Some fixed point results via measure of noncompactness
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Authors
Chi-Ming Chen
- Institute for Computational and Modeling Science, National Tsing Hua University, Taiwan.
Erdal Karapinar
- Department of Mathematics, Atılım University, 06586 Incek, Ankara, Turkey.
- Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, King Abdulaziz University, 21589, Jeddah, Saudi Arabia.
Abstract
In this paper, by using the measure of noncompactness and Meir-Keeler type mappings, we prove some new fixed point
theorems for some certain mappings, namely, the weaker \(\varphi\)-Meir-Keeler type contractions, asymptotic weaker \(\varphi\)-Meir-Keeler
type contractions, asymptotic sequence \(\{\phi_i\}\)-Meir-Keeler type contraction, \(\xi\)-generalized comparison type contraction, and R-
functional type \(\psi\)-contractions. Our results improve and hence cover the well-known Darbo’s fixed point theorem, and several
related recent fixed point results.
Share and Cite
ISRP Style
Chi-Ming Chen, Erdal Karapinar, Some fixed point results via measure of noncompactness, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 7, 4015--4024
AMA Style
Chen Chi-Ming, Karapinar Erdal, Some fixed point results via measure of noncompactness. J. Nonlinear Sci. Appl. (2017); 10(7):4015--4024
Chicago/Turabian Style
Chen, Chi-Ming, Karapinar, Erdal. "Some fixed point results via measure of noncompactness." Journal of Nonlinear Sciences and Applications, 10, no. 7 (2017): 4015--4024
Keywords
- Measure of noncompactness
- Meir-Keeler-type set contraction
- fixed points.
MSC
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