COMMON BEST PROXIMITY RESULTS FOR SEVERAL GENERALIZED NON-SELF ALPHA-CONJOINT PROXIMAL BETA-QUASI CONTRACTION MAPPINGS | ||
| Journal of the Egyptian Mathematical Society | ||
| Volume 33, Issue 1, 2025, Pages 113-126 PDF (286.22 K) | ||
| Document Type: Original Article | ||
| DOI: 10.21608/joems.2025.365906.1028 | ||
| Authors | ||
| Salwa Hamdy* 1; Sarah Tawfeek2; Nashat Faried3; HLEIL ALRWEILI4 | ||
| 1Meteorologist at the Egyptian Meteorological Authority | ||
| 2Department of Mathematics, Faculty of Science, Ain Shams University, Cairo, Egypt. | ||
| 3Department of Mathematics, Faculty of Science, Ain Shams Univerisity, Cairo, Egypt. | ||
| 4Department of Mathematics, College of Science, Northern Border University, Arar, Saudi Arabia. | ||
| Abstract | ||
| Fixed point theory is a fundamental concept in mathematics, which ensures the existence and uniqueness of fixed points for self-mappings in complete metric spaces. The Banach contraction principle, explicitly stated in Banach’s 1922 thesis, laid the groundwork for this field. However, for non-self mappings H: F!K, where F and K are subsets of a metric space E, fixed points may not exist. This led to the development of the best proximity point theory, which seeks to find elements f in F where d(f, Hf) = d(F, K). This study introduces new concepts in the field of best proximity point theory, extending the existing framework with the formulation of conjoint proximal b-quasi contraction, a-generalized conjoint proximal b-quasi contraction, and generalized conjoint b-quasi contraction. These innovative constructs are utilized to investigate the existence of common best proximity points on metric spaces for both double and multiple non-self mappings. The research also presents a concrete example involving two non-self mappings, thereby illustrating the practical application of these theoretical concepts. Furthermore, the study explores various implications and consequences arising from these new formulations. | ||
| Keywords | ||
| Best proximity point; non-self mapping; P-property; approximately compact and special generalized proximal beta-quasi contraction | ||
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