Variations of generalized weak contractions in partially ordered b-metric space

Area of Science:

• Fixed point theory
• Metric spaces
• Order theory

Background:

• Explores fixed point results in complete partially ordered b-metric spaces.
• Builds upon prior work by Mituku et al. and Seshagiri et al. on similar concepts.
• Investigates mappings that satisfy generalized weak contractive conditions.

Purpose of the Study:

• To establish new fixed point results for self-mappings in ordered b-metric spaces.
• To analyze mappings under variant generalized weak contraction conditions.
• To generalize and extend existing theorems in the literature.

Main Methods:

• Utilizes the framework of complete partially ordered b-metric spaces.
• Applies generalized weak contraction conditions to mappings.
• Employs fixed point theory principles.

Main Results:

• Proves novel fixed point results for self-mappings.
• Demonstrates that the established results generalize previously known theorems.
• Validates the theoretical findings with illustrative examples.

Conclusions:

• The study successfully establishes new fixed point theorems.
• The results contribute to the generalization of existing literature in metric spaces.
• The findings are supported by provided examples, enhancing their applicability.