On approximation properties of certain multidimensional nonlinear integrals
-
1429
Downloads
-
2264
Views
Authors
Sevgi Esen Almali
- Faculty of Sciences and Art, Depatment of Mathematics, Kirikkale University, Kirikkale, Turkey.
Akif D. Gadjiev
- National Academy of Sciences of Azerbaijan, 9 F. Agaev Street, 1141, Baku, Azerbaijan.
Abstract
We prove theorems on convergence of multidimensional nonlinear integrals in Lebesgue points of generated function, and show that the main results are applicable to a wide class of exponentially nonlinear
integral operators, which may be constructed by using well known positive kernels in approximation theory.
Share and Cite
ISRP Style
Sevgi Esen Almali, Akif D. Gadjiev, On approximation properties of certain multidimensional nonlinear integrals, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 5, 3090--3097
AMA Style
Almali Sevgi Esen, Gadjiev Akif D., On approximation properties of certain multidimensional nonlinear integrals. J. Nonlinear Sci. Appl. (2016); 9(5):3090--3097
Chicago/Turabian Style
Almali, Sevgi Esen, Gadjiev, Akif D.. "On approximation properties of certain multidimensional nonlinear integrals." Journal of Nonlinear Sciences and Applications, 9, no. 5 (2016): 3090--3097
Keywords
- Nonlinear integral operators
- positive kernels
- Lebesgue points
- approximation
- exponentially nonlinear integrals.
MSC
References
-
[1]
I. A. Aliiev, A. D. Gadjiev, A. Aral, On approximation properties of a family of linear operators at critical value of parameter, J. Approx. Theory, 38 (2006), 242-253.
-
[2]
F. Altomare, M. Campiti, Korovkin-Type Approximation Theory And Its Applications, Walter de Gruyter, Berlin (1994)
-
[3]
L. Angeloni, G. Vinti , Convergence in variation and rate of approximation for nonlinear integral operators of convolution type, Results Math., 49 (2006), 1-23.
-
[4]
C. Bardaro, J. Musielak, G. Vinti, Nonlinear integral operators and applications, Walter de Gruyter, Berlin (2003)
-
[5]
C. Bardaro, G. Vinti, H. Karsli , Nonlinear integral operators with homogeneous kernels: pointwise approximation theorems , Appl. Anal., 90 (2011), 463-474.
-
[6]
P. L. Butzer, R. J. Nessel, Fourier Analysis And Approximation, Academic Press, New York-London (1971)
-
[7]
A. D. Gadjiev, A. Aral, I. A. Aliev, On behaviour of the Riesz and generalized Riesz potentials as order tends to zero , Math. Ineq. Appl., 10 (2007), 875-888.
-
[8]
H. Karsli , On approximation properties of non-convolution type nonlinear integral operators, Anal. Theory Appl., 26 (2010), 140{152.
-
[9]
J. Musielak, Approximation by nonlinear singular integral operators in generalized Orlicz spaces, Comment. Math. Prace Mat., 31 (1991), 79-88.
-
[10]
L. Rempulska, A. Thiel, Approximation of functions by certain nonlinear integral operators, Lith. Math. J., 48 (2008), 451-462.
-
[11]
L. M. Stein, G. Weiss, Introduction To Fourier Analysis On Euclidean Spaces, Princeton University Press, New Jersey (1971)
-
[12]
T. Swiderski, E. Wachnicki , Nonlinear singular integral depending on two parameters, Comment. Math. Prace Mat., 40 (2000), 181-189.