Advancements in Fixed Point Theorems for α-Geraghty Contractions in Complete Metric Space
Received:November 27, 2023  Revised:February 23, 2024
Key Words: Fixed point theorems   Contractive mappings   α-geraghty contractions   Complete metric spaces   Lebesgue integrals   α-admissible   α-orbital   α-orbital attractive.  
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Saeed A. A. Al-Salehi* Aden University, Aden, Yemen. Room no. 19, Guest House, Nanded, India.
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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.
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