ON RANDOM COINCIDENCE & FIXED POINTS FOR A PAIR OF HYBRID MEASURABLE MAPPINGS

Yıl 2017, Cilt: 30 Sayı: 1, 269 - 281, 14.03.2017

Umesh Dongre R. D. Daheriya Manoj Ughade , Bhawna Parkhey

Öz

In this paper,  we establish some random Coincidence point and random fixed point theorems for a pair of hybrid measurable mappings, which is generalizes and extends  many results in the literature.

Anahtar Kelimeler

Separable metric space, random Coincidence point, random fixed point, measurable mappings, non-expansive.

Kaynakça

• Bharucha-Ried, A.T., Fixed point theorem in
• probabilistic analysis, Bull. Amer. Math. Soc.,
• (1976), 641-645.
• Bogin, J., A generalization of a fixed point theo-
• rem og Gebel, Kirk and Shimi, Canad. Math.
• Bull., 19(1976), 7-12.
• Chandra, M., Mishra, S., Singh, S., Rhoades,
• B.E., Coincidence and fixed points of non-
• expansive type multi-valued and single-valued
• maps, Indian J. Pure Appl. Math.,26(5):393-
• ,1995.
• Chang, S.S., Huang, N.J., On the principle of
• randomization of fixed points for set valued
• mappings with applications, North-eastern
• Math. J., 7(1991), 486-491.
• Ciric, Lj. B., Non-expansive type mappings and
• a fixed point theorem in convex metric spaces,
• Rend. Accad. Naz. Sci. XL Mem. Mat., (5)
• vol.XIX (1995), 263-271.
• Ciric, Lj. B., On some mappings in metric
• spaces and fixed point theorems, Acad. Roy.
• Belg. Bull. Cl. Sci., (5) T.VI (1995), 81-89.[7] Ciric, Lj. B., On some non-expansive type
• mappings and fixed points, Indian J. Pure Appl.
• Math., 24(3), (1993), 145-149.
• Ciric, Lj. B., Ume, J.S., and Jesic, S.N, On
• random coincidence and fixed points for a pair
• of multi-valued and single-valued mappings, J.
• Ineq. Appl., Vol. 2006(2006), Article ID 81045,
• pages.
• Ciric Lj. B. and Ume J. S., Some common fixed
• point theorems for weakly compatible
• mappings, J. Math. Anal. Appl. 314 (2) (2006),
• -499.
• Gregus, M., A fixed point theorem in Banach
• spaces, Boll. Un. Mat. Ital..A, 5(1980), 193-198.
• Hans, O., Random operator equations, Proc. 4th
• Berkeley Symp. Mathematics Statistics and
• Probability, Vol. II, Part I, pp. 185-202. Univer-
• sity of California Press, Berkeley (1961).
• Hans, O., Reduzierende Zufallige transformati-
• onen, Czech. Math. J. 7(1957), 154-158.
• Himmelberg, C.J., Measurable relations. Fund.
• Math. 87(1975), 53-72.
• Huang, N.J., A principle of randomization of
• coincidence points with applications, Applied
• Math. Lett., 12(1999), 107-113.
• Itoh, S., A random fixed point theorem for
• multi-valued contraction mapping, Pacific J.
• Math., 68(1977), 85-90.
• Jhade, P.K., Saluja, A.S., On Random Coincid-
• ence & Fixed Points for a Pair of Multi-Valued
• & Single-Valued Mappings, Inter. J. Ana. and
• Appl., Vol.4, No.1 (2014), 26-35.
• Kubiak, T., Fixed point theorems for contractive
• type multi-valued mappings, Math. Japonica,
• (1985), 89-101.
• Kuratowski, K., Ryll-Nardzewski, C., A general
• theorem on selectors, Bull. Acad. Polon. Sci.
• Ser. Sci. Math. Astronom. Phys., 13(1965), 397-
• Liu, T.C., Random approximations and random
• fixed points for non-self maps, Proc. Amer.
• Math. Soc., 103(1988), 1129-1135.
• Papageorgiou, N. S., Random fixed point theo-
• rems for measurable multifunctions in Banach
• spaces, Proc. Amer. Math. Soc., 97(1986), 507-
• Papageorgiou, N.S., Random fixed point
• theorems for multifunctions, Math. Japonica,
• (1984), 93-106.
• Rhoades, B.E., A generalization of a fixed point
• theorem of Bogin, Math. Sem. Notes, 6(1987),
• -7.
• Rhoades, B.E., Singh, S.L., Kulshrestha, C.,
• Coincidence theorems for some multi-valued
• mappings, Internat. J. Math. Math. Sci.,
• (1984), 429-434.
• Rockafellar, R.T., Measurable dependence of
• convex sets and functions in parameters, J.
• Math. Anal. Appl.,28(1969), 4-25.
• Sehgal, V.M., Singh, S.P., On random
• approxima-tions and a random fixed point
• theorem for set valued mappings, Proc. Amer.
• Math. Soc., 95 (1985), 91-94.
• Shahzad, N. Latif, A., A random coincidence
• point theorem, J. Math. Anal. Appl., 245 (2000),
• -638.
• Shahzad, N., Hussain, N. Deterministic and
• random coincidence point results for - non
• expansive maps, J. Math. Anal. Appl., 323
• (2006), No. 2, 1038-1046.
• Singh, S.L. Mishra, S.N., On a Ljubomir Ciric's
• fixed point theorem for nonexpansive type maps
• with applications, Indian J. Pure Appl. Math.,
• (2002), no. 4, 531-542.
• Spacek, A., Zufallige Gleichungen, Czech Math.
• J., 5(1955), 462-466.
• Tan, K.K., Yuan, X.Z., Huang, N.J., Random
• fixed point theorems and approximations in
• cones, J. Math. Anal. Appl., 185(1994), 378-
• Wagner D. H., Survey of measurable selection
• theorems, SIAM, J, Control Optim., 15, (1977),
• -903.
• Hadzic, O., A random fixed point theorem for
• multi valued mappings of Ciric’s type. Mat.
• Vesnik 3 (16) (31) (1979), no. 4, 397–401.
• Kubiaczyk I., Some fixed point theorems,
• Demonstratio Math. 6 (1976), 507-515.
• Kubiak T., Fixed point theorems for contractive
• type multi-valued mappings, Math. Japonica, 30
• (1985), 89-101.
• Ray B. K., On Ciric’s fixed point theorem,
• Fund. Math. 94 (1977), 221-229.