Studying the Triple Higgs Self-Coupling Via e+e- --> b bar b HH, t bar t HH at Future Linear e+e- Colliders

We study the triple Higgs self-coupling at future $e^{+}e^{-}$ colliders energies, with the reactions $e^{+}e^{-}\to b \bar b HH$ and $e^{+}e^{-}\to t \bar t HH$. We evaluate the total cross section of $b\bar bHH$, $t\bar tHH$ and calculate the total number of events considering the complete set of Feynman diagrams at tree-level. The sensitivity of the triple Higgs coupling is considered in the Higgs mass range 110-190 $GeV$, for the energy which is expected to be available at a possible Next Linear $e^{+}e^{-}$ Collider with a center-of-mass energy $800, 1000, 1500$ $GeV$ and luminosity 1000 $fb^{-1}$.