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

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

(2) The first sentence in Definition 2.2, we replace

$f i x + s x | D i ≮ f i x 0 + s x 0 | D i$

to

$f x + s x | D ≮ f x 0 + s x 0 | D .$

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

(4) The second sentence in Definition 2.3, we replace

$f i x + s x | D i ≮ f i x 0 + s x 0 | D i + c i | | x - x 0 | | m$

to

$f x + s x | D ≮ f x 0 + s x 0 | D + c | | x - x 0 | | m .$

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

(6) The second sentence in Definition 2.4, we replace

$′ ′ f i x + s x | D i ≮ f i x 0 + s x 0 | D i + c i | | x - x 0 | | m$

to

$f x + s x | D ≮ f x 0 + s x 0 | D + c | | x - x 0 | | m . ′ ′ .$

(7) The second sentence in the proof of Theorem 2.1, we replace. ′′ c i > 0, i = 1, ,p ′′ to ′′ $c∈int R + p$′′.

(8) The second sentence in the proof of Theorem 2.1, we replace

$f i x + s x | D i ≮ f i x 0 + s x 0 | D i + c i | | x - x 0 | | m$

to

$f x + s x | D ≮ f x 0 + s x 0 | D + c | | x - x 0 | | m .$

(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 Rp" 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 Rp" 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 Rp," 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".

(23) The fourth sentence in the proof of Theorem 4.2, we replace

$f i ( x 0 ) + ( x 0 ) T w i 0 + c i | | u - x 0 | | m ≮ f i ( u ) + u T w i , i = 1 , ⋅ ⋅ ⋅ , p .$

to

$f ( x 0 ) + ( x 0 ) T w 0 + c | | u - x 0 | | m ≮ f ( u ) + u T w .$

## References

1. 1.

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

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Authors

### Corresponding author

Correspondence to Do Sang Kim.

The online version of the original article can be found at 10.1186/1687-1812-2011-42

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