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Some Fixed Point Theorems for Countably Condensing

Our aim in this article is to establish the principles results of a fixed point theorems for multivalued mappings of Krasnoselskii type setting in general classes Mönch’s type. We seek to do that, we introduce and recall some theorems to aid our study. The beginning of this work has been introduced some properties of the measure of weak noncompactness under the weak topology and the definitions of countably condensing operators. We have shown that the operator H(S) is relatively weakly compact by using some properties of weak topology. We investigate that all hypotheses guarantee that the operator (B + H)(S) is relatively weakly compact and than simply to apply Himmelberg’s theorem in Banach spaces. We extended two fixed point theorems for weakly sequentially upper semicontinuous mappings subjected the perturbation map satisfies the Mönch’s type and we obtain our results in the second theorem with a less restrictive hypothesis. Using abstract measures of weak noncompactness, these results are applied to derive some fixed point theorems for a weakly sequentially upper semicontinuous countably µ-condensing multivalued mappins.

Fixed Point Theorems, Weakly Sequentially Continuous Multivalued Maps, Measure of Noncompactness, Countably µ-condensing Perturbation

APA Style

Abdul-Majeed Al-izeri, Ahmed Al-Haysah. (2023). Some Fixed Point Theorems for Countably Condensing. International Journal of Theoretical and Applied Mathematics, 9(2), 10-13. https://doi.org/10.11648/j.ijtam.20230902.11

ACS Style

Abdul-Majeed Al-izeri; Ahmed Al-Haysah. Some Fixed Point Theorems for Countably Condensing. Int. J. Theor. Appl. Math. 2023, 9(2), 10-13. doi: 10.11648/j.ijtam.20230902.11

AMA Style

Abdul-Majeed Al-izeri, Ahmed Al-Haysah. Some Fixed Point Theorems for Countably Condensing. Int J Theor Appl Math. 2023;9(2):10-13. doi: 10.11648/j.ijtam.20230902.11

Copyright © 2023 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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