Skip to Main Content

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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


An integral inequality
HTML articles powered by AMS MathViewer

by J. Ernest Wilkins PDF
Proc. Amer. Math. Soc. 113 (1991), 345-353 Request permission


We furnish conditions on the functions $p(t),f(t)$, and $g(t)$ that are sufficient for the validity of the inequality, ${\alpha ^2}\delta \geq {\gamma ^2}\beta$, in which $\alpha ,\beta ,\gamma$, and $\delta$ respectively, are the integrals over a measurable set $E$ of $p(t)g(t),p(t){g^2}(t),p(t)f(t)$, and $p(t){f^2}(t)$.
  • Milton Abramowitz and Irene A. Stegun (eds.), Handbook of mathematical functions with formulas, graphs, and mathematical tables, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York; John Wiley & Sons, Inc., New York, 1984. Reprint of the 1972 edition; Selected Government Publications. MR 757537
  • Edwin F. Beckenbach and Richard Bellman, Inequalities, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Band 30, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1961. MR 0158038
  • G. H. Hardy, J. E. Littlewood, and G. Polya, Inequalities, Cambridge Univ. Press, Cambridge, 1934.
  • D. S. Mitrinović, Analytic inequalities, Die Grundlehren der mathematischen Wissenschaften, Band 165, Springer-Verlag, New York-Berlin, 1970. In cooperation with P. M. Vasić. MR 0274686
  • G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, England; The Macmillan Company, New York, 1944. MR 0010746
  • J. E. Wilkins, Jr., Apodization for maximum Strehl criterion and specified Sparrow limit of resolution for coherent illumination, J. Optical Soc. Amer. 67 (1977), 553-557.
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 26D15
  • Retrieve articles in all journals with MSC: 26D15
Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 113 (1991), 345-353
  • MSC: Primary 26D15
  • DOI:
  • MathSciNet review: 1086585