On Edelstein Type Multivalued Random Operators

Abstract

The purpose of this paper is to provide stochastic versions of severalresults on fixed point theorems in the literature.

Keywords

• Common fixed point, Multivalued mappings, Random operator, Metricspace2000 AMS Classification:47H09, 47H10, 47H40, 54H25, 60H25

On Edelstein Type Multivalued Random Operators

Abstract

-

Keywords

• -

References

1. Assad N. A. and Kirk, W. A. Fixed point theorems for set-valued mappings of contractive type, Pacific J. Math., 43, 553–562, 1972.
2. Azam A. and Arshad, M. Fixed points of sequence of locally contractive multivalued maps, Comp. Math Appl., 57, 96–100, 2008.
3. Beg, I. and Abbas, M. Iterative procedure for solution of random operator equations in Banach spaces, J. Math. Anal. Appl., 315 (1), 181–201, 2006.
4. Beg, I. and Abbas, M. Random fixed point theorems for a random operator on an unbounded subset of a Banach space, Appl. Math. Lett., 21, 1001–1004, 2008.
5. Bharucha-Reid, A. T. Fixed point theorems in probabilistic analysis, Bull. Amer. Math. Soc., 82, 641–657, 1976.
6. Castaing, C. and Valadier, M. Convex analysis and measurable multifunctions, Lecture Notes in Math., 580, Springer-Verlag, Berlin, 1977.
7. Ding, X. P. Criteria for the existence of solutions to random integral and differential equations, Appl. Math. Mech., 6, 269–275, 1985.
8. Fierro, R., Martinez, C. and Morales, C. H. Fixed point theorems for random lower semicontinuous mappings, Fixed Point Theory Appl., 2009, 7 pages, 2009. Himmelberg, C. J. Measurable relations, Fund. Math., 87, 53–72, 1975. Itoh, S. Random fixed point theorems with an application to random differential equations in Banach spaces, J. Math. Anal. Appl., 67, 261–273, 1979.

9. Itoh, S. A random fixed point theorem for a multivalued contraction mapping, Pacific J. Math., 68, 85–90, 1977.
10. Kuratowski, K. and Ryll-Nardzewski, C. A general theorem on selectors, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys., 13, 397–403, 1965.
11. Shahzad, N. Random fixed points of multivalued maps in Fr´ echet spaces, Arch. Math. (Brno), 38, 95–100, 2002.
12. Shahzad, N. and Hussain, N. Deterministic and random coincidence results for fnonexpansive maps, J. Math. Anal. Appl., 323, 1038–1046, 2006.
13. Shatanawi, W. and Mustafa, Z. On coupled random fixed point results in partially ordered metric spaces, Matematicki Vesnik, 64 (2), 139–146, 2012.