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Fixed point theorems in generating spaces of quasi-norm family and applications

Fixed Point Theory and Applications volume 2006, Article number: 61623 (2006) Cite this article

Abstract

Some new concepts of generating spaces of quasi-norm family are introduced and their linear topological structures are studied. These spaces are not necessarily locally convex. By virtue of some properties in these spaces, several Schauder-type fixed point theorems are proved, which include the corresponding theorems in locally convex spaces as their special cases. As applications, some new fixed point theorems in Menger probabilistic normed spaces and fuzzy normed spaces are obtained.

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References

  1. Fan K: A generalization of Tychonoff's fixed point theorem. Mathematische Annalen 1961, 142: 305–310. 10.1007/BF01353421

    Article  MathSciNet  MATH  Google Scholar 

  2. Fang J-X, Song G-A: -contractor and the solutions for nonlinear operator equations in fuzzy normed spaces. Fuzzy Sets and Systems 2001,121(2):267–273. 10.1016/S0165-0114(00)00016-6

    Article  MathSciNet  MATH  Google Scholar 

  3. Istrăţescu VI: Fixed Point Theory. An Introduction, Mathematics and Its Applications. Volume 7. D. Reidel, Dordrecht; 1981:xv+466.

    Google Scholar 

  4. Kelley JL, Namioka I: Linear Topological Spaces, Graduate Texts in Mathematics, no. 36. Springer, New York; 1976:xv+256.

    Google Scholar 

  5. Krasnoselskii I, et al.: Approximation Solution of Operator Equations. Wolters-Noordhoff, Groningen; 1978.

    Google Scholar 

  6. Lin X: Fixed-point theorems in probabilistic normed linear spaces. Journal of Mathematics (Wuhan) 1983,3(1):73–82.

    MathSciNet  MATH  Google Scholar 

  7. Serstnev AN: On the notion of a random normed space. Doklady Akademii Nauk USSR 1963,149(2):280–283. Soviet Mathematics 4 (1963), no. 2, 388–391

    MathSciNet  Google Scholar 

  8. Xiao JZ, Zhu XH: Probabilistic norm of operators and resonance theorems. Applied Mathematics and Mechanics 1999,20(7):781–788. 10.1007/BF02454900

    Article  MathSciNet  MATH  Google Scholar 

  9. Xiao JZ, Zhu XH: On linearly topological structure and property of fuzzy normed linear space. Fuzzy Sets and Systems 2002,125(2):153–161. 10.1016/S0165-0114(00)00136-6

    Article  MathSciNet  MATH  Google Scholar 

  10. Zhang SS: Basic theory and applications of probabilistic metric spaces. I. Applied Mathematics and Mechanics 1988,9(2):123–133. 10.1007/BF02456008

    Article  MathSciNet  MATH  Google Scholar 

  11. Zhang SS, Guo JL: Probability integrals, Gateaux differentials and the Schauder principle in probabilistic normed linear spaces. Journal of Sichuan University. Natural Science Edition 1989,26(2):127–135.

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Jian-Zhong Xiao & Xing-Hua Zhu

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  1. Jian-Zhong Xiao
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  2. Xing-Hua Zhu
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Correspondence to Jian-Zhong Xiao.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Xiao, JZ., Zhu, XH. Fixed point theorems in generating spaces of quasi-norm family and applications. Fixed Point Theory Appl 2006, 61623 (2006). https://doi.org/10.1155/FPTA/2006/61623

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