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New fixed point theorems for the sum of two mixed monotone operators of Meir–Keeler type and their applications to nonlinear elastic beam equations

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Abstract

In this paper, we present a new fixed point theorem for the sum of two mixed monotone operators of Meir–Keeler type on ordered Banach spaces through projective metric, which extends the existing corresponding results. As applications, we utilize the results obtained in this paper to study the existence and uniqueness of positive solutions for nonlinear singular fourth-order elastic beam equations with nonlinear boundary conditions.

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Acknowledgements

The authors would like to thank the referee for his/her very important comments that improved the results and the quality of the paper. The authors were supported financially by the National Natural Science Foundation of China (11871302).

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Authors and Affiliations

  1. School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, Shandong, People’s Republic of China

    Xinqiu Zhang & Lishan Liu

  2. Department of Mathematics and Statistics, Curtin University, Perth, WA, 6845, Australia

    Yonghong Wu

Authors
  1. Xinqiu Zhang
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  2. Lishan Liu
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  3. Yonghong Wu
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Correspondence to Lishan Liu.

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Zhang, X., Liu, L. & Wu, Y. New fixed point theorems for the sum of two mixed monotone operators of Meir–Keeler type and their applications to nonlinear elastic beam equations. J. Fixed Point Theory Appl. 23, 1 (2021). https://doi.org/10.1007/s11784-020-00835-z

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  • DOI: https://doi.org/10.1007/s11784-020-00835-z

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