Random Fixed Point Theorems for Multivalued Subsequentially Limit-Contractive Maps Satisfying Inwardness Conditions
Let (Omega, Sigma) be a measurable space, with Sigma a sigma-algebra of subset of Omega, and let C be a nonempty bounded closed convex and separable subset of a Banach space X, satisfying property (D), KC(X) the family of all compact convex subsets of X. We prove that a continuous 1-x contractive mutivalued subsequentially limit-contractive map from C into KC(X) satisfying an inwardness condition has a random fixed point. Our work also extends and improves stochastic version of the results of Shahzad and Lone [Fixed point of multimaps which are not necessarily nonexpansive, Fixed Point Theory Applications, 2 (2005), 169-176] and connected with Khan and Domlo, [Random fixed points of multivalited inward random operators, journal of Applied Mathematics and Stochastic Analysis, Volume 2006 (2006), Article ID 19428, 8 pages], Plubtieng and Kumam [Random fixed point theorems for multivalued nonexpansive non-selfrandom operators, Journal of Applied Mathematics and Stochastic Analysis, 2006 (2006), Article ID 43796, 9 pages).
random fixed point inwardness condition multivalued mappings dominguez-lorenzo condition sl maps