Weak proximal normal structure and coincidence quasi-best proximity points

• Fouladi, Farhad ^[1] ; Abkar, Ali ^[1] ; Karapinar, Erdal ^[2]
  1. [1] Imam Khomeini International University

     Imam Khomeini International University

     Irán

     
  2. [2] ETSI Division of Applied Mathematics, Thu Dau Mot University, Binh Duong Province
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 21, Nº. 2, 2020, págs. 331-347
• Idioma: inglés
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• Resumen

  • We introduce the notion of pointwise cyclic-noncyclic relatively nonexpansive pairs involving orbits. We study the best proximity point problem for this class of mappings. We also study the same problem for the class of pointwise noncyclic-noncyclic relatively nonexpansive pairs involving orbits. Finally, under the assumption of weak proximal normal structure, we prove a coincidence quasi-best proximity point theorem for pointwise cyclic-noncyclic relatively nonexpansive pairs involving orbits. Examples are provided to illustrate the observed results.