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Abstract generalized fractional Landau inequalities over $\mathbb{R}$

Yıl 2021, Cilt: 4 Sayı: 1, 34 - 47, 01.03.2021
https://doi.org/10.33205/cma.764161

Öz

We present uniform and $L_p$ mixed Caputo-Bochner abstract generalized fractional Landau inequalities over $\mathbb{R}$ of fractional orders $2 < \alpha \leq 3 $. These estimate the size of first and second derivatives of a composition with a Banach space valued function over $\mathbb{R}$. We give applications when $α = 2.5$.

Kaynakça

  • A. Aglic Aljinovic, Lj. Marangunic and J. Pecaric: On Landau type inequalities via Ostrowski inequalities, Nonlinear Funct. Anal. Appl. Vol., 10, 4 (2005), pp. 565-579.
  • G. Anastassiou: Fractional Differentiation inequalities, Research monograph, Springer, New York, 2009.
  • G. A. Anastassiou: Advances on Fractional Inequalities, Springer, New York, 2011.
  • G. A. Anastassiou: Intelligent Computations: Abstract Fractional Calculus, Inequalities, Approximations, Springer, Heidelberg, New York, 2018.
  • N. S. Barnett, S. S. Dragomir: Some Landau type inequalities for functions whose derivatives are of locally bounded variation, Tamkang Journal of Mathematics, 37, No. 4, 301-308, winter 2006.
  • Z. Ditzian: Remarks, questions and conjectures on Landau-Kolmogorov-type inequalities, Math. Inequal. Appl., 3 (2000), 15-24.
  • G. H. Hardy, J. E. Littlewood: Some integral inequalities connected with the calculus of variations, Quart. J. Math. Oxford Ser., 3 (1932), 241-252.
  • G. H. Hardy, E. Landau and J. E. Littlewood: Some inequalities satisfied by the integrals or derivatives of real or analytic functions, Math. Z., 39 (1935), 677-695.
  • R. R. Kallman, G. C. Rota: On the inequality $\Vert f' \Vert^2 \leq 4\Vert f'' \Vert$, in Inequalities, Vol. II, (O. Shisha, Ed.), 187-192, Academic Press, New York, 1970.
  • E. Landau: Einige Ungleichungen für zweimal differentzierban funktionen, Proc. London Math. Soc., 13 (1913), 43-49.
  • J. Mikusinski: The Bochner integral, Academic Press, New York, 1978.
  • G. E. Shilov: Elementary Functional Analysis, Dover Publications Inc., New York, 19
Yıl 2021, Cilt: 4 Sayı: 1, 34 - 47, 01.03.2021
https://doi.org/10.33205/cma.764161

Öz

Kaynakça

  • A. Aglic Aljinovic, Lj. Marangunic and J. Pecaric: On Landau type inequalities via Ostrowski inequalities, Nonlinear Funct. Anal. Appl. Vol., 10, 4 (2005), pp. 565-579.
  • G. Anastassiou: Fractional Differentiation inequalities, Research monograph, Springer, New York, 2009.
  • G. A. Anastassiou: Advances on Fractional Inequalities, Springer, New York, 2011.
  • G. A. Anastassiou: Intelligent Computations: Abstract Fractional Calculus, Inequalities, Approximations, Springer, Heidelberg, New York, 2018.
  • N. S. Barnett, S. S. Dragomir: Some Landau type inequalities for functions whose derivatives are of locally bounded variation, Tamkang Journal of Mathematics, 37, No. 4, 301-308, winter 2006.
  • Z. Ditzian: Remarks, questions and conjectures on Landau-Kolmogorov-type inequalities, Math. Inequal. Appl., 3 (2000), 15-24.
  • G. H. Hardy, J. E. Littlewood: Some integral inequalities connected with the calculus of variations, Quart. J. Math. Oxford Ser., 3 (1932), 241-252.
  • G. H. Hardy, E. Landau and J. E. Littlewood: Some inequalities satisfied by the integrals or derivatives of real or analytic functions, Math. Z., 39 (1935), 677-695.
  • R. R. Kallman, G. C. Rota: On the inequality $\Vert f' \Vert^2 \leq 4\Vert f'' \Vert$, in Inequalities, Vol. II, (O. Shisha, Ed.), 187-192, Academic Press, New York, 1970.
  • E. Landau: Einige Ungleichungen für zweimal differentzierban funktionen, Proc. London Math. Soc., 13 (1913), 43-49.
  • J. Mikusinski: The Bochner integral, Academic Press, New York, 1978.
  • G. E. Shilov: Elementary Functional Analysis, Dover Publications Inc., New York, 19
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

George Anastassiou 0000-0002-3781-9824

Yayımlanma Tarihi 1 Mart 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 4 Sayı: 1

Kaynak Göster

APA Anastassiou, G. (2021). Abstract generalized fractional Landau inequalities over $\mathbb{R}$. Constructive Mathematical Analysis, 4(1), 34-47. https://doi.org/10.33205/cma.764161
AMA Anastassiou G. Abstract generalized fractional Landau inequalities over $\mathbb{R}$. CMA. Mart 2021;4(1):34-47. doi:10.33205/cma.764161
Chicago Anastassiou, George. “Abstract Generalized Fractional Landau Inequalities over $\mathbb{R}$”. Constructive Mathematical Analysis 4, sy. 1 (Mart 2021): 34-47. https://doi.org/10.33205/cma.764161.
EndNote Anastassiou G (01 Mart 2021) Abstract generalized fractional Landau inequalities over $\mathbb{R}$. Constructive Mathematical Analysis 4 1 34–47.
IEEE G. Anastassiou, “Abstract generalized fractional Landau inequalities over $\mathbb{R}$”, CMA, c. 4, sy. 1, ss. 34–47, 2021, doi: 10.33205/cma.764161.
ISNAD Anastassiou, George. “Abstract Generalized Fractional Landau Inequalities over $\mathbb{R}$”. Constructive Mathematical Analysis 4/1 (Mart 2021), 34-47. https://doi.org/10.33205/cma.764161.
JAMA Anastassiou G. Abstract generalized fractional Landau inequalities over $\mathbb{R}$. CMA. 2021;4:34–47.
MLA Anastassiou, George. “Abstract Generalized Fractional Landau Inequalities over $\mathbb{R}$”. Constructive Mathematical Analysis, c. 4, sy. 1, 2021, ss. 34-47, doi:10.33205/cma.764161.
Vancouver Anastassiou G. Abstract generalized fractional Landau inequalities over $\mathbb{R}$. CMA. 2021;4(1):34-47.