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Positivity

pp 1–11 | Cite as

New fixed point results for E-metric spaces

  • Nayyar Mehmood
  • Ahmed Al Rawashdeh
  • Stojan RadenovićEmail author
Article

Abstract

A new convergence criteria using the concept of semi-interior points has been defined in E-metric spaces with non-solid and non-normal set of positive elements \(E^{+}\) of a real normed space E, also known as a positive cone. Many examples are provided to insure the existence of semi-interior points of \(E^{+}\) with empty interior. New generalizations of Banach, Kannan and Chatterjea fixed point theorems are proved.

Keywords

Semi-interior points Non-solid cones Fixed points e-Convergence 

Mathematics Subject Classification

Primary 46S40 47H10 54H25 

Notes

Acknowledgements

Authors are thankful to the reviewers, and Professor I. Polyrakis, (School of Applied Mathematics and Physical Sciences, Department of Mathematics, National Technical University of Athens, Greece), for their comments and suggestions to improve the quality of this paper. The second author gratefully acknowledges with thanks the Department of Research Affairs at UAEU. This article is supported by the grant: UPAR(11) 2016, Fund No. 31S249(COS). The paper has been prepared during the first named author visit as a post doc researcher to the Department of Mathematical Sciences in UAEU, and would like to thank the Department of Mathematical Sciences, UAEU for their support. Also the Department of Mathematics and Statistics International Islamic University, H-10, Islamabad, Pakistan for their cooperation.

Funding

Funding was provided by National Institute on Aging (Grant No. 877690054).

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Nayyar Mehmood
    • 1
    • 2
  • Ahmed Al Rawashdeh
    • 2
  • Stojan Radenović
    • 3
    Email author
  1. 1.Department of Mathematics and StatisticsInternational Islamic UniversityIslamabadPakistan
  2. 2.Department of Mathematical Sciences, College of ScienceUAE UniversityAl AinUAE
  3. 3.Department of Mathematics, College of ScienceKing Saud UniversityRiyadhSaudi Arabia

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