The paper is devoted approximation of real-valued functions defined on an unbounded interval by linear and non-linear operators. The publication pays special attention to defining class of operators and examining their certain approximation properties. The form of the class of operators given in the present paper makes the achieved results more helpful from the computational point of view.
REFERENCES
1.
M.
Becker
, Global approximation theorems for Szasz-Mirakyan and Baskakov operators in polynomial weight spaces
, Indiana Univ. Math. J.
27
,1978
, pp. 127
–142
.2.
P. L.
Butzer
, R. J.
Nessel
, Fourier Analysis and Approximation I
, Academic Press
, New York-London
, 1971
.3.
A.
Ciupa
, Approximation by a generalized Szasz type operator
, J. Comput. Anal. Appl.
5
, 2003
, pp. 413
–424
.4.
A.
Ciupa
, Positive linear operators for the approximation in polynomial weighted spaces
, Bull. Allahabad Math. Soc. (BAMS)
24
, 2009
, pp. 233
–240
.5.
R. A.
DeVore
, The approximation of continuous functions by positive linear operators
, Lecture Notes in Mathematics 293, Springer-Verlag
, Berlin
, 1972
.6.
R. A.
DeVore
, G. G.
Lorentz
, Constructive Approximation
, Springer-Verlag
, Berlin
, 1993
.7.
Z.
Finta
, Pointwise approximation by generalized Szasz-Mirakjan operators
, Stud. Univ. Babes-Bolyai, Math.
XLVI
, 2001
, 61
–66
.8.
M.
Herzog
, Approximation theorems for modified Szasz-Mirakjan operators in polynomial weight spaces
, Matematiche(Catania)
54
, 1999
, pp. 77
–90
.9.
M.
Herzog
, A note on the convergence of partial Szasz-Mirakyan operators
, Ann. Univ. Paedagog. Crac. Stud. Math.
13
, 2014
, pp. 45
–50
.10.
N.
Ispir
, C.
Atakut
, Approximation by modified Szasz-Mirakjan operators on weighted spaces
, Proc. Indian Acad. Sci. (Math. Sci.)
112
, 2002
, pp. 571
–578
.11.
N.
Ispir
, Approximation by modified complex Szasz-Mirakyan operators
, Azerbaijan J. Math.
3
, 2013
, pp. 95
–107
.12.
R.
Păltănea
, Approximation theory using positive linear operators
, Birkhauser
Boston
, 2004
.13.
L.
Rempulska
, A.
Thiel
, Approximation of functions by certain nonlinear integral operators
, Lithuanian Math. J.
48
, 2008
, pp. 451
–462
.14.
Z.
Walczak
, On approximation by modified Szasz-Mirakyan operators
, Glas. Mat.
37
, 2002
, pp. 303
–319
.15.
Z.
Walczak
, On certain positive linear operators in weighted polynomial spaces
, Acta Math. Hungar.
101
, 2003
, pp. 179
–191
.16.
Z.
Walczak
, Approximation theorems for a general class of truncated operators
, Appl. Math. Comput.
217
, 2010
, pp. 2142
–2148
.17.
Z.
Walczak
, On approximation of functions of one variable in spaces with a polynomial wight
, Stud. Univ. Babes-Bolyai, Math.
58
, 2013
, pp. 371
–380
.18.
Z.
Walczak
, V.
Gupta
, A note on the convergence of Baskakov type operators
, Appl. Math. Comput.
202
, 2008
, pp. 370
–375
.
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