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In this paper, we investigate the additivity of map $\\Phi$ from $\\mathcal{A}$ onto $\\mathcal{B}$ that are bijective unital and satisfies $$\\Phi(AP+\\lambda PA^{*})=\\Phi(A)\\Phi(P)+\\lambda \\Phi(P)\\Phi(A)^{*},$$ for all $A\\in\\mathcal{A}$ and $P\\in\\{P_{1},I_{\\mathcal{A}}-P_{1}\\}$ where $P_{1}$ is a nontrivial projection in $\\mathcal{A}$ and $\\lambda\\in\\{-1,+1\\}$. 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In this paper, we investigate the additivity of map $\\Phi$ from $\\mathcal{A}$ onto $\\mathcal{B}$ that are bijective unital and satisfies $$\\Phi(AP+\\lambda PA^{*})=\\Phi(A)\\Phi(P)+\\lambda \\Phi(P)\\Phi(A)^{*},$$ for all $A\\in\\mathcal{A}$ and $P\\in\\{P_{1},I_{\\mathcal{A}}-P_{1}\\}$ where $P_{1}$ is a nontrivial projection in $\\mathcal{A}$ and $\\lambda\\in\\{-1,+1\\}$. 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