Fixed point theorem in probabilistic inner product spaces and its applications



In this paper, we obtain a new fixed point theorem in complete probabilistic Δ-inner product space. As an example of applications, we utilize the results of this paper to study the existence and uniqueness of solutions for linear Valterra integral equation.

AMS Mathematics Subject Classification


Key words and phrases

Probabilistic inner product space fixed point Valterra integral equation t-norm of h-type 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Jong Kyu Kim and Byoung Jae Jin,Differential equation on closed subsets of a probabilistic normed space, J. Appl. Math. & Computing5 (1998), 223–235.MATHMathSciNetGoogle Scholar
  2. 2.
    Ion Iancu,A method for constructing t-norms, J. Appl. Math. & Computing5 (1998), 407–415.MATHMathSciNetGoogle Scholar
  3. 3.
    R. Subramanian and K. Balachandran,Controllability of stochastic Volterra integro differential systems, J. Appl. Math. & Computing9 (2002), 583–591.Google Scholar
  4. 4.
    S. S. Chang, B. S. Lee and Y. J. Cho,Generalized contraction mapping principle and differential equations in probabilistic metric spaces, Proceedings of the American mathematical society124 (1996), 2367–2376.MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Claudi Alsina, Berthold Schweizer and Abe Sklar,Continuity properties of probabilistic norms, J. Math. Anal. Appl.208 (1997), 446–452.MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    E. Pap, Hadzić. O and R. Mesiar,A fixed point theorem in probabilistic metric, J. Math. Anal. Appl.202 (1996), 433–449.MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    R. M. Tardiff,Topologies for probabilistic metric spaces Pacific J. Math.65 (1976), 233–251.MATHMathSciNetGoogle Scholar
  8. 8.
    Zhu Chuan-xi,Some new fixed point theorems in probabilistic metric spaces, J. Appl. Math. Mech.16 (1995), 179–185.CrossRefGoogle Scholar
  9. 9.
    Zhu Chuan-xi,Some theorems in the X-M-PN spaces, J. Appl. Math. Mech.21 (2000), 181–184.CrossRefGoogle Scholar
  10. 10.
    Huang Xiao-qin and Zhu chuan-xi,Existence and uniqueness problems of solutions for setvalued nonlinear operator equations in PN-spaces, Acta Analysis Functionalis Applicata4 (2002), 222–225 (in Chinese).MathSciNetGoogle Scholar

Copyright information

© Korean Society for Computational and Applied Mathematics 2005

Authors and Affiliations

  1. 1.Faculty of scienceXi'an Jiaotong UniversityXi'anChina
  2. 2.Institute of MathematicsNanchang UniversityNanchangChina
  3. 3.Institute of MathematicsShijiazhuang No.2 middle schoolShijiazhuangChina

Personalised recommendations