On integral inequalities associated with a linear operator equation

Author:
M. B. Subrahmanyam

Journal:
Proc. Amer. Math. Soc. **92** (1984), 342-346

MSC:
Primary 45A05; Secondary 26D10

MathSciNet review:
759650

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Abstract: In this paper we apply control theoretic concepts to formulate and solve a generalized problem for the determination of best possible constants in integral inequalities. We investigate the problem of existence of functions for which the best constant is attained, and also the conditions satisfied by these functions.

**[1]**M. B. Subrahmanyam,*On applications of control theory to integral inequalities*, J. Math. Anal. Appl.**77**(1980), no. 1, 47–59. MR**591261**, 10.1016/0022-247X(80)90260-7**[2]**M. B. Subrahmanyam,*On applications of control theory to integral inequalities. II*, SIAM J. Control Optim.**19**(1981), no. 4, 479–489. MR**618239**, 10.1137/0319028**[3]**M. B. Subrahmanyam,*A control problem with application to integral inequalities*, J. Math. Anal. Appl.**81**(1981), no. 2, 346–355. MR**622823**, 10.1016/0022-247X(81)90068-8**[4]**M. B. Subrahmanyam,*An extremal problem for convolution inequalities*, J. Math. Anal. Appl.**87**(1982), no. 2, 509–516. MR**658030**, 10.1016/0022-247X(82)90140-8**[5]**I. V. Girsanov,*Lectures on mathematical theory of extremum problems*, Springer-Verlag, Berlin-New York, 1972. Edited by B. T. Poljak; Translated from the Russian by D. Louvish; Lecture Notes in Economics and Mathematical Systems, Vol. 67. MR**0464021**

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DOI:
https://doi.org/10.1090/S0002-9939-1984-0759650-6

Article copyright:
© Copyright 1984
American Mathematical Society