Fixed point theorems in α-complete metric spaces

This thesis presents a comprehensive review of recent developments concerning fixed point theorems in α-complete metric spaces. It begins with an introduction to the notion of fixed points and the Banach Fixed Point Theorem, illustrated with examples. Subsequent sections examine approximate fixed point theorems for partially generalized convex contractions, fixed points of generalized (α, ψ, ϕ)-rational contractions, and new results related to (α, ψ, ξ)- multivariable contraction mappings. These findings aim to enrich the understanding of fixed point theory within generalized metric frameworks.