Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J.M. Ash. A characterization of the Peano derivatives Trans. Amer. Math. Soc. 149 (1970) 489–501.
P.L. Butzer and W. Kozakiewez. On Riemann derivatives of integrated functions. Cand. J. Math. 6 (1954) 572–581.
S. Dayal, Local representation of function on normal linear spaces, Ph.D. Thesis, Case Western Reserve University, Cleveland Ohio, 1972.
S. Dayal, A converse of Taylor’s Theorem for functions on banach spaces, Proc. Amer. Math. Soc. Vol. 65, No. 2, Aug. 1977, 265–273.
S. Dayal, K-discrete differential of certain operators on Banach spaces, Proc. Amer. Math. Soc. Vol. 83, No. 1 1981, 77–82.
J. Dieúdonné, Foundations of Modern Analysis, Academic Press, New York 1960 MR 12 # 110074.
T.M. Flett, Differential Analysis, Cambridge University Press, Cambridge, 1980.
R. Ger, n-convex functions in linear spaces, Aequationes Math 10 (1974), 172–176.
R. Ger, Convex functions of higher orders in Euclidean spaces. Ann. Polon. Math. 25 (1972) 293–302.
Hilderbrand, F.B. Introduction to Numerical Analysis, McGraw-Hill, New York, 1956, MR 17 # 788.
J. Kopec and J. Musielak, On the estimation of the norm of the n-linear symmetric operators, Studia Math. 15 (1955), 29–30, MR 17, # 5 12.
E.B. Leach, Differential calculus of sub-convex functionals. Unpublished note, 1968.
E.B. Leach, and Whitefield, J.H.M., Differentiable functions and rough norms on Banach spaces, Proc. Amer. Math. Soc. Vol. 33, Number 1, 1972, 120–126.
J. Kolomy, On the Differentiability of Mapping and Convex Functionals (Commt. Math. Univ. Carolinae 84 (1967) 735–751).
M.Z. Nashed Differentiability and related properties of non-linear operators. Some aspects of the role of differentials in non-linear analysis, Non-linear Functional. Anal. and Appl. (Proc. Advanced Sem. Math. Res. Centre, Univ. of Wisconsin, Madison 1970) Academic Press, New York 1971. pp. 103–309.
A.E. Taylor, Addition in the theory of polynomials in normed linear spaces, Tôhoku Math. J. 44 (1938), 302–318.
C.E. Weil, On approximation and Peano derivatives, Proc. Amer. Math. Soc. 20 (1969), 487–490.
Author information
Authors and Affiliations
Editor information
Additional information
Dedicated to the memory of U.N. Singh
Rights and permissions
Copyright information
© 1992 Springer-Verlag
About this paper
Cite this paper
Dayal, S. (1992). Higher Fréchet and discrete Gâteaux differenttiability of n-convex functions on Banach spaces. In: Yadav, B.S., Singh, D. (eds) Functional Analysis and Operator Theory. Lecture Notes in Mathematics, vol 1511. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0093809
Download citation
DOI: https://doi.org/10.1007/BFb0093809
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-55365-6
Online ISBN: 978-3-540-47041-0
eBook Packages: Springer Book Archive