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Some fixed point results in b-metric spaces approach to the existence of a solution to nonlinear integral equations

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Abstract

The purpose of this paper is to improve some recent fixed point results from Refs. Parvaneh et al. (Sahand Commun Math Anal 7(1):85–104, 2017), Paunović et al. (J Nonlinear Sci Appl 10(8):4162–4174, 2017) and Faraji and Nourouzi (Sahand Commun Math Anal 7(1):49–62, 2017) in the context of b-metric spaces. The techniques used in our proofs are quite different and most remarkably some of the proofs become simpler and more straightforward. Some examples are used to show that the improvements are indeed genuine. In addition, by using our results, we obtain the existence and uniqueness of a solution to a class of nonlinear integral equations. Furthermore, we provide the precise mathematical expression of the solution.

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Acknowledgements

The authors thank the editor and the referees for their valuable comments and suggestions which improved greatly the quality of this paper. The first author is thankful to the Science and Technology Research Project of the Education Department in Hubei Province of China (No. Q20172505). The second author is thankful to the Ministry of Education, Sciences and Technological Development of Serbia (No. MNTRRS-174009) and the Provincial Secretariat for higher education and scientific research in the Province of Vojvodina of Serbia (No. 142-451-2838/2017-01).

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Authors and Affiliations

  1. School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing Normal University, Beijing, 100875, China

    Huaping Huang

  2. Faculty of Technology, University of Novi Sad, Bulevar cara Lazara 1, Novi Sad, Serbia

    Tatjana Došenović

  3. Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11 120, Beograd 35, Serbia

    Stojan Radenović

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  1. Huaping Huang
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  2. Tatjana Došenović
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  3. Stojan Radenović
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Correspondence to Huaping Huang.

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Huang, H., Došenović, T. & Radenović, S. Some fixed point results in b-metric spaces approach to the existence of a solution to nonlinear integral equations. J. Fixed Point Theory Appl. 20, 105 (2018). https://doi.org/10.1007/s11784-018-0577-7

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  • DOI: https://doi.org/10.1007/s11784-018-0577-7

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