Multi-valued \'Ciri\'c contractions on metric spaces with applications

Abstract

In this paper, using the concept of w-distance, we obtain fixed
point results for multi-valued generalized w-contractive maps
not involving the extended Hausdorf metric. Presented theorems are generalizations of recent fixed point theorems due to L.B.\'{C}iri\'{c} [Nonlinear Analysis 71 (2009), 2716-2723], D. Klim and D. Wardowski [ J. Math. Anal. Appl. 334 (2007), 132-139], Y. Feng and S. Liu [J. Math. Anal. Appl. 317 (2006), 103-112], Latif and Abdou [Nonlinear Analysis 74 (2011), 1436-1444 and Fixed Point Theory and Appl., Volume 2009 (2009) Article ID 487161, 8 pp.] and several others. As an application of our results we establish common fixed point results for newly defined class of Banach operator pairs.