Cyclic α Meir–Keeler contraction and iterated function system on Branciari b-metric spaces
Abstract
We introduce a cyclic α Meir Keeler contraction within a generalized metric space and prove the existence and the uniqueness of a fixed point in the Branciari b-metric space. We also demonstrate that these results extend to hyperspaces or Hausdorff metric spaces. In addition, we create the iterated function system (IFS) known as the cyclic α Meir Keeler IFS, which produces a fractal (attractor). This context also enables us to illustrate the countable cyclic α Meir Keeler IFS, which generalizes the results in the existing literature. Moreover, we verify the approximation to the fractal by utilizing non-affine α Meir Keeler contraction maps. Finally, we obtain the fractal interpolation function through the α Meir Keeler IFS.
Fields of Study & Subjects
Fixed Point Theorems Analysis
Mathematical Dynamics and Fractals
Functional Equations Stability Results
Publication details
- Journal / source
- The Journal of Difference Equations and Applications
- Volume
- 32
- Issue
- 4
- Pages
- 509–526
- Publication date
- 12 February 2026
- Language
- EN