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Improvement of fixed point theorems for Hardy–Rogers contraction type in b-metric spaces without F-contraction assumption

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Abstract

Fixed point results are established in the generalized b-metric spaces under the condition of contraction of Hardy–Rogers type which improve, extend or represent an alternative to several theorems obtained in metric spaces or in b-metric spaces. Those results are established using weaker assumptions and without assuming the notions of F-contraction, F-weak contraction and extended F-contraction. Moreover, the estimate of the order of convergence is obtained, for the first time, under the general Hardy–Rogers contraction condition in the setting of b-metric spaces. Several examples illustrate that the obtained results are quite flexible and tractable in applications. As an application of our results, we establish the existence and uniqueness of solutions for some dynamic programming functional equation and integral equation.

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Acknowledgements

The authors are very grateful to the reviewers for their careful check of details, useful suggestions and valuables comments.

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  1. Radhowane Chaib, Fayçel Merghadi and Zahir Mouhoubi are contributed equally to this work.

Authors and Affiliations

  1. Laboratory