# Erratum to: On second-order duality of minimax fractional programming with square root term involving generalized \({\varvec{B}}\)-\({\varvec{(p,\,r)}}\)-invex functions

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## 1 Erratum to: Ann Oper Res (2016) 244:603–617 DOI 10.1007/s10479-016-2147-y

**Abstract** In this erratum, we have pointed out some typo errors in Eq. (9) and statement of Theorems 3.1 and 3.3 [Sonali, Kailey, N., and Sharma, V. (2016). On second-order duality of minimax fractional programming with square root term involving generalized B-(p, r)-invex functions. Annals of Operations Research, 244, 603–617].

**Keywords** Minimax programming \(\cdot \) Fractional programming \(\cdot \) Nondifferentiable programming \(\cdot \) Second-order duality \(\cdot \) *B*-(*p*, *r*)-invexity

In Model-I, (9) should be read as \(\sum _{j=1}^{m}\mu _jg_j(z)+\frac{1}{2}l^T\nabla ^2\psi _1(z)l\ge 0\) instead of \(\sum _{j=1}^{m}\mu _jg_j(z)-\frac{1}{2}l^T\nabla ^2\psi _1(z)l\ge 0\) and in Theorem 3.1 (second assumption) and 3.3 (third assumption) should be taken as negative semidefinite instead of positive semidefinite.