Abstract
The purpose of this article is to define notions of I-involution on Γ-rings, existence and prove some interesting results: (i) Let M be a 2-torsion free semiprime Γ-ring with I-involution and satisfying a certain assumption. If T : M → M is a Jordan left centralizer on M , then T is a left centralizer. (ii) Let M be a 2-torsion free semiprime Γ-ring with I-involution and T : M → M an additive mapping such that T (xαI(x )+ I(x)αx )= T (x)αI(x )+ I(x)αT (x)
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