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Orthogonal sets: The axiom of choice and proof of a fixed point theorem

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Abstract

In this paper, we prove some fixed point theorem on orthogonal spaces. Our result improve the main result of the paper by Eshaghi Gordji et al. [On orthogonal sets and Banach fixed point theorem, to appear in Fixed Point Theory]. Also we prove a statement which is equivalent to the axiom of choice. In the last section, as an application, we consider the existence and uniqueness of a solution for a Volterra-type integral equation in L p space.

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Correspondence to Madjid Eshaghi Gordji.

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Baghani, H., Eshaghi Gordji, M. & Ramezani, M. Orthogonal sets: The axiom of choice and proof of a fixed point theorem. J. Fixed Point Theory Appl. 18, 465–477 (2016). https://doi.org/10.1007/s11784-016-0297-9

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Mathematics Subject Classification

  • 34A12
  • 65R10
  • 65R20

Keywords

  • The axiom of choice
  • fixed point
  • orthogonal set
  • Picard operator