Advancements in Fixed Point Theorems for $\alpha$-Geraghty Contractions in Complete Metric Space
Received:November 27, 2023  Revised:March 04, 2024
Key Words: fixed point theorems   contractive mappings   $\alpha$-Geraghty contractions   complete metric spaces   Lebesgue integrals   $\alpha$-admissible   $\alpha$-orbital   $\alpha$-orbital attractive  
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Author NameAffiliation
V. C. BORKAR School of Mathematical at Yeshwant Mahavidyalaya, Swami Ramanand Teerth Marathwada University, Nanded-431606, India 
Mohammed M. A. TALEB School of Mathematical at Science College, Swami Ramanand Teerth Marathwada University, Nanded-431606, India
Department of Mathematics, Hodeidah University, Al-Hodeidah, Yemen 
Saeed A. A. AL-SALEHI School of Mathematical at Science College, Swami Ramanand Teerth Marathwada University, Nanded-431606, India
Department of Mathematics, Aden University, Aden, Yemen 
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Abstract:
      This article improves and advances the results achieved by Vishal and Naveen, leveraging the use of Lebesgue integrable functions. Going beyond, we investigate fixed point theorems associated with a concept introduced by Ovidiu Popescu. Our research not only bolsters the theoretical framework but also unveils practical applications in the domain of Lebesgue integrals as in Example 3.6. Furthermore, our contribution enhances the understanding of fixed point theorems in metric spaces and introduces novel perspectives in the study of generalized $\alpha$-Geraghty contractive mappings on Lebesgue integrals.
Citation:
DOI:10.3770/j.issn:2095-2651.2024.05.010
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