论文信息 - Several Examples for Generalized Invariant Monotonicity

Several Examples for Generalized Invariant Monotonicity

In order to show the relations between generalized monotonicity and generalized invariant monotonicity. This paper present nine examples for explaining some relations between (pseudo, quasi) monotonicity and invariant (pseudo, quasi) monotonicity. Moreover, we give eight counterexamples, which show that some examples in [X.M. Yang et al., J.Optim.Theory.Appl. 117(2003) 607-625] are incorrect.

Liya Fan | Yunlian Guo

[1] Kok Lay Teo,et al. Generalized Invexity and Generalized Invariant Monotonicity , 2003 .

[2] Muhammad Aslam Noor,et al. Some characterizations of strongly preinvex functions , 2006 .

[3] Jafar Zafarani,et al. Generalized Invariant Monotonicity and Invexity of Non-differentiable Functions , 2006, J. Glob. Optim..

[4] Sanyang Liu,et al. Generalized monotonicity and convexity of non-differentiable functions☆ , 2003 .

[5] Liya Fan,et al. On strongly α-preinvex functions☆ , 2007 .