Abstract
We give uniform and Lp Caputo-Bochner abstract sequential generalized right fractional Landau inequalities over $\mathbb{R}_{-}$. These estimates the size of second and third sequential abstract generalized right fractional derivatives of a Banach space valued function over $\mathbb{R}_{-}$. We give an application when the basic fractional order is 1
Keywords
Sequential abstract generalized right fractional Landau inequality inequalities fractional integral
References
- A. A. Aljinovic, Lj. Marangunic and J. Pecaric: On Landau type inequalities via Ostrowski inequalities, Nonlinear Funct. Anal. Appl., 10 (4) (2005), 565-579.
- G. A. 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, (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 ||f′||2 ≤ 4 ||f|| ||f′′||, 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, (1996).
Abstract
References
- A. A. Aljinovic, Lj. Marangunic and J. Pecaric: On Landau type inequalities via Ostrowski inequalities, Nonlinear Funct. Anal. Appl., 10 (4) (2005), 565-579.
- G. A. 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, (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 ||f′||2 ≤ 4 ||f|| ||f′′||, 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, (1996).
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Articles |
| Authors | |
| Publication Date | September 16, 2021 |
| Published in Issue | Year 2021 |
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