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One of the main objectives of almost all future (lepton) colliders is tomeasure the self-coupling of triple Higgs in the Standard Model. By elongatingthe Standard Model's scalar sector, using incipient Higgs doublet along with aquadratic (Higgs) potential should reveal many incipient features of the modeland the possibility of the emergence of additional Higgs self-couplings. Theself-coupling of the Higgs boson helps in reconstructing the scalar potential.The main objective of this paper is to extract Higgs self-coupling bynumerically analyzing several scattering processes governed by two Higgsdoublet models (2HDM). These scattering processes include various possiblecombinations of final states in the triple Higgs sector. The determination ofproduction cross-section of scattering processes is carried out using twodifferent scenarios, with and without polarization of incoming beam and isextended to a center of mass energy up to $\sqrt{s}$ = 3 $TeV$. The computationis carried out in Type-1 2HDM. Here we consider the case of exact alignmentlimit ($s_{\beta \alpha}$ = 1) and masses of extra Higgs state are equal thatis $m_H = m_{H^0} = m_{A^0} = m_{H^\pm}$. This choice is made to minimize theoblique parameters. The decays of the final state of each process areinvestigated to estimate the number of events at integrated luminosity of$1ab^{-1}$ and $3ab^{-1}$.

Probing triple higgs self coupling and effect of beam polarization in lepton colliders