Fixed points of two interpolative cyclic contractions in b-metric spaces

Area of Science:

• Topology and Analysis
• Metric Space Theory
• Fixed Point Theory

Background:

• The b-metric space is a significant generalization of traditional metric spaces.
• Fixed point theory is crucial for solving equations and understanding dynamical systems.
• Cyclic contractions are important in metric spaces for guaranteeing fixed point existence.

Purpose of the Study:

• To introduce Kannan type and Ćirić-Reich-Rus type cyclic contractions in b-metric spaces.
• To investigate the existence and uniqueness of fixed points for these new contraction types.
• To generalize and improve upon existing results in the field, specifically referencing Edraoui et al. (2023).

Main Methods:

• Development of novel cyclic contraction mappings within the framework of b-metric spaces.
• Application of interpolation techniques to define and analyze these contractions.
• Rigorous mathematical proofs to establish existence and uniqueness theorems for fixed points.

Main Results:

• Successful introduction of Kannan type and Ćirić-Reich-Rus type cyclic contractions in b-metric spaces.
• Demonstration of the existence and uniqueness of fixed points for the proposed mappings.
• Validation of theoretical results through illustrative examples.

Conclusions:

• The newly defined cyclic contractions provide a valuable extension to fixed point theory in b-metric spaces.
• The study offers improved and generalized results compared to prior research.
• The findings have potential implications for various mathematical and applied fields relying on fixed point theorems.