On α-ψ-Meir-Keeler contractive mappings

Under what conditions can an α-ψ-Meir-Keeler-type mapping admit a fixed point, and when is that point unique?

The paper introduces the α-ψ-Meir-Keeler contractive mapping through a triangular α-admissible mapping and studies fixed-point existence and uniqueness in complete metric spaces.

• Define the contractive condition
• Use α-admissibility
• Prove existence and uniqueness
• Provide illustrative examples

The main result gives conditions for existence and uniqueness of fixed points for these mappings in complete metric spaces. Several examples illustrate the results.

This is an example of working from precise constraints and structural properties rather than treating an algorithm as a black box: the problem's structure determines what can be guaranteed.