Generalized hybrid $B-(b,\rho,\theta,\tilde{p},\tilde{r})-$invexities and efficiency conditions for multiobjective fractional programming

Abstract

This communication deals with first introducing the exponential type hybrid $B-(b,\rho,\theta,\tilde{p},\tilde{r})$- invexities and then establishing a class of the $\epsilon-$ efficiency conditions applying to multiobjective fractional programming problems. The exponential type hybrid $B-(b,\rho,\theta,\tilde{p},\tilde{r})$-invexities encompass most of the existing generalized higher order invexities as well as the exponential type generalized invexities, including the Antczak type first order $B-(\tilde{p},\tilde{r})-$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.