Exploring strong controlled partial metric type spaces: Analysis of fixed points and theoretical contributions

Area of Science:

• Topology and Analysis
• Metric Spaces
• Fixed Point Theory

Background:

• Partial metric spaces and strong controlled metric type spaces are foundational in analysis.
• Generalizing these spaces offers broader applicability for theoretical and applied problems.
• Fixed point theory is crucial for solving equations and understanding dynamical systems.

Purpose of the Study:

• To introduce and define strong controlled partial metric type spaces.
• To investigate the existence and uniqueness of fixed points for Kannan-type contractions within these novel spaces.
• To demonstrate the utility of the proposed framework through examples and applications.

Main Methods:

• Generalization of existing metric space concepts.
• Application of fixed point theorems for Kannan-type contractions (linear and nonlinear).
• Construction of illustrative examples and relevant applications.

Main Results:

• The successful introduction of strong controlled partial metric type spaces.
• Establishment of fixed point results for Kannan contractions in the generalized spaces.
• Validation of theoretical findings through practical examples.

Conclusions:

• The study successfully extends the theory of metric spaces.
• The new framework provides a valuable tool for fixed point analysis.
• The findings have potential implications in various fields of mathematics and applied sciences.