Some Fixed Point Theorems for Countably Condensing

Abdul-Majeed Al-izeri; Ahmed Al-Haysah

doi:doi:10.11648/j.ijtam.20230902.11

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Some Fixed Point Theorems for Countably Condensing

Abdul-Majeed Al-izeri, Ahmed Al-Haysah

Published in International Journal of Theoretical and Applied Mathematics (Volume 9, Issue 2)

Received: 25 July 2023 Accepted: 11 September 2023 Published: 24 September 2023

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Abstract

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.

Published in	International Journal of Theoretical and Applied Mathematics (Volume 9, Issue 2)
DOI	10.11648/j.ijtam.20230902.11
Page(s)	10-13
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

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

References

[1]	MY, Abdallah, A. Al-Izeri & K. Latrach (2021). Some remarks on fixed sets for perturbed multivalued mappings. J. Fixed Point Theory Appl. 23 (3), Paper No. 38, 14 pp.
[2]	A. Al-Izeri & K. Latrach. (2023). A note on fixed point theory for multivalued mappings. Fixed Point Theory 24 (1): 233-239
[3]	A. Al-Izeri & K. Latrach. Krasnosel’skii-type fixed point results for weakly sequentially upper semicontinuous multivalued mappings. Journal of Mathematics and Applications (to appear).
[4]	R. P. Agarwal, W. Hussain & M. A. Taoudi. (2012). Fixed point theorems inAB ordered Banach spaces and applications to nonlinear integral equations. Abstr. Appl. Anal.Art. ID 245872, 15 pp.
[5]	R. P. Agarwal, D. O’Regan & M. A. Taoudi. (2010). Browder-Krasnoleskii-Type Fixed point theorems in Banach spaces. Fixed Point Theory Appl. 243716, 20 pp.
[6]	CD. Aliprantis & K. C. Border. (1985). Infinite dimensional analysis. Springer-Verlag, Berlin Heidelberg. New York.
[7]	J. Bana´ s & J. Rivero. (1988). On measures of weak noncompactness. Ann. Mat. Pura Appl. 151 (4): 213- 224.
[8]	G. Cai & S. Bu. (2013). Krasnosel’skii-type fixed point theorems with applications to Hammerstein integral equations in L¹-spaces. Math. Nachr. 14-15: 1452-1465.
[9]	K. Floret. (1980). Weakly compact sets. Springer-Verlag, Berlin, Heidelberg, New York.
[10]	J. Garcia-Falset. (1971). Existence of fixed points and measure of weak noncompactness. Nonlinear Anal. 71: 2625-2633.
[11]	JR. Graef, J. Henderson & A. Ouahab. (2017). Multivalued versions of a Krasnosel’skii-type fixed point theorem. J. Fixed Point Theory Appl. 19: 1059-1082.
[12]	Himmelberg CJ. (1972). Fixed points of compact multifunctions. J. Math. Anal. Appl. 38: 205-207.
[13]	Y. Liu & Z. Li. (2006). Schaefer type theorem and periodic solutions of evolution equations. J. Math. Anal. Appl. 316: 237-255.
[14]	K. Latrach, MA. Taoudi & A. Zeghal. (2006) Some fixed point theorems of the Schauder and the Krasnosel’skii type and application to nonlinear transport equations. J. Differential Equations. 221 (1): 256-271.
[15]	EA. Ok. (2009). Fixed set theorems of Krasnoselskii type. Proc. Amer. Math. Soc. 137: 511-518.
[16]	D. O’Regan. (2000). Fixed point theory of Mönch type forweaklysequentiallyuppersemicontinuousmaps. Bull. Austral. Math. Soc. 61 (3): 439-449.
[17]	D. O’Regan. (1998). Fixed point theory for weakly contractive maps with applications to operator inclusions in Banach spaces relative to the weak topology. Z. Anal. Anwend. 17 (2): 281-296.
[18]	D. O’Regan. (2000). Fixed point theorems for weakly sequentially closed maps. Arch. Math. (Brno). 36 (1): 61-70.
[19]	W. Rudin. (1973). Functional analysis McGraw Hill. New York.
[20]	P. Somyot & T. Thammathiwat. (2013). Fixed point theorems of Krasnosel’skii type for the sum of two multivalued mappings in Banach spaces. J. Nonlinear Convex Anal. 14: 183-191.
[21]	F. Wang. (2013). Fixed point theorems for the sum of two operators under ω-condensing. Fixed point theory and applications. 102: 1-13.

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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

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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

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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

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@article{10.11648/j.ijtam.20230902.11,
  author = {Abdul-Majeed Al-izeri and Ahmed Al-Haysah},
  title = {Some Fixed Point Theorems for Countably Condensing},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {9},
  number = {2},
  pages = {10-13},
  doi = {10.11648/j.ijtam.20230902.11},
  url = {https://doi.org/10.11648/j.ijtam.20230902.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20230902.11},
  abstract = {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.},
 year = {2023}
}

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TY  - JOUR
T1  - Some Fixed Point Theorems for Countably Condensing
AU  - Abdul-Majeed Al-izeri
AU  - Ahmed Al-Haysah
Y1  - 2023/09/24
PY  - 2023
N1  - https://doi.org/10.11648/j.ijtam.20230902.11
DO  - 10.11648/j.ijtam.20230902.11
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 10
EP  - 13
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20230902.11
AB  - 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.
VL  - 9
IS  - 2
ER  -

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Author Information

Abdul-Majeed Al-izeri

Departement Mathematics (CNRS, LMBP), Clermont Auvergne University, Clermont-Ferrand, France
Ahmed Al-Haysah

Departement Mathematics, Albaydha University, Albaydha, Yemen

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Plain Text BibTeX RIS

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

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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

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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

Copy | Download

@article{10.11648/j.ijtam.20230902.11,
  author = {Abdul-Majeed Al-izeri and Ahmed Al-Haysah},
  title = {Some Fixed Point Theorems for Countably Condensing},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {9},
  number = {2},
  pages = {10-13},
  doi = {10.11648/j.ijtam.20230902.11},
  url = {https://doi.org/10.11648/j.ijtam.20230902.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20230902.11},
  abstract = {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.},
 year = {2023}
}

Copy | Download

TY  - JOUR
T1  - Some Fixed Point Theorems for Countably Condensing
AU  - Abdul-Majeed Al-izeri
AU  - Ahmed Al-Haysah
Y1  - 2023/09/24
PY  - 2023
N1  - https://doi.org/10.11648/j.ijtam.20230902.11
DO  - 10.11648/j.ijtam.20230902.11
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 10
EP  - 13
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20230902.11
AB  - 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.
VL  - 9
IS  - 2
ER  -

Copy | Download