Fixed point theorems for generalized multivalued nonlinear \(\mathcal{F}\)-contractions
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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].
Share and Cite
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
Keywords
- \(\alpha-\eta-\mathcal{GF}\)-contraction
- \(\alpha-\eta-\mathcal{F}\)-contraction of Hardy-Rogers type
- nonlinear \(\mathcal{F}\)-contraction.
MSC
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