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


Authors

Iram Iqbal - Department of Mathematics, University of Sargodha, Sargodha, Pakistan. Nawab Hussain - Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia.


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 \(\mathcal{F}\)-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].


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ISRP Style

Iram Iqbal, Nawab Hussain, Fixed point theorems for generalized multivalued nonlinear \(\mathcal{F}\)-contractions, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 11, 5870--5893

AMA Style

Iqbal Iram, Hussain Nawab, Fixed point theorems for generalized multivalued nonlinear \(\mathcal{F}\)-contractions. J. Nonlinear Sci. Appl. (2016); 9(11):5870--5893

Chicago/Turabian Style

Iqbal, Iram, Hussain, Nawab. "Fixed point theorems for generalized multivalued nonlinear \(\mathcal{F}\)-contractions." Journal of Nonlinear Sciences and Applications, 9, no. 11 (2016): 5870--5893


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