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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A converse of Taylor’s theorem for functions on Banach spaces
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by S. Dayal PDF
Proc. Amer. Math. Soc. 65 (1977), 265-273 Request permission

Abstract:

The main results are the local representation theorems associating the local weak n-Taylor series expansion of a function defined on a Banach space to a local n-Taylor series expansion of the coefficients. These theorems are used to prove a converse of Taylor’s theorem which uses weaker hyptohesis than used by others. Another useful application of the above results is done in [2] to study a class of functions called n-convex functions.
References
  • Ralph Abraham and Joel Robbin, Transversal mappings and flows, W. A. Benjamin, Inc., New York-Amsterdam, 1967. An appendix by Al Kelley. MR 0240836
    • S. Dayal, Local representation and higher differentiability of n-convex operators on Banach spaces (to appear). —, Local representation of functions on normed linear spaces, Ph.D Thesis, Case Western Reserve Univ., Cleveland, Ohio, 1972. —, A converse of Taylor’s theorem for functions on locally convex and topological linear spaces (to appear).
  • J. Dieudonné, Foundations of modern analysis, Pure and Applied Mathematics, Vol. X, Academic Press, New York-London, 1960. MR 0120319
  • Georges Glaeser, Étude de quelques algèbres tayloriennes, J. Analyse Math. 6 (1958), 1–124; erratum, insert to 6 (1958), no. 2 (French). MR 101294, DOI 10.1007/BF02790231
  • F. B. Hildebrand, Introduction to numerical analysis, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1956. MR 0075670
  • J. Kopeć and J. Musielak, On the estimation of the norm of the $n$-linear symmetric operation, Studia Math. 15 (1955), 29–30. MR 73944, DOI 10.4064/sm-15-1-29-30
  • E. B. Leach, A note on inverse function theorems, Proc. Amer. Math. Soc. 12 (1961), 694–697. MR 126146, DOI 10.1090/S0002-9939-1961-0126146-9
    • J. Marcinkiewicz and A. Zygmund, On the differentiability of functions and summability of trignometric series, Fund. Math. 26 (1936), 1-43.
  • Robert M. McLeod, Mean value theorems for vector valued functions, Proc. Edinburgh Math. Soc. (2) 14 (1964/65), 197–209. MR 185052, DOI 10.1017/S0013091500008786
  • M. Z. Nashed, Differentiability and related properties of nonlinear operators: Some aspects of the role of differentials in nonlinear functional analysis, Nonlinear Functional Anal. and Appl. (Proc. Advanced Sem., Math. Res. Center, Univ. of Wisconsin, Madison, Wis., 1970) Academic Press, New York, 1971, pp. 103–309. MR 0276840
    • A. E. Taylor, Addition to the theory of polynomials in normed linear spaces, Tôhoku Math. J. 44 (1938), 302-318.
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Additional Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 65 (1977), 265-273
  • MSC: Primary 58C20; Secondary 46G05
  • DOI: https://doi.org/10.1090/S0002-9939-1977-0448394-2
  • MathSciNet review: 0448394