The purpose of this note is to present some fixed point and data dependence theorems in complete gauge spaces and in hyperconvex metric spaces for the so-called Meir-Keeler multivalued operators and admissible multivalued aα-contractions. Our results extend and generalize several theorems of Espínola and Kirk [R. Espínola, W.A. Kirk, Set-valued contractions and fixed points, Nonlinear Anal. 54 (2003) 485-494] and Rus, Petruşel, and Sîntamarian [I.A. Rus, A. Petruşel, A. Sîntamarian, Data dependence of the fixed point set of some multivalued weakly Picard operators, Nonlinear Anal. 52 (2003) 1947-1959]. © 2004 Elsevier Inc. All rights reserved.
Espínola, R., & Petruşel, A. (2005). Existence and data dependence of fixed points for multivalued operators on gauge spaces. Journal of Mathematical Analysis and Applications, 309(2), 420–432. https://doi.org/10.1016/j.jmaa.2004.07.006