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Fixed point theorems for multivalued mappings in some classes of fuzzy metric spaces. (English) Zbl 0681.54023

This paper presents a fixed point theorem for multivalued mappings in probabilistic metric spaces using the probabilistic function of noncompactness. As an application a fixed point theorem for multivalued mappings in fuzzy metric spaces has been obtained.
Reviewer: B.K.Dass

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54A40 Fuzzy topology
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[1] Banas, J.; Goebel, K., Measures of Noncompactness in Banach spaces (1980), Marcel Dekker: Marcel Dekker New York-Basel · Zbl 0441.47056
[2] Bharucha-Reid, A. T., Fixed point theorems in probabilistic analysis, Bull. Amer. Math. Soc., 32, 641-657 (1976) · Zbl 0339.60061
[3] Bocsan, Gh., Some applications of functions of Kuratowski, Sem. Teor. Funct. si. Mat. Apl., no. 5 (1973), Timisoara, RS Romania · Zbl 0444.60049
[4] Bocsan, Gh., On the Kuratowski functions in random normed spaces, Sem. Teor. Funct. si Mat. Apl., No. 8 (1974), Timisoara, RS Romania · Zbl 0444.60049
[5] Bocsan, Gh., On some fixed point theorems in random normed spaces, Sem. Teor. Funct. si Mat. Apl., No. 13 (1974), Timisoara, RS Romania · Zbl 0444.60049
[6] Bocsan, Gh., On some fixed point theorems in probabilistic metric spaces, Sem. Teor. Funct. si Mat. Apl., No. 24 (1974), Timisoara, RS Romania · Zbl 0444.60049
[7] Bocsan, Gh.; Constantin, Gh., The Kuratowski function and some applications to the probabilistic metric spaces, Sem. Teor. Funct. si Mat. Apl., No. 1 (1973), Timisoara, RS Romania · Zbl 0436.60014
[8] Cain, G., Fixed points and stability of multifunctions on random normed spaces (1986), School of Mathematics, Georgia Inst. Tech: School of Mathematics, Georgia Inst. Tech Atlanta, GA, Preprint
[9] Cain, G. L.; Kasriel, R. H., Fixed and periodic points of local contraction mappings on probabilistic metric spaces, Math. Systems Theory, 9, 289-297 (1976) · Zbl 0334.60004
[10] Constantin, Gh., On some classes of contraction mappings in Menger spaces, Sem. Teor. Prob. Apl., No. 76 (1985), Timisoara, RS Romania
[11] Constantin, Gh.; Istratescu, I., Elemente de Analiza Probabilista si Aplicatii (1981), Editura Academiei Republici Socialiste Romania: Editura Academiei Republici Socialiste Romania Bucuresti · Zbl 0508.60005
[12] Hadžić, O., A fixed point theorem for multivalued mappings in random normed spaces, Anal. Numér. Théor. Approx., 81, 49-52 (1979) · Zbl 0428.47034
[13] Hadžić, O., Fixed point theorems for multivalued mappings in probabilistic metric spaces, Mat. Vesnik, 3, 16, 125-133 (1979), (31) · Zbl 0446.47052
[14] Hadžić, O., Some theorems on the fixed points in probabilistic metric and random normed spaces, Boll. Unione Mat. Ital., 1-B, 6, 381-391 (1982) · Zbl 0488.47028
[15] Hadžić, O., Fixed point theory in topological vector spaces, ((1984), University of Novi Sad, Faculty of Science, Institute of Mathematics: University of Novi Sad, Faculty of Science, Institute of Mathematics Novi Sad), 337 · Zbl 0576.47030
[16] Hicks, T. L., Fixed point theory in probabilistic metric spaces, Univ. u Novom Sadu Zb. Rad. Prir.-Mat. Fak. Ser. Mat., 13, 63-72 (1983) · Zbl 0574.54044
