International Journal of Advances in Mathematics
International Journal of Advances in Mathematics
2456-6098
Volume 2017
Number 3
2017
May
8
Semiinfinite multiobjective fractional programming problems using exponential type generalized invexities
16
33
EN
Ram
U
Verma
International Publications USA
1200 Dallas Drive Suite 912, Denton, Texas 76205, USA.
verma99@msn.com
In this paper, first a class of second order exponential type hybrid $(\alpha$, $\beta$, $\gamma$, $\eta$, $\rho$, $h(\cdot,\cdot)$, $\kappa(\cdot,\cdot)$, $\omega(\cdot,\cdot,\cdot)$, $\varpi(\cdot,\cdot,\cdot)$, $\theta)$-invexities is introduced, and then a class of parametrically sufficient efficiency conditions based on the second order exponential type hybrid invexities is established. Finally some parametric sufficient efficiency theorems under the higher order exponential type hybrid $(\alpha$, $\beta$, $\gamma$, $\eta$, $\rho$, $h(\cdot,\cdot)$, $\kappa(\cdot,\cdot)$, $\omega(\cdot,\cdot,\cdot)$, $\varpi(\cdot,\cdot,\cdot)$, $\theta)$-invexities are investigated to the context of solving a semiinfinite multiobjective fractional programming problem. The notions of the second order exponential type hybrid $(\alpha$, $\beta$, $\gamma$, $\eta$, $\rho$, $h(\cdot,\cdot)$, $\kappa(\cdot,\cdot)$, $\omega(\cdot,\cdot,\cdot)$, $\varpi(\cdot,\cdot,\cdot)$, $\theta)$-invexities are new and encompass most of the generalized invexity concepts in the literature. To the best of our knowledge, the results on semiinfinite multiobjective fractional programming problems established in this paper are new and application-oriented toward multitime multiobjective problems as well as multiobjective control problems.
Semiinfinite fractional programming, multiobjective fractional programming, Hanson-Antczak-type generalized $HA(\alpha$, $\beta$, $\gamma$, $\eta$, $\rho$, $\theta)$-V-invex functions, hybrid $(\alpha$, $\beta$, $\gamma$, $\eta$, $\rho$, $h(\cdot,\cdot)$, $\kappa(\cdot,\cdot)$, $\omega(\cdot,\cdot,\cdot)$, $\varpi(\cdot,\cdot,\cdot)$, $\theta)$-invexity.
http://adv-math.com/2017/05/08/ram-u-verma-semiinfinite-multiobjective-fractional-programming-problems-using-exponential-type-generalized-invexities-volume-2017-number-3-pages-16-33-2017/
http://adv-math.com/wp-content/uploads/2017/05/MS-ID-ADV-20176_Verma.pdf