Some fixed point results via measure of noncompactness

Volume 10, Issue 7, pp 4015--4024 http://dx.doi.org/10.22436/jnsa.010.07.50

Publication Date: July 27, 2017 Submission Date: March 02, 2017

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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.

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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

54H25
47H10

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