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

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

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), 47-59. MR**591261 (83e:49016a)****[2]**-,*On applications of control theory to integral inequalities*. II, SIAM J. Control Optim.**19**(1981), 479-489. MR**618239 (83e:49016b)****[3]**-,*A control problem with application to integral inequalities*, J. Math. Anal. Appl.**81**(1981), 346-355. MR**622823 (83d:49008)****[4]**-,*An extremal problem for convolution inequalities*, J. Math. Anal. Appl.**87**(1982), 509-516. MR**658030 (84c:49023)****[5]**I. V. Girsanov, Lecture Notes in Econom. and Math. Systems, no. 67, Springer-Verlag, New York, 1972. MR**0464021 (57:3958)**

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Additional Information

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

Article copyright:
© Copyright 1984
American Mathematical Society