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A Sequence of Kantorovich-Type Operators on Mobile Intervals

Yıl 2019, Cilt: 2 Sayı: 3, 130 - 143, 01.09.2019
https://doi.org/10.33205/cma.571078

Öz

In this paper, we introduce and study a new sequence of positive linear operators, acting on both spaces of continuous functions as well as spaces of integrable functions on $[0, 1]$. We state some qualitative properties of this sequence and we prove that it is an approximation process both in $C([0, 1])$ and in $L^p([0, 1])$, also providing  some estimates of the rate of convergence. Moreover, we determine an asymptotic formula and, as an application,  we  prove that certain iterates of the operators converge, both in $C([0, 1])$ and, in some cases,  in $L^p([0, 1])$, to a limit semigroup. Finally, we show that our operators, under suitable hypotheses, perform better than  other existing ones in the literature. 

Destekleyen Kurum

INdAM - GNAMPA

Proje Numarası

Project 2019 - Approssimazione di semigruppi tramite operatori lineari e applicazioni

Kaynakça

  • [1] T. Acar, A. Aral, I. Ras ̧a, Positive linear operators preserving τ and τ2, Constr. Math. Anal. 2 (3) (2019), 98–102.
  • [2] T.Acar,M.CappellettiMontano,P.Garrancho,V.Leonessa,OnsequencesofJ.P.King-typeoperators,J.Funct.Spaces, 2019, Article ID 2329060.
  • [3] F. Altomare, M. Campiti, Korovkin-type approximation theory and its applications, de Gruyter Studies in Mathe- matics 17, Walter de Gruyter & Co., Berlin, 1994.
  • [4] F. Altomare, M. Cappelletti Montano, V. Leonessa, On a generalization of Kantorovich operators on simplices and hypercubes, Adv. Pure Appl. Math. 1(3) (2010), 359-385.
  • [5] F. Altomare, M. Cappelletti Montano, V. Leonessa, Iterates of multidimensional Kantorovich-type operator and their associated positive C0-semigroups, Studia Universitatis Babes-Bolyai. Mathematica 56(2) (2011), 236-251.
  • [6] F. Altomare, M. Cappelletti Montano, V. Leonessa, I. Ras ̧a, Markov Operators, Positive Semigroups and Approximation Processes, de Gruyter Studies in Mathematics 61, Walter de Gruyter GmbH, Berlin/Boston, 2014.
  • [7] F. Altomare, V. Leonessa, On a sequence of positive linear operators associated with a continuous selection of Borel mea- sures, Mediterr. J. Math. 3 (2006), 363-382.
  • [8] H. Bauer, Probability Theory, de Gruyter Studies in Mathematics 23, Walter de Gruyter & Co., Berlin, 1996.
  • [9] D. Cardenas-Morales, P. Garrancho, F.J. Muños-Delgado, Shape preserving approximation by Bernstein-type operators which fix polinomials, Appl. Math. Comput. 182 (2006) 1615–1622.
  • [10] D. Cardenas-Morales, P. Garrancho, I. Raşa, Bernstein-type operators which preserve polynomials, Comput. Math. Appl. 62(1) (2011), 158–163.
  • [11] G. Freud, On approximation by positive linear methods I, II, Stud. Scin. Math. Hungar. 2 (1967) 63–66, 3 (1968), 365– 370.
  • [12] H. Gonska, P. Pitul, I. Raşa, General King-type operators, Results Math. 53(3-4) (2009) 279–286.
  • [13] J.P. King, Positive linear operators which preserve x2, Acta Math. Hungar. 99(3) (2003) 203–208.
  • [14] A.-J. López-Moreno, F.-J. Muñoz-Delgado, Asymptotic expression of derivatives of Bernstein type operators, Suppl. Cir. Mat. Palermo Ser. II 68 (2002), 615-624.
  • [15] R. Paltanea, Approximation theory using positive linear operators, Birkhäuser, Boston, (2004).
  • [16] J. J. Swetits, B. Wood, Quantitative estimates for Lp approximation with positive linear operators, J. Approx. Theory 38 (1983), 81–89.
  • [17] Z. Ziegler, Linear approximation and generalized convexity, J. Approx. Theory 1 (1968), 420–433.
Yıl 2019, Cilt: 2 Sayı: 3, 130 - 143, 01.09.2019
https://doi.org/10.33205/cma.571078

Öz

Proje Numarası

Project 2019 - Approssimazione di semigruppi tramite operatori lineari e applicazioni

