Abstract
In this paper, we introduce certain new concepts of alpha-eta-lower semi-continuous and alpha-eta-upper semi continuous mappings. By using these concepts, we prove some fixed point results for generalized multivalued nonlinear F-contractions in metric spaces and ordered metric spaces. As an application of our results we deduce Suzuki-Wardowski type fixed point results and fixed point results for orbitally lower semi-continuous mappings in complete metric spaces. Our results generalize and extend many recent fixed point theorems including the main results of Minak et al. [G. Minak, M. Olgun, I. Altun, Carpathian J. Math., 31 (2015), 241-248], Altun et al. [I. Altun, G. Minak, M. Olgun, Nonlinear Anal. Model. Control, 21 (2016), 201-210] and Olgun et al. [M. Olgun, G. Minak, I. Altun, J. Nonlinear Convex Anal., 17 (2016), 579-587]. (C) 2016 All rights reserved.