Generalized hybrid B − ( b , ρ , θ , p̃ , r̃ ) − invexities and efficiency conditions for multiobjective fractional programming

This communication deals with first introducing the exponential type hybrid B − (b, ρ, θ, p̃, r̃)invexities and then establishing a class of the ε− efficiency conditions applying to multiobjective fractional programming problems. The exponential type hybrid B − (b, ρ, θ, p̃, r̃)-invexities encompass most of the existing generalized higher order invexities as well as the exponential type generalized invexities, including the Antczak type first order B− (p̃, r̃)−invexities. To the best of our knowledge, the obtained results seem to be most advanced on generalized invexities available in the literature, while offer more suitable applications to other fields and beyond. 2010 Mathematics Subject Classification. 90C30. 90C32, 90C34