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Fixed Points of Monotone Mappings via Generalized-Measure of Noncompactness

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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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

Keywords

  • E-metric space
  • Partially continuous
  • Partially compact
  • Partially bounded
  • Partially closed
  • Fixed points
  • Sum of monotone mappings

Mathematics Subject Classification (2010)

  • Primary 46S40
  • 47H10
  • 54H25