Uniqueness of fixed point for sum of operators in ordered Banach spaces and application

• Benmezai, Abdelhamid ^[1]
  1. [1] National High School of Mathematics.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 41, Nº. 4, 2022, págs. 949-964
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-5407
• Enlaces
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• Resumen

  • In this article, we are concerned by existence and uniqueness of a fixed point for the sum of two operators A and B, defined on a closed convex subset of an ordered Banach space, where the order is induced by a normal and minihedral cone. In such a structure, an absolute value function is generated by the order and this provide the ability to introduce new versions of the concepts of lipschitzian and expansive mappings. Therefore we prove that if A is expansive and B is contractive, then the sum A + B has a unique fixed point.

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