A Suzuki-type multivalued contraction on weak partial metric spaces and applications

Area of Science:

• Fixed-point theory
• Multivalued analysis
• Metric spaces

Background:

• Building upon prior work by Beg and Pathak (2018).
• Introducing a novel class of mappings: omega-type Suzuki multivalued contraction mappings.
• Expanding the scope of fixed-point theorems in generalized metric spaces.

Purpose of the Study:

• To introduce and define omega-type Suzuki multivalued contraction mappings.
• To establish a fixed-point theorem for these mappings in complete weak partial metric spaces.
• To explore applications and future research directions in related spaces.

Main Methods:

• Definition of omega-type Suzuki multivalued contraction mappings.
• Utilizing techniques from fixed-point theory in the context of weak partial metric spaces.
• Illustrative example provided for clarity.

Main Results:

• A fixed-point theorem is proven for omega-type Suzuki multivalued contractions in complete weak partial metric spaces.
• Demonstrated applicability to homotopy theory and Fredholm-type integral inclusions.
• Identified open problems for the more general 0-complete weak partial metric spaces.

Conclusions:

• The study successfully introduces a new class of mappings and proves a significant fixed-point theorem.
• The findings have practical implications in areas like homotopy and integral equations.
• Opens avenues for further research in generalized metric spaces and multivalued mappings.