- Erratum
- Open Access

# Erratum to: Optimality and duality theorems in nonsmooth multiobjective optimization

- Kwan Deok Bae
^{1}and - Do Sang Kim
^{1}Email author

**2012**:28

https://doi.org/10.1186/1687-1812-2012-28

© Deok Bae and Kim; licensee Springer. 2012

**Received:**6 February 2012**Accepted:**27 February 2012**Published:**27 February 2012

The original article was published in Fixed Point Theory and Applications 2011 2011:42

We wish to indicate the following corrections to our original paper [1].

(1) The first sentence in Definition 2.2, we delete "*i*∈{1,2,···,*p*}".

(3) The second sentence in Definition 2.3, we delete "*i*∈{1,2,···,*p*}".

(5) The second sentence in Definition 2.4, we delete "*i*∈{1,2,···,*p*}".

(7) The second sentence in the proof of Theorem 2.1, we replace. ′′ *c*_{
i
} > 0, *i* = 1, ⋯,*p* ′′ to ′′ $c\in int{R}_{+}^{p}$′′.

(9) In equation (3.8), we replace "*c*_{
i
}" to "*d*_{
i
}".

(10) The eighth sentence in the proof of Theorem 3.3, we replace "where *c* = *ae*," to "where *d* = *ae*".

(11) The ninth sentence in the proof of Theorem 3.3, we replace "*c* ∈ *int R*^{
p
}" to "*d*_{
i
} > 0, *i* = 1,···,*p*,".

(12) The ninth sentence in the proof of Theorem 3.3, we replace "*c*_{
i
}" to "*d*_{
i
}".

(13) The tenth sentence in the proof of Theorem 3.3, we replace "*c*_{
i
}" to "*d*_{
i
}".

(14) The tenth sentence in the proof of Theorem 3.3, we replace "*c*_{
i
}" to "*d*_{
i
}".

(15) In equation (4.8), we replace "*c*_{
i
}" to "*d*_{
i
}".

(16) The tenth sentence in the proof of Theorem 4.1, we replace "where *c* = *ae*," to "where *d* = *ae*".

(17) The eleventh sentence in the proof of Theorem 4.1, we replace "*c* ∈ *int R*^{
p
}" to "*d*_{
i
} > 0, *i* = 1,···, *p*,".

(18) The eleventh sentence in the proof of Theorem 4.1, we replace "*c*_{
i
}" to "*d*_{
i
}".

(19) The twelfth sentence in the proof of Theorem 4.1, we replace "*c* ∈ *int R*^{
p
}," to "*d*_{
i
} > 0, *i* = 1,···, *p*,".

(20) The twelfth sentence in the proof of Theorem 4.1, we replace "*c*_{
i
}" to "*d*_{
i
}".

(21) The twelfth sentence in the proof of Theorem 4.1, we replace "*i* = 1,···, *p*." to "*i* = 1,···,*p*,".

(22) The fourth sentence in the proof of Theorem 4.2, we replace "*c*_{
i
}" to "*c*".

## Notes

## Authors’ Affiliations

## References

- Bae , Kim : Optimality and Duality Theorems in Nonsmooth Multiobjective Optimization.
*Fixed Point Theory and Applications*2011, 2011: 42. 10.1186/1687-1812-2011-42MathSciNetView ArticleGoogle Scholar

## Copyright

This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.