Ram U. Verma, Semiinfinite multiobjective fractional programming problems using exponential type generalized invexities, Volume 2017, Number 3, Pages 16-33, 2017

# Ram U. Verma, Semiinfinite multiobjective fractional programming problems using exponential type generalized invexities, Volume 2017, Number 3, Pages 16-33, 2017

Abstract: 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.

Keywords: 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.

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