A fixed point stability theorem for nonexpansive set valued mappings

Stability results for fixed point sets of α*- Ψ contractive multivalued mappings

“…The consideration of multivalued mappings provide us normally with a larger fixed point sets which sometimes have very interesting structures. Stability result of fixed point sets for multivalued mapping have appeared in a large number of papers [3,9,10,12,16]. Such stability was also discussed in the paper of Nadler [13,14].…”

Stability of Fixed Point Sets of a Class of Multivalued Nonlinear Contractions

“…The limiting behaviors of sequences of mappings have been considered in a number of papers in recent time as, for instances, in [3][4][5] the chaotic behavior under uniform convergence is investigated. Particularly, stability of fixed point sets has been considered in [6][7][8][9][10].…”

Continuous Dependence of Fixed Points on Parameters and Initial Conditions

“…The theorem regarding the continuity of fixed points of contraction mappings was proved by [3]. Subsequently [9] obtained results concerning sequence of contraction mappings and also gave an application suggested by [7], [8], [9] established conditions implying the strong convergence of the fixed points of a sequence of set-valued contractions. A similar result concerning the weak convergence of the fixed points of the set-valued non-expansive mappings in a Banach space was obtained by [7] who used it to obtain a stability result for generalized differential equations.…”