scholarly journals On errors of a unified family of approximation forms of bivariate continuous functions

2003 ◽  
Vol 34 (4) ◽  
pp. 371-382
Author(s):  
Chung-Siung Kao
Keyword(s):  
Error Bounds ◽  
Continuous Functions ◽  
Bivariate Functions

Approximation forms for a regular bivariate functions $f(x,y)$ were obtained by putting expectation on a convergent bivariate stochastic sequence for which some proper error bounds are herein derived to evaluate the applicability of the approximation forms when actually applied to be approximates of regular bivariate functions.

scholarly journals A test function theorem and apporoximation by pseudopolynomials

1986 ◽  
Vol 34 (1) ◽  
pp. 53-64 ◽  
Author(s):  
C. Badea ◽  
I. Badea ◽  
H. H. Gonska
Keyword(s):  
Type Theorem ◽  
Continuous Functions ◽  
Korovkin Type Theorem ◽  
Test Function ◽  
Bivariate Functions

We prove a Korovkin-type theorem on approximation of bivariate functions in the space of B-continuous functions (introduced by K. Bögel in 1934). As consequences, some sequences of uniformly approximating pseudopolynomials are obtained.

Approximation in statistical sense to B -continuous functions by positive linear operators

2010 ◽  
Vol 47 (3) ◽  
pp. 289-298 ◽  
Author(s):  
Fadime Dirik ◽  
Oktay Duman ◽  
Kamil Demirci
Keyword(s):  
Compact Subset ◽  
Real Line ◽  
Statistical Convergence ◽  
Approximation Theorem ◽  
Continuous Functions ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Statistical Approximation ◽  
Classical Version ◽  
Statistical Sense

In the present work, using the concept of A -statistical convergence for double real sequences, we obtain a statistical approximation theorem for sequences of positive linear operators defined on the space of all real valued B -continuous functions on a compact subset of the real line. Furthermore, we display an application which shows that our new result is stronger than its classical version.

Almost Somewhat Near Continuity and Near Regularity

2021 ◽  
Vol 7 (1) ◽  
pp. 88-99
Author(s):  
Zanyar A. Ameen
Keyword(s):  
Continuous Function ◽  
Continuous Functions ◽  
One To One ◽  
Nearly Continuous

AbstractThe notions of almost somewhat near continuity of functions and near regularity of spaces are introduced. Some properties of almost somewhat nearly continuous functions and their connections are studied. At the end, it is shown that a one-to-one almost somewhat nearly continuous function f from a space X onto a space Y is somewhat nearly continuous if and only if the range of f is nearly regular.

On existence result of a class of nonlinear integral equation

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3593-3597
Author(s):  
Ravindra Bisht
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Existence Result ◽  
Nonlinear Integral Equation ◽  
Continuous Functions ◽  
Concave Functions ◽  
Real Numbers ◽  
Fixed Point Techniques ◽  
Uniqueness Of A Solution

Combining the approaches of functionals associated with h-concave functions and fixed point techniques, we study the existence and uniqueness of a solution for a class of nonlinear integral equation: x(t) = g1(t)-g2(t) + ? ?t,0 V1(t,s)h1(s,x(s))ds + ? ?T,0 V2(t,s)h2(s,x(s))ds; where C([0,T];R) denotes the space of all continuous functions on [0,T] equipped with the uniform metric and t?[0,T], ?,? are real numbers, g1, g2 ? C([0, T],R) and V1(t,s), V2(t,s), h1(t,s), h2(t,s) are continuous real-valued functions in [0,T]xR.

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