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Fixed Points of Monotone Mappings via Generalized-Measure of Noncompactness

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Abstract

In this article, the notions of partially continuous mappings, partially bounded, partially compact and partially closed sets of an ordered E-metric space are defined. These notions are used to introduce partial E-measure of noncompactness and prove the fixed point results of monotone mappings and sum of two monotone mappings. In this way we generalize many results including the well known results of Schauder, Darbo and Krasnoselskii, in the settings of ordered E-metric and ordered Banach spaces. We also provide nontrivial examples and existence results for a class of integral equations to validate the significance of our theory and results.

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Acknowledgements

The first author gratefully acknowledges with thanks the Department of Research Affairs at UAEU. This article is supported by the grant: UPAR-2019, Fund No. 31S397.

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Authors and Affiliations

  1. Department of Mathematical Sciences, College of Science, UAE University, 15551, Al Ain, UAE

    Niaz Ahmad

  2. Department of Mathematics and Statistics, International Islamic University, H-10, Islamabad, Pakistan

    Ahmed Al-Rawashdeh & Nayyar Mehmood

  3. Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120, Beograd 35, Serbia

    Stojan Radenović

Authors
  1. Niaz Ahmad
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  2. Ahmed Al-Rawashdeh
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  3. Nayyar Mehmood
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  4. Stojan Radenović
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Correspondence to Nayyar Mehmood.

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Ahmad, N., Al-Rawashdeh, A., Mehmood, N. et al. Fixed Points of Monotone Mappings via Generalized-Measure of Noncompactness. Vietnam J. Math. 50, 275–285 (2022). https://doi.org/10.1007/s10013-021-00498-4

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  • DOI: https://doi.org/10.1007/s10013-021-00498-4

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