[17] Himmelberg, C. J.; Porter, J. R.; Van Vleck, F. S., Fixed point theorems for condensing multifunctions, (Proc. Amer. Math. Soc., 23 (1969)), 635-641 · Zbl 0195.14902
[18] Kaleva, O.; Seikkala, S., On fuzzy metric spaces, Fuzzy Sets and Systems, 12, 215-229 (1984) · Zbl 0558.54003
[19] Menger, K., Statistical metric, (Proc. Nat. Acad. Sci. USA, 28 (1942)), 535-537 · Zbl 0063.03886
[20] Nadler, S. B., Multivalued contraction mappings, Pacific J. Math., 30, 475-488 (1969) · Zbl 0187.45002
[21] Radu, V., A remark on contractions in Menger spaces, Sem. Teor. Prob. Apl., No. 64 (1983), Timisoara, RS Romania · Zbl 0541.54060
[22] Radu, V., On the t-norms of Hadžić type and fixed points in probabilistic metric spaces, Sem. Teor. Prob. Apl., No. 66 (1983), Timisoara, RS Romania · Zbl 0586.47063
[23] Radu, V., On the contraction principle in Menger spaces, Sem. Teor. Prob. Apl., No. 68 (1983), Timisoara, RS Romania · Zbl 0541.54062
[24] Radu, V., On the t-norms with the fixed point property, Sem. Teor. Prob. Apl., No. 72 (1984), Timisoara, RS Romania · Zbl 0567.60009
[25] Radu, V., On some fixed point theorems in probabilistic metric spaces, Sem. Teor. Prob. Apl., No. 74 (1984), Timisoara, RS Romania
[26] Schweizer, B.; Sklar, A., Statistical Metric Spaces, (North-Holland Series in Probability and Applied Mathematics, Vol. 5 (1983), North-Holland: North-Holland Amsterdam) · Zbl 0091.29801
[27] Schweizer, B.; Sklar, A.; Thorp, E., The metrization of statistical metric spaces, Pacific J. Math., 10, 673-675 (1960) · Zbl 0096.33203
[28] Sehgal, V.; Bharucha-Reid, A., Fixed points of contraction mappings on probabilistic metric spaces, Math. System Theory, 6, 97-102 (1972) · Zbl 0244.60004
[29] Sherstnev, A. N., The notion of random normed spaces, DAN USSR, 149, 2, 280-283 (1963) · Zbl 0127.34902
[30] Sherwood, H., Complete probabilistic metric spaces, Z. Wahrsch. Verw. Gebiete, 20, 117-128 (1971) · Zbl 0212.19304
[31] Chang, Shih-Sen, On some fixed point theorems in probabilistic metric spaces and its applications, Z. Wahrsch. Verw. Gebiete, 63, 463-474 (1983) · Zbl 0521.54033
[32] Chang, Shih-Sen, Fixed point theorems of mappings on probabilistic metric spaces with applications, Scientia Sinica Ser. A, 26, 11, 1144-1155 (1983) · Zbl 0515.54032
[33] Swierniak, A., A unified approach to controllers design for uncertain systems, Internat. J. Control, 37, 463-470 (1983) · Zbl 0516.93030
[34] Swierniak, A., The uncertain systems stabilization via fixed point theorem in Menger spaces, (Third International Conference Functional-Differential Systems and Related Topics III. Third International Conference Functional-Differential Systems and Related Topics III, Zielona Gora (1983), Math. Inst. Polish Acad. Sci., Inst. Autom. Techn. Univ. Warsaw, Inst. Math. Phys. Higher Coll. Eng: Math. Inst. Polish Acad. Sci., Inst. Autom. Techn. Univ. Warsaw, Inst. Math. Phys. Higher Coll. Eng Zielona Gora) · Zbl 0545.93048
[35] Tan, D. H., On probabilistic condensing mappings, Rev. Roum. Math. Pures Appl., 26, 10, 1305-1317 (1981) · Zbl 0494.47035
[36] Tan, D. H., On the probabilistic inner measure of noncompactness, Univ. u Novom Sadu Zb. Rad. Prir.-Mat. Fak. Ser. Mat., 13, 73-85 (1983) · Zbl 0571.47046
[37] Zadeh, L. A., Fuzzy sets, Inform and Control, 8, 338-353 (1965) · Zbl 0139.24606
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