Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 393940, 16 pages
Research Article

Generalized (ρ,θ)-η Invariant Monotonicity and Generalized (ρ,θ)-η Invexity of Nondifferentiable Functions

1College of Mathematics Science, Inner Mongolia University, Hohhot 010021, China
2College of Mathematics and Computer Science, Chongqing Normal University, Chongqing 400047, China

Received 11 December 2008; Accepted 9 February 2009

Academic Editor: Charles E. Chidume

Copyright © 2009 Caiping Liu and Xinmin Yang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


New concepts of generalized (ρ,θ)-η invex functions for non-differentiable functions and generalized (ρ,θ)-η invariant monotone operators for set-valued mappings are introduced. The relationships between generalized (ρ,θ)-η invexity of functions and generalized (ρ,θ)-η invariant monotonicity of the corresponding Clarke's subdifferentials are studied. Some of our results are extension and improvement of some results obtained in (Jabarootion and Zafarani (2006); Behera et al. (2008)).