COMMON BEST PROXIMITY RESULTS FOR SEVERAL GENERALIZED NON-SELF ALPHA-CONJOINT PROXIMAL BETA-QUASI CONTRACTION MAPPINGS

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.