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

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

Keywords


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

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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.