Fixed point theorems for generalized multivalued nonlinear \(\mathcal{F}\)contractions

In this paper, we introduce certain new concepts of \(\alpha\eta\)lower semicontinuous and \(\alpha\eta\)upper semi continuous mappings. By using these concepts, we prove some fixed point results for generalized multivalued nonlinear \(\mathcal{F}\)contractions in metric spaces and ordered metric spaces. As an application of our results we deduce SuzukiWardowski type fixed point results and fixed point results for orbitally lower semicontinuous 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),241248], Altun et al. [I. Altun, G. Minak, M. Olgun, Nonlinear Anal. Model. Control, 21 (2016), 201210] and Olgun et al. [M. Olgun, G. Minak, I. Altun, J. Nonlinear Convex Anal., 17 (2016), 579587].