Fuzzy Fixed Point Theorems in <inline-formula><math display="inline"><semantics><mi mathvariant="script">S</mi></semantics></math></inline-formula>-Metric Spaces: Applications to Navigation and Control Systems

Abstract

This manuscript examines fuzzy fixed point results using the concepts of S-metric space. We introduce two contractive maps, γ- and γ-weak contractions, within the context of S-metric spaces. These contractive maps form the cornerstone of our research, offering a novel approach to solving mathematical problems. We explore fixed point results derived from the application of these maps, showcasing their utility in finding solutions in diverse mathematical scenarios. Furthermore, we provide concrete examples that illustrate the practical relevance and versatility of our theorems, emphasizing their potential applications across a wide range of scientific and engineering domains. This manuscript presents the novel concepts of γ- and γ-weak contractions and establishes their importance in mathematical research. By demonstrating their effectiveness in solving real-world problems and offering illustrative examples, our work contributes valuable tools and insights to the broader scientific community, enhancing our understanding of contractive maps and their applications.

Keywords

• S -metric space%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> <named-content content-type="equation"> <mml:math id="mm4222"> <mml:semantics> <mml:mi mathvariant="script">S</mml:mi> </mml:semantics> </mml:math></named-content>-metric space
• fixed point
• γ -contraction%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> <named-content content-type="equation"><mml:math id="mm5111"> <mml:semantics> <mml:mi>γ</mml:mi> </mml:semantics> </mml:math></named-content>-contraction