Approximation properties in fuzzy normed spaces

2016 ◽  
Vol 282 ◽  
pp. 115-130 ◽  
Author(s):  
Keun Young Lee
Keyword(s):  
Approximation Properties ◽  
Normed Spaces

scholarly journals Approximation Properties in Felbin Fuzzy Normed Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 1003 ◽  
Author(s):  
Ju Myung Kim ◽  
Keun Young Lee
Keyword(s):  
Comparative Study ◽  
Finite Rank ◽  
Approximation Properties ◽  
Bounded Operators ◽  
Normed Spaces ◽  
New Concepts

In this paper, approximation properties in Felbin fuzzy normed spaces are considered. These approximation properties are new concepts in Felbin fuzzy normed spaces. Definitions and examples of such properties are given and we make a comparative study among approximation properties in Bag and Samanta fuzzy normed spaces and Felbin fuzzy normed spaces. We develop the representation of finite rank bounded operators in our context. By using this representation, characterizations of approximation properties are established in Felbin fuzzy normed spaces.

scholarly journals A Study of Approximation Properties in Felbin-Fuzzy Normed Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 161
Author(s):  
Ju Myung Kim ◽  
Keun Young Lee
Keyword(s):  
Approximation Properties ◽  
Normed Spaces ◽  
Dual Problems ◽  
Dual Spaces ◽  
Infinite Sequences

In this paper, approximation properties in Felbin-fuzzy normed spaces are studied. These approximation properties have been recently introduced in Felbin-fuzzy normed spaces. We make topological tools to analyze such approximation properties. We especially develop the representation of dual spaces related to our contexts. By using this representation, we establish characterizations of approximation properties in terms of infinite sequences. Finally, we provide dual problems for approximation properties and their results in our contexts.

Modified algorithm for fast bandwidth selection for kernel estimates of multidimensional probability densities

2020 ◽  
pp. 9-13
Author(s):  
A. V. Lapko ◽  
V. A. Lapko
Keyword(s):  
Probability Density ◽  
Optimal Parameter ◽  
Random Variables ◽  
Kernel Functions ◽  
Independent Random Variables ◽  
Functional Dependencies ◽  
Approximation Properties ◽  
Probability Density Estimation ◽  
Multidimensional Probability ◽  
Selection Of

An original technique has been justified for the fast bandwidths selection of kernel functions in a nonparametric estimate of the multidimensional probability density of the Rosenblatt–Parzen type. The proposed method makes it possible to significantly increase the computational efficiency of the optimization procedure for kernel probability density estimates in the conditions of large-volume statistical data in comparison with traditional approaches. The basis of the proposed approach is the analysis of the optimal parameter formula for the bandwidths of a multidimensional kernel probability density estimate. Dependencies between the nonlinear functional on the probability density and its derivatives up to the second order inclusive of the antikurtosis coefficients of random variables are found. The bandwidths for each random variable are represented as the product of an undefined parameter and their mean square deviation. The influence of the error in restoring the established functional dependencies on the approximation properties of the kernel probability density estimation is determined. The obtained results are implemented as a method of synthesis and analysis of a fast bandwidths selection of the kernel estimation of the two-dimensional probability density of independent random variables. This method uses data on the quantitative characteristics of a family of lognormal distribution laws.

On the stability of a nonic functional equation in quasi-normed spaces

2016 ◽  
Vol 12 (3) ◽  
pp. 4368-4374
Author(s):  
Soo Hwan Kim
Keyword(s):  
Functional Equation ◽  
Ulam Stability ◽  
Normed Spaces ◽  
The Stability

In this paper, we extend normed spaces to quasi-normed spaces and prove the generalized Hyers-Ulam stability of a nonic functional equation:$$\aligned&f(x+5y) - 9f(x+4y) + 36f(x+3y) - 84f(x+2y) + 126f(x+y) - 126f(x)\\&\qquad + 84f(x-y)-36f(x-2y)+9f(x-3y)-f(x-4y) = 9 ! f(y),\endaligned$$where $9 ! = 362880$ in quasi-normed spaces.

Solutions and Stability of Generalized Mixed Type QCA-Functional Equations in Random Normed Spaces

2013 ◽  
Vol 59 (2) ◽  
pp. 299-320
Author(s):  
M. Eshaghi Gordji ◽  
Y.J. Cho ◽  
H. Khodaei ◽  
M. Ghanifard
Keyword(s):  
Functional Equation ◽  
General Solution ◽  
Functional Equations ◽  
Mixed Type ◽  
Additive Functional ◽  
Normed Spaces ◽  
Additive Functional Equation ◽  
Probabilistic Normed Spaces ◽  
Random Normed Spaces ◽  
Generalized Stability

Abstract In this paper, we investigate the general solution and the generalized stability for the quartic, cubic and additive functional equation (briefly, QCA-functional equation) for any k∈ℤ-{0,±1} in Menger probabilistic normed spaces.

Approximation properties of Szász type operators involving Charlier polynomials

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 479-487
Author(s):  
Didem Arı
Keyword(s):  
Asymptotic Formula ◽  
Weighted Space ◽  
Approximation Properties ◽  
Charlier Polynomials

In this paper, we give some approximation properties of Sz?sz type operators involving Charlier polynomials in the polynomial weighted space and we give the quantitative Voronovskaya-type asymptotic formula.

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