Advancements in Fixed Point Theorems for α-Geraghty Contractions in Complete Metric Space

Abstract:

      This article improves and advances the results achieved by Vishal and Naveen in their 2013 publication, leveraging the use of Lebesgue integrable functions. Going beyond, we investigate fixed point theorems associated with a concept introduced by Ovidiu Popescu in 2014. Our research not only bolsters the theoretical framework but also unveils practical applications in the domain of Lebesgue integrals as in the example (3.6). Furthermore, our contribution enhances the understanding of fixed point theorems in metric spaces and introduces novel perspectives in the study of ageneralized α-geraghty contractive mappings on lebesgue integrals.