Orthogonal sets: The axiom of choice and proof of a fixed point theorem |
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| Authors: | Hamid Baghani Madjid Eshaghi Gordji Maryam Ramezani |
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| Institution: | 1.Department of Mathematics, Faculty of Mathematics,University of Sistan and Baluchestan,Zahedan,Iran;2.Department of Mathematics,Semnan University,Semnan,Iran;3.Department of Science, Faculty of Mathematics,University of Bojnord,Bojnord,Iran |
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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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