Yıl: 2021 Cilt: 4 Sayı: 1 Sayfa Aralığı: 34 - 47 Metin Dili: İngilizce DOI: 10.33205/cma.764161 İndeks Tarihi: 29-07-2022

Abstract generalized fractional Landau inequalities over R

Öz:
We present uniform and Lp mixed Caputo-Bochner abstract generalized fractional Landau inequalitiesover R of fractional orders 2 < α ≤ 3. These estimate the size of first and second derivatives of a composition with aBanach space valued function over R. We give applications when α = 2.5.
Anahtar Kelime:

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
  • [1] 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.
  • [2] G. Anastassiou: Fractional Differentiation inequalities, Research monograph, Springer, New York, 2009.
  • [3] G. A. Anastassiou: Advances on Fractional Inequalities, Springer, New York, 2011.
  • [4] G. A. Anastassiou: Intelligent Computations: Abstract Fractional Calculus, Inequalities, Approximations, Springer, Heidelberg, New York, 2018.
  • [5] 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.
  • [6] Z. Ditzian: Remarks, questions and conjectures on Landau-Kolmogorov-type inequalities, Math. Inequal. Appl., 3 (2000), 15-24.
  • [7] G. H. Hardy, J. E. Littlewood: Some integral inequalities connected with the calculus of variations, Quart. J. Math. Oxford Ser., 3 (1932), 241-252.
  • [8] 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.
  • [9] R. R. Kallman, G. C. Rota: On the inequality kf 0k 2 ≤ 4 kfk · kf 00k, in Inequalities, Vol. II, (O. Shisha, Ed.), 187-192, Academic Press, New York, 1970.
  • [10] E. Landau: Einige Ungleichungen für zweimal differentzierban funktionen, Proc. London Math. Soc., 13 (1913), 43-49.
  • [11] J. Mikusinski: The Bochner integral, Academic Press, New York, 1978.
  • [12] G. E. Shilov: Elementary Functional Analysis, Dover Publications Inc., New York, 1
APA Anastassiou G (2021). Abstract generalized fractional Landau inequalities over R. , 34 - 47. 10.33205/cma.764161
Chicago Anastassiou George Abstract generalized fractional Landau inequalities over R. (2021): 34 - 47. 10.33205/cma.764161
MLA Anastassiou George Abstract generalized fractional Landau inequalities over R. , 2021, ss.34 - 47. 10.33205/cma.764161
AMA Anastassiou G Abstract generalized fractional Landau inequalities over R. . 2021; 34 - 47. 10.33205/cma.764161
Vancouver Anastassiou G Abstract generalized fractional Landau inequalities over R. . 2021; 34 - 47. 10.33205/cma.764161
IEEE Anastassiou G "Abstract generalized fractional Landau inequalities over R." , ss.34 - 47, 2021. 10.33205/cma.764161
ISNAD Anastassiou, George. "Abstract generalized fractional Landau inequalities over R". (2021), 34-47. https://doi.org/10.33205/cma.764161
APA Anastassiou G (2021). Abstract generalized fractional Landau inequalities over R. Constructive mathematical analysis (Online), 4(1), 34 - 47. 10.33205/cma.764161
Chicago Anastassiou George Abstract generalized fractional Landau inequalities over R. Constructive mathematical analysis (Online) 4, no.1 (2021): 34 - 47. 10.33205/cma.764161
MLA Anastassiou George Abstract generalized fractional Landau inequalities over R. Constructive mathematical analysis (Online), vol.4, no.1, 2021, ss.34 - 47. 10.33205/cma.764161
AMA Anastassiou G Abstract generalized fractional Landau inequalities over R. Constructive mathematical analysis (Online). 2021; 4(1): 34 - 47. 10.33205/cma.764161
Vancouver Anastassiou G Abstract generalized fractional Landau inequalities over R. Constructive mathematical analysis (Online). 2021; 4(1): 34 - 47. 10.33205/cma.764161
IEEE Anastassiou G "Abstract generalized fractional Landau inequalities over R." Constructive mathematical analysis (Online), 4, ss.34 - 47, 2021. 10.33205/cma.764161
ISNAD Anastassiou, George. "Abstract generalized fractional Landau inequalities over R". Constructive mathematical analysis (Online) 4/1 (2021), 34-47. https://doi.org/10.33205/cma.764161