International Journal of Mathematics and Mathematical Sciences 
Volume 27 (2001), Issue 11, Pages 689-694
doi:10.1155/S016117120101078X

Flett's mean value theorem in topological vector spaces

Robert C. Powers, Thomas Riedel, and Prasanna K. Sahoo

Department of Mathematics, University of Louisville, Louisville 40292, KY, USA

Received 23 August 2000; Revised 22 February 2001

Abstract

We prove some generalizations of Flett's mean value theorem for a class of Gateaux differentiable functions f:XY, where X and Y are topological vector spaces.