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On Maximal Inequalities Arising in Best Approximation
Best approximants $arPhi$-approximants $sigma$-lattices Maximal inequalities
2010/1/22
Let be a function in an Orlicz space and be the set of all the best -approximants to given a lattice Weak type inequalities are proved for the maximal operator where is any selection of func...
Approximation of $B$-Continuous and $B$-Differentiable Functions by GBS Operators Defined by Infinite Sum
Linear positive operators GBS operators $B$-continuous and $B$- differentiable functions approximation of $B$-continuous and $B$-differentiable functions by GBS operators
2010/1/22
In this paper we start from a class of linear and positive operators defined by infinite sum. We consider the associated GBS operators and we give an approximation of B-continuous and B-differentiable...
Approximation, Numerical Differentiation and Integration Based on Taylor Polynomial
Degree of approximation Taylor polynomial $P_n$-simple functionals least concave majorant of $omega(f,cdot)$
2010/1/22
We represent new estimates of errors of quadrature formula, formula of numerical differentiation and approximation using Taylor polynomial. To measure the errors we apply representation of the remaind...
Approximation of a Mixed Functional Equation in Quasi-Banach Spaces
Generalized Hyers-Ulam stability additive function cubic function quasi-Banach space $p$-Banach space
2010/1/22
In this paper we establish the general solution of the functional equation and investigate its generalized Hyers-Ulam stability in quasi-Banach spaces. The concept of Hyers-Ulam-Rassias stab...
Geometric Approximation of Proximal Normals
Nonsmooth analysis distance function $\delta$-projection proximal normal proximal subdifferential
2009/2/5
For $x\in H\setminus S$ and $\delta \ge 0$, the $\delta$-projection of $x$ onto $S$, is the set $\operatorname{proj}_S^\delta(x):=\left\{s\in S \colon \|s-x\|^2 \le d_S(x)^2 + \delta^2 \right\}.$ We p...
Homographic Approximation for Some Nonlinear Parabolic Unilateral Problems
Homographic Nonlinear Parabolic Unilateral Problems
2009/1/15
We deal with nonlinear parabolic unilateral problems by means of the homographic approximation, introduced by C. M. Brauner and B. Nicolaenko [in: "Nonlinear Partial Diff. Equations and Their Applicat...
Closed form approximation solutions for the restricted circular three body problem
Lambert’s wave function spherically symmetric masses
2009/1/8
An approach is developed to find approximate solutions to the restricted
circular three body problem. The solution is useful in approximately describing
the position vectors of three spherically sym...
Adiabatic expansion approximation solutions for the three-body problem
three-body system adiabatic expansion method bound states energy levels Born-Oppenheimer method
2009/1/5
The motion of a muon in two centers coulomb ¯eld is one of
the interesting problems of quantum mechanics. The adiabatic expansion
method is powerful approach to study the muonic three-body syst...
Derivative approximation by interpolation polynomials of Bernstein type of the third kind
interpolation polynomial of Bernstein type derivative approximation
2010/9/14
In this paper, we mainly study the problems of derivative approximation of interpolation polynomials. Based on the zero nodes of the Chebyshev polynomials of the second kind, we construct an interpola...
Approximation methods for equilibrium problems and common solution for a finite family of inverse strongly-monotone problems in Hilbert spaces
Tikhonov regularization proximal point method contraction
2010/9/10
The purpose of the paper is to investigate approximation methods for finding an element that is not only a solution of a equilibrium problem but also a common solution for a finite family of inverse s...
Viscosity approximation methods for mean non-expansive mappings in Banach spaces
Viscosity approximation method Mean non-expansive mappings
2010/9/10
Let C be a nonempty closed convex subset of a real reflexive
Banach space X that has weakly continuous duality mapping J. Let T : C → C be a Mean non-expansive mapping with F(T) = ∅. For any t...
The best gradient approximation to an observed function
gradient operator best approximation Sobolev spaces
2010/9/13
We wish to find the potential function whose gradient best approximates an observed square integrable function. With an appropriate choice of topology we show that the gradient operator is a bounded l...
Minimal Achievable Approximation Ratio for MAX-MQ in Finite Fields
Multivariate quadratic polynomial equations MAX-MQ approximation algorithm approximation ratio
2013/9/9
Given a multivariate quadratic polynomial system in a niteeld Fq, theproblem MAX-MQ is to ˉnd a solution satisfying the maximal number of equations. We prove that the probability of a random assignmen...
BEST APPROXIMATION FOR WEIERSTRASS TRANSFORM CONNECTED WITH RIEMANN-LIOUVILLE OPERATOR
Weierstrass transform best approximation Riemann-Liouville operator reproducing kernel extremal function
2008/11/26
Using reproducing kernels for Hilbert spaces, we give best approximation for Weierstrass
transform associated with Riemann-Liouville operator. Also, estimates of extremal
functions are checked.
Universal Approximation by Ridge Computational Models and Neural Networks: A Survey
nonlinear computational models ridge computational units universal approximation com-plexity
2008/11/10
Computational models made up of linear combinations of ridge basis functions, widely used in machine learning and artificial intelligence, are considered. For such models, the literature on the so-cal...