Some fixed point theorems via g-ps S-contractions on S-metric spaces

Introduction: This paper focuses on extending the theory of fixed points in S-metric spaces by introducing new generalized contractive conditions. These developments aim to enrich the analytical tools available for studying such spaces. Methods: A variety of fixed-point theorems is established by applying the newly defined contractive conditions. The methodology includes both standard and integral-type contractive mappings. Furthermore, a geometric approach is utilized to obtain novel fixed-circle theorems within the S-metric framework. Results: Several fixed-point and fixed-circle theorems are proved under the proposed conditions. Illustrative examples are provided to validate the theoretical findings and demonstrate the applicability of the results. Conclusion: The findings of this study not only broaden the scope of fixed-point theory in S-metric spaces but also offer potential implications for real-world applications. In particular, the results may contribute to developments in computational mathematics and the design of neural network activation functions.