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

Year 2017, Volume: 30 Issue: 1, 269 - 281, 14.03.2017

Abstract

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.

References

  • 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.
Year 2017, Volume: 30 Issue: 1, 269 - 281, 14.03.2017

Abstract

References

  • 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.
There are 111 citations in total.

Details

Journal Section Mathematics
Authors

Umesh Dongre This is me

R. D. Daheriya This is me

Manoj Ughade

Bhawna Parkhey This is me

Publication Date March 14, 2017
Published in Issue Year 2017 Volume: 30 Issue: 1

Cite

APA Dongre, U., Daheriya, R. D., Ughade, M., Parkhey, B. (2017). ON RANDOM COINCIDENCE & FIXED POINTS FOR A PAIR OF HYBRID MEASURABLE MAPPINGS. Gazi University Journal of Science, 30(1), 269-281.
AMA Dongre U, Daheriya RD, Ughade M, Parkhey B. ON RANDOM COINCIDENCE & FIXED POINTS FOR A PAIR OF HYBRID MEASURABLE MAPPINGS. Gazi University Journal of Science. March 2017;30(1):269-281.
Chicago Dongre, Umesh, R. D. Daheriya, Manoj Ughade, and Bhawna Parkhey. “ON RANDOM COINCIDENCE & FIXED POINTS FOR A PAIR OF HYBRID MEASURABLE MAPPINGS”. Gazi University Journal of Science 30, no. 1 (March 2017): 269-81.
EndNote Dongre U, Daheriya RD, Ughade M, Parkhey B (March 1, 2017) ON RANDOM COINCIDENCE & FIXED POINTS FOR A PAIR OF HYBRID MEASURABLE MAPPINGS. Gazi University Journal of Science 30 1 269–281.
IEEE U. Dongre, R. D. Daheriya, M. Ughade, and B. Parkhey, “ON RANDOM COINCIDENCE & FIXED POINTS FOR A PAIR OF HYBRID MEASURABLE MAPPINGS”, Gazi University Journal of Science, vol. 30, no. 1, pp. 269–281, 2017.
ISNAD Dongre, Umesh et al. “ON RANDOM COINCIDENCE & FIXED POINTS FOR A PAIR OF HYBRID MEASURABLE MAPPINGS”. Gazi University Journal of Science 30/1 (March 2017), 269-281.
JAMA Dongre U, Daheriya RD, Ughade M, Parkhey B. ON RANDOM COINCIDENCE & FIXED POINTS FOR A PAIR OF HYBRID MEASURABLE MAPPINGS. Gazi University Journal of Science. 2017;30:269–281.
MLA Dongre, Umesh et al. “ON RANDOM COINCIDENCE & FIXED POINTS FOR A PAIR OF HYBRID MEASURABLE MAPPINGS”. Gazi University Journal of Science, vol. 30, no. 1, 2017, pp. 269-81.
Vancouver Dongre U, Daheriya RD, Ughade M, Parkhey B. ON RANDOM COINCIDENCE & FIXED POINTS FOR A PAIR OF HYBRID MEASURABLE MAPPINGS. Gazi University Journal of Science. 2017;30(1):269-81.