(Φ, Δ)型概率收缩与Menger PN-空间中非线性算子方程的解*
(Φ, Δ)-Type Probabilistic Contractor and Solutions for a Nonlinear operator Equations in Menger PN-Spaces
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摘要: 本文在Menser概率赋范空间中引入了(Φ,Δ)型概率收缩的概念,研究了Menger概率赋范空间中具有这类概率收缩的非线性算子方程的解的存在性与唯一性。发展和改进了引文[1]、[4~8]的相应结果。
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关键词:
- Menger PN-空间 /
- h型t-范数 /
- 概率收缩 /
- 算子方程
Abstract: The purpose of this paper is to introduce the coneept of (Φ,△)-type probabilistic contractor in Menger PN-spaces and to study the existence and uniqueness of solutions for the nonlinear operator equations with such probabilistic contractor in Menger PN-spaces.The results presented in this paper improve and extend the corresponding results in [1] and [4-8].-
Key words:
- Menger PN-space /
- t-norm of h-type /
- probabilistic contractor /
- operator equation
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[1] 张石生,概率收缩与概率赋范空间中非线性方程的解,科学通报.35(19) (1990), 1451-1454. [2] 张石生、彭永成,概率收缩偶与非阿基米德Menger概率赋范空间中非线性方程组的解.应用数学和力学,12(11) (1991), 965-971. [3] 张石生,《不动点理论及应用梦》,重庆出版社(1984). [4] 曾文智,概率收缩和PN-空间的方程,数学研究与评论.11(1) (1991), 47-51. [5] M. Altman, Contractors and Contractor Directions Theory and Applications, Marcel Dekker, New York(1977). [6] A. C. Lee and W. J. Padgett, Random contractors with random nonlinear majorant functions, Nonlinear Anal, TMA, 3(1979), 707-715. [7] A. C. Lee and W. J.Padgett, Solutions of random operator equations by random step-contractors, Nonlinear Anal. TMA, 4(1980), 145-151. [8] A. C. Lee and W. J. Padgett. Random contracrors and the solution of random nonlinear equations, Nonlinear Anal. TMA, 1(1977), 173-185. [9] O. Hadzit, Fixed point theorems for mufti-valued mapping in probabilistic metric space, Mat. Vesnik, 3, 16(1979), 125-133.
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