In this paper we introduce the concept of On γ - generalized α - Continuous Mappings in Topological Spaces and study its relationship with other mappings. Further we declare the concepts of γ-α continuous mappings and γ -g α continuous mappings which coincide when the space is α-γ T-1/2. In addition, we define the concept of γ -g α-irresolute mappings in topological spaces; also we attain the relationships between γ -g α-continuous and γ -g α-irresolute mappings and obtain some of its basic properties.