Kaynakça

  • [1] T. Acar, A. Aral, I. Ras ̧a, Positive linear operators preserving τ and τ2, Constr. Math. Anal. 2 (3) (2019), 98–102.
  • [2] T.Acar,M.CappellettiMontano,P.Garrancho,V.Leonessa,OnsequencesofJ.P.King-typeoperators,J.Funct.Spaces, 2019, Article ID 2329060.
  • [3] F. Altomare, M. Campiti, Korovkin-type approximation theory and its applications, de Gruyter Studies in Mathe- matics 17, Walter de Gruyter & Co., Berlin, 1994.
  • [4] F. Altomare, M. Cappelletti Montano, V. Leonessa, On a generalization of Kantorovich operators on simplices and hypercubes, Adv. Pure Appl. Math. 1(3) (2010), 359-385.
  • [5] F. Altomare, M. Cappelletti Montano, V. Leonessa, Iterates of multidimensional Kantorovich-type operator and their associated positive C0-semigroups, Studia Universitatis Babes-Bolyai. Mathematica 56(2) (2011), 236-251.
  • [6] F. Altomare, M. Cappelletti Montano, V. Leonessa, I. Ras ̧a, Markov Operators, Positive Semigroups and Approximation Processes, de Gruyter Studies in Mathematics 61, Walter de Gruyter GmbH, Berlin/Boston, 2014.
  • [7] F. Altomare, V. Leonessa, On a sequence of positive linear operators associated with a continuous selection of Borel mea- sures, Mediterr. J. Math. 3 (2006), 363-382.
  • [8] H. Bauer, Probability Theory, de Gruyter Studies in Mathematics 23, Walter de Gruyter & Co., Berlin, 1996.
  • [9] D. Cardenas-Morales, P. Garrancho, F.J. Muños-Delgado, Shape preserving approximation by Bernstein-type operators which fix polinomials, Appl. Math. Comput. 182 (2006) 1615–1622.
  • [10] D. Cardenas-Morales, P. Garrancho, I. Raşa, Bernstein-type operators which preserve polynomials, Comput. Math. Appl. 62(1) (2011), 158–163.
  • [11] G. Freud, On approximation by positive linear methods I, II, Stud. Scin. Math. Hungar. 2 (1967) 63–66, 3 (1968), 365– 370.
  • [12] H. Gonska, P. Pitul, I. Raşa, General King-type operators, Results Math. 53(3-4) (2009) 279–286.
  • [13] J.P. King, Positive linear operators which preserve x2, Acta Math. Hungar. 99(3) (2003) 203–208.
  • [14] A.-J. López-Moreno, F.-J. Muñoz-Delgado, Asymptotic expression of derivatives of Bernstein type operators, Suppl. Cir. Mat. Palermo Ser. II 68 (2002), 615-624.
  • [15] R. Paltanea, Approximation theory using positive linear operators, Birkhäuser, Boston, (2004).
  • [16] J. J. Swetits, B. Wood, Quantitative estimates for Lp approximation with positive linear operators, J. Approx. Theory 38 (1983), 81–89.
  • [17] Z. Ziegler, Linear approximation and generalized convexity, J. Approx. Theory 1 (1968), 420–433.
Toplam 17 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Mirella Cappellettı Montano Bu kişi benim 0000-0003-1850-0428

Vita Leonessa 0000-0001-9547-8397

Proje Numarası Project 2019 - Approssimazione di semigruppi tramite operatori lineari e applicazioni
Yayımlanma Tarihi 1 Eylül 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 2 Sayı: 3

Kaynak Göster

APA Cappellettı Montano, M., & Leonessa, V. (2019). A Sequence of Kantorovich-Type Operators on Mobile Intervals. Constructive Mathematical Analysis, 2(3), 130-143. https://doi.org/10.33205/cma.571078
AMA Cappellettı Montano M, Leonessa V. A Sequence of Kantorovich-Type Operators on Mobile Intervals. CMA. Eylül 2019;2(3):130-143. doi:10.33205/cma.571078
Chicago Cappellettı Montano, Mirella, ve Vita Leonessa. “A Sequence of Kantorovich-Type Operators on Mobile Intervals”. Constructive Mathematical Analysis 2, sy. 3 (Eylül 2019): 130-43. https://doi.org/10.33205/cma.571078.
EndNote Cappellettı Montano M, Leonessa V (01 Eylül 2019) A Sequence of Kantorovich-Type Operators on Mobile Intervals. Constructive Mathematical Analysis 2 3 130–143.
IEEE M. Cappellettı Montano ve V. Leonessa, “A Sequence of Kantorovich-Type Operators on Mobile Intervals”, CMA, c. 2, sy. 3, ss. 130–143, 2019, doi: 10.33205/cma.571078.
ISNAD Cappellettı Montano, Mirella - Leonessa, Vita. “A Sequence of Kantorovich-Type Operators on Mobile Intervals”. Constructive Mathematical Analysis 2/3 (Eylül 2019), 130-143. https://doi.org/10.33205/cma.571078.
JAMA Cappellettı Montano M, Leonessa V. A Sequence of Kantorovich-Type Operators on Mobile Intervals. CMA. 2019;2:130–143.
MLA Cappellettı Montano, Mirella ve Vita Leonessa. “A Sequence of Kantorovich-Type Operators on Mobile Intervals”. Constructive Mathematical Analysis, c. 2, sy. 3, 2019, ss. 130-43, doi:10.33205/cma.571078.
Vancouver Cappellettı Montano M, Leonessa V. A Sequence of Kantorovich-Type Operators on Mobile Intervals. CMA. 2019;2(3):130-43.