Abstract
In this paper, we establish common fixed point theorems in an ordered complete metric space using distance functions. Our main result, improves and extends the results of Yan et al. (Fixed Point Theory Appl. 2012, Article id: 152, 2012) and some other existing results announced in the literature. As applications, we discuss some fixed point theorems for contraction of integral type and some existence theorem for solution of integral equation, and for solution of first and second order ordinary differential equations with periodic boundary conditions.
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We wish to confirm that there has been no significant financial support for this work that could have influenced its outcome and the authors declare that they have no conflict of interest.
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Gupta, V., Shatanawi, W. & Mani, N. Fixed point theorems for \((\psi , \beta )\)-Geraghty contraction type maps in ordered metric spaces and some applications to integral and ordinary differential equations. J. Fixed Point Theory Appl. 19, 1251–1267 (2017). https://doi.org/10.1007/s11784-016-0303-2
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DOI: https://doi.org/10.1007/s11784-016-0303-2