Acta mathematica scientia,Series A ›› 1999, Vol. 19 ›› Issue (4): 456-460.
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(Department of Applied Mathematics and Applied Sofware, Central South University of Technology, Changsha 410083)
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Abstract:
This paper proves that every probabilistic contraction map from complete set C to C has a unique fixed point, where C is a subset of a locally bounded probability normed space or a locally N-convex probabilistic normed space, and gives some applications in metric linear spaces.
Key words: ｐｒｏｂａｂｉｌｉｓｔｉｃｃｏｎｔｒａｃｔｉｏｎｍａｐ, ｃｏｍｐｌｅｔｅｓｅｔ, ｆｉｘｅｄｐｏｉｎｔ, ｐｒｏｂａｂｉｌｉｓｔｉｃｎｏｒｍｅｄｓｐａｃｅ．
CLC Number:
Xiang Shuhuang. a futher analysisi of fixed point theorems on probabilistic normed spaces and their applications[J].Acta mathematica scientia,Series A, 1999, 19(4): 456-460.
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http://121.43.60.238/sxwlxbA/EN/Y1999/V19/I4/456
１ ＳｅｈｇａｌＶ Ｍ，ＢｈａｒｕｃｈａｒｅｉｄＡ Ｔ．Ｆｉｘｅｄｐｏｉｎｔｓｏｎｃｏｎｔｒａｃｔｉｏｎｍａｐｐｉｎｇｓｏｆｐｒｏｂａｂｉｌｉｓｔｉｃｍｅｔｒｉｃｓｐａｃｅｓ．ＭａｔｈＳｙｓｔｅｍｓＴｈｅｏｒｙ，１９７２，２：９７－１０２ ２ ＩｓｔｒａｔｅｓｃｕＩ，Ｓ＾ａｃｕｉｕＩ．Ｆｉｘｅｄｐｏｉｎｔｔｈｅｏｒｅｍｓｆｏｒｃｏｎｔｒａｃｔｉｏｎ ｍａｐｐｉｎｇｓｏｎｐｒｏｂａｂｉｌｉｓｔｉｃｍｅｔｒｉｃｓｐａｃｅｓ．ＲｅｖＲｏｕｍａｉｎｅＭａｔｈＰｕｒｅｓＡｐｐｌ，１９７３，１８：１３７５－１３８０ ３ Ｈａｄ＾ｚｉｃＯ．Ａｆｉｘｅｄｐｏｉｎｔｔｈｅｏｒｅｍｉｎｒａｎｄｏｍｎｏｒｍｅｄｓｐａｃｅｓ．ＲｅｖＲｏｕｍａｉｎｅＭａｔｈＰｕｒｅｓＡｐｐｌ，１９７８，２３：７３５－７４４ ４ 张石生．概率度量空间映象的不动点定理及其应用．中国科学（Ａ 辑），１９８３，６：４９５－５０４ ５ ＳｈｅｒｗｏｏｄＨ．Ｃｏｍｐｌｅｔｅｐｒｏｂａｂｉｌｉｓｔｉｃｍｅｔｒｉｃｓｐａｃｅｓ．Ｚ ＷａｈｒｓｃｈｅｉｎｌｉｃｈｋｅｉｔａｔｈｅｏｒｔｅＶｅｒｗ Ｇｅｂ，１９７１，２０：１１７－１２８ ６ 游兆永，朱林户．概率度量空间的等距度量化．中国科学（Ａ 辑），１９８９，１：１９－２４ ７ ＳｃｈｗｅｉｚｅｒＢ，ＳｋｌａｒＡ．Ｐｒｏｂａｂｉｌｉｓｔｉｃｍｅｔｒｉｃｓｐａｃｅｓ．ＮｏｒｔｈＨｏｌｌａｎｄ，１９８３ ８ ＳｅｒｓｔｎｅｖＡ Ｎ．Ｏｎｔｈｅｎｏｔｉｏｎｏｆｒａｎｄｏｍｎｏｒｍｅｄｓｐａｃｅｓ．ＤｏｋｌＡｋａｄＮａｕｋＵＳＳＲ，１９６３，１４（２）：２８０－２８３ ９ 向淑晃，龚怀云，游兆永等．ＰＮ 空间的邻域结构与t-模．工程数学学报，１９９５，３（１２）：１２４－１２６
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