESTIMATOR | Finite element method | Fatigue tests | Radial basis function | Algorithms | Boussinesq equations | Stress distribution | Meshless methods | Contact pressure | Fatigue failure | Ultrasonic testing | Continuity (mathematics)

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2007, Volume 331, Issue 1, pp. 342 - 357

We apply semigroup theory and other operator-theoretic methods to prove Hölder-continuous dependence on modeling for the inhomogeneous ill-posed Cauchy problem in Banach space...

Continuous dependence on modeling | Ill-posed problems | Abstract Cauchy problem | MATHEMATICS | MATHEMATICS, APPLIED | abstract Cauchy problem | GENERATORS | HOLOMORPHIC SEMIGROUPS | continuous dependence on modeling | III-posed problems | CAUCHY-PROBLEM | EVOLUTION-EQUATIONS

Continuous dependence on modeling | Ill-posed problems | Abstract Cauchy problem | MATHEMATICS | MATHEMATICS, APPLIED | abstract Cauchy problem | GENERATORS | HOLOMORPHIC SEMIGROUPS | continuous dependence on modeling | III-posed problems | CAUCHY-PROBLEM | EVOLUTION-EQUATIONS

Journal Article

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