, Volume 55, Issue 1, pp 196–201 | Cite as

Remarks on duality for second order minimax fractional programming with B-(p,r)-invex functions

  • Indira P. Debnath
  • S. K. Gupta
  • D. Dangar
Technical Note


In this paper, we have pointed out that the proofs of the Theorems 3.1 and 3.3 in the recent paper (Sonali et al. in Ann Oper Res 244:603–617, 2016) are erroneous. A modified dual to the second order minimax fractional programming problem has been formulated and the rectified proofs of these results under generalized B-(p,r)-invexity have been established.


Minimax programming Fractional programming Nondifferentiable programming Second order duality B-(p,r)-invexity 

Mathematics Subject Classification

90C26 90C29 90C30 90C47 49N15 



Indira P. Debnath is grateful to the Ministry of Human Resource and Development, India for financial support, to carry out this work.


  1. 1.
    Sonali, Kailey, N., Sharma, V.: On second order duality of minimax fractional programming with square root term involving generalized B-(p,r)-invex functions. Ann. Oper. Res. 244, 603–617 (2016)Google Scholar

Copyright information

© Operational Research Society of India 2017

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology RoorkeeRoorkeeIndia
  2. 2.Department of MathematicsAdamas UniversityBarasatIndia

Personalised recommendations