New reproducing kernel functions in the reproducing kernel Sobolev spaces

Ali Akgül; Esra Karatas Akgül; Sahin Korhan; Ali Akgül; Esra Karatas Akgül; Sahin Korhan

doi:10.3934/math.2020032

AIMS Mathematics

2020, Volume 5, Issue 1: 482-496. doi: 10.3934/math.2020032

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New reproducing kernel functions in the reproducing kernel Sobolev spaces

1.
Siirt University, Art and Science Faculty, Department of Mathematics, TR-56100 Siirt, Turkey
2.
Siirt University, Faculty of Education, Department of Mathematics, TR-56100 Siirt, Turkey

Received: 04 October 2019 Accepted: 29 November 2019 Published: 06 December 2019
MSC : 46E35, 46E22

In this paper we construct some new reproducing kernel functions in the reproducing kernel Sobolev space. These functions are new in the literature. We can solve many problems by these functions in the reproducing kernel Sobolev spaces.
- reproducing kernel functions,
- reproducing kernel Sobolev spaces
Citation: Ali Akgül, Esra Karatas Akgül, Sahin Korhan. New reproducing kernel functions in the reproducing kernel Sobolev spaces[J]. AIMS Mathematics, 2020, 5(1): 482-496. doi: 10.3934/math.2020032

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Abstract

In this paper we construct some new reproducing kernel functions in the reproducing kernel Sobolev space. These functions are new in the literature. We can solve many problems by these functions in the reproducing kernel Sobolev spaces.

References

[1]	E. F. Gregory, Y. Qi, Reproducing kernels of Sobolev spaces via a green kernel approach with differential operators and boundary operators, Adv. Comput. Math., 38 (2013), 891-921. doi: 10.1007/s10444-011-9264-6
[2]	M. G. Sakar, Iterative reproducing kernel Hilbert spaces method for Riccati differential equations, J. Comput. Appl. Math., 309 (2017), 163-174. doi: 10.1016/j.cam.2016.06.029
[3]	M. Cui, Y. Lin, Nonlinear Numerical Analysis in the Reproducing Kernel Space, Nova Science Publishers Inc, New York, 2009.
[4]	S. Zaremba, Sur le calcul numérique des fonctions demandées dan le probléme de dirichlet et le probleme hydrodynamique, Bulletin International l'Académia des Sciences de Cracovie, 68 (1908), 125-195.
[5]	S. Bergman, The Kernel Function and Conformal Mapping, American Mathematical Society, New York, 1950.
[6]	M. Zorzi, A. Chiuso, The harmonic analysis of kernel functions, Automatica, 94 (2018), 125-137. doi: 10.1016/j.automatica.2018.04.015
[7]	M. Zorzi, A. Chiuso, Sparse plus low rank network identification: A nonparametric approach, Automatica, 76 (2017), 355-366. doi: 10.1016/j.automatica.2016.08.014
[8]	M. Zorzi, Empirical Bayesian learning in AR graphical models, Automatica, 109 (2019), 108516.
[9]	E. Novak, Reproducing Kernels of Sobolev Spaces on R^d and Applications to Embedding Constants and Tractability, Arxiv.
[10]	O. A. Arqub, Fitted reproducing kernel Hilbert space method for the solutions of some certain classes of time-fractional partial differential equations subject to initial and Neumann boundary conditions, Comput. Math. Appl., 73 (2017), 1243-1261. doi: 10.1016/j.camwa.2016.11.032
[11]	S. Momani, O. A. Arqub, T. Hayat, et al. A computational method for solving periodic boundary value problems for integro-differential equations of Fredholm-Voltera type, Appl. Math. Comput., 240 (2014), 229-239.
[12]	B. Azarnavid, K. Parand, An iterative reproducing kernel method in Hilbert space for the multipoint boundary value problems, J. Comput. Appl. Math., 328 (2018), 151-163. doi: 10.1016/j.cam.2017.07.015
[13]	A. Akgül, New reproducing kernel functions, Math. Probl. Eng., 2015 (2015), 1-10.
[14]	A. Akgül, On solutions of variable-order fractional differential equations, An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 7 (2017), 112-116.
[15]	A. Akgül, E. K. Akgül, D. Baleanu, Numerical solutions of fractional differential equations of Lane-Emden type by an accurate technique, Adv. Differ. Equ., 2015 (2015), 220.

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