COINCIDENCE POINT THEOREMS IN PROBABILISTIC METRIC SPACES WITH A CONVEX STRUCTURES

Abstract

Abstract: In this paper we draw some coincidence and common fixed point theorems for nonlinear hybrid contraction mappings on probabilistic metric spaces with a convex structure.

Key words: free-surface wave, viscous wake, viscosity, submergence depth, Oseenlet, Lighthill’s two-stage scheme, asymptotic solution, probabilistic metric spaces, a convex structure, commuting mappings, coincidence and common fixed points

Wee Tae Park;Keun Saeng Park;Yeol Je Cho;Jong Kyu Kim. COINCIDENCE POINT THEOREMS IN PROBABILISTIC METRIC SPACES WITH A CONVEX STRUCTURES. Applied Mathematics and Mechanics (English Edition), 1994, 15(8): 721-733.

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[1] Bharucha-Reid, A. T, Fixed point theorems in probabilistic analysis, Bull. Amer. Math.Sot., 82 (1976), 641-657.
[2] Bocsan, Gh. and Gh. Constantin, The Kuratowski function and some application to probabilistic metric spaces, Atti Acad. Naz. Lincei, 55 (1973), 235-240.
[3] Bocsan, Gh., On some fixed point theorems in probabilistic metric spaces, Math.Balkanica 4 (1974), 67-70.
[4] Cain. G. L., Jr. and R. H. Kasricl, Fixed and periodic points of local contraction mappings on probabilistic metric spaces, Math. Systems Theory, 9 (1976), 289-297.
[5] Chang, S. S., Fixed point theorem of mappings on probabilistic metric spaces with application, Scinetia Sinica (Series A), 26 (1983), 1144-1155.
[6] Ciric, kj. B., On fixed points of generalized contraction on probabilistic metric spaces,Puhl. Inst. Moth. (Beograd) (N. S.), 18, 32 (1975), 71-78.
[7] Ding Xie-ping, Common fixed points for non-expansive type mappings in convex and probabilistic convex metric spaces, Review of Research, Faculty of Science, Mathematics Series, Univ. of Novi Sad, 16, 1 (1986), 73-84.
[8] Egbert, R. J., Products and quotients of probabilistic metric spaces, pacific J. Math., 24(1968), 437-455.
[9] Hadzic, O.and M. Budincevic, A class of T-norm in the fixed point theory on probabilistic metric spaces, Zb. rad. Prir.-mat. fak., Univ. of Novi Sad, 9 (1979), 37-41
[10] A fixed point theorem in probabilistic locally convex spaces, Rev. Roum.Appl., 23 (1978), 735-744.
[11] Hadzic, O., On common fixed points in metric and probabilistic metric spaces with convex structures, Zb. rad., Prir.-mat. fak., Univ. of Novi Sad, 14 (1980), 13-24.
[12] Hadzic, O., Some fixed point and almost fixed point theorems for multi-valued mapping sin topological vector' space, Nonlinear Analysis, Theory, Methods and Applications, 5 (1981), 1009-1019.
[13] Hadzic, O., Some theorems on the fixed points in probabilistic metric and random normed spaces, Boll. Un. Mat. Ital. B, 18, 5 (1981), I-11.
[14] Hadzic, O., On coincidence points in metric and probabilistic metric spaces with a convex structure, Zb. rad., Prir.-mat. fak., Unvi Sad, 15, 1 (1985), 11-22.
[15] Hadzic, O., Fixed point theorems for multi-valued mappings in probabilistic metric spaces with a convex structure, Zb. rad., Prir.-mat. fak., Univ. of Novi Sad, 17, 1(1987), 39-51.
[16] Istratescu, V. I. and I. Saeuiu, Fixed point theorems for contraction mappings on probabilistic metric spaces, Rev. Roumaine Math. Pures Appl., 18 (1973), 1375-1380.
[17] Itoh, S. and W. Takahashi, Single-valued mappings multi-valued mappings and fixed point theorems, J. Math. Anal. Appl., 59 (1977), 514-521.
[18] Machado, H.,V., A characterization of convex subsets of normed spaces, Kodai Math.Sem. Rep., 25 (1973), 307-220.
[19] Menger, K., Statistical metric, Proc, Nat. Acad. Sci. USA, 28 (1942), 535-537.
[20] Naimpally, S. A., K. k. Singh and J. H. M. Whitfield, Common fixed points for nonexpansive and asymptotically nonexpansive mappings, Comm. Math. Univ.Corolinae, 24, 2 (1983), 287-300.
Radu, V., On the t-norms of Hadzic type. and fixed points in probabilistic metric spaces, Sere. Teoria Prob. Apl., Timisoara, 66 (1983).
[22] Radu, V., On the t-norms of Hadzic type and locally convex random normal spaces,Sere. Teoria Probl. Apl., Timisoara, 70 (1984).
[23] Radu, V., On some fixed points theorems in probabilistic metric spaces,Sem. Teoria Prob. Apl., Timisoara, 74 (1985).
[24] Rhoades, B. E., K. L. Singh and J. H. M. Whitfield, Fixed points for generalized nonexpans]ve mappings, Comment. Math. Unit,. Carolinae, 23, 3 (1982), 443-4511
[25] Schweizer, B. and A Sklar, Statistical metric spaces, Pacific J. Math., 10 (1960), 313-334.
[26] Schweizer. B., A Sklar and E. Thorp, The metrization of statistical metric spaces,Pacific J. Math., 10 (1960), 673-675.
[27] Schweizer, B. and A. Sklar, Probabilistic metric spaces, Noth-Holland Series. in Probability and Applied Mathematics, 5 (1983).
[28] Sherwood, H., Complete probabilistic metric spaces 2, Wahrsch. Verw Gebiete, 29,(1971), 117-128.
[29] Singh, S. L. and B. D. Pant, Coincidence and fixed point theorems for a family of mappings on Menger spaces and extension to uniform spaces, Math. Japon, 33, 6(1988), 957-973.
[30] Stojakovic, M., Common fixed point theorems in complete metric and probabilistic metric spaces, Bull. Austral. Math. Soc., 36 (1987), 73-88.
[31] Takanashi, W., Fixed point theorems for amenable semigroup of nonexpansive mappings, Kodai Math. Sem. Rep., 21 (1969), 383-386.
[32] Takahashi, W., A convexity in metric space and nonexpansive mappings I., Kodai\Math. Sem. Rep., 22 (1970), 142-139.
[33] Tallman, L. A., Fixed points for condensing multi-functions ifi metric spaces with convex structures, Kodai Math. Sere. Rep., 29 (1977), 62-70.
[34] Tan, D. H., On probabilistic densifying mappings, Rev. Roumaine Math. Pures Appl., 26(1981), 1305-1217.
[35] Tan, N. X., Generalized probabilistic metric spaces and fixed point theorems, Math.Nachr., 129 (1986). 205-218.
[36] Zeidler, E., Vorlesungen fiber nichtlineare Funktionalanalysis I., Fixepunkts~.tze, Teubner-Texte zur Mathematik (1976)

COINCIDENCE POINT THEOREMS IN PROBABILISTIC METRIC SPACES WITH A CONVEX STRUCTURES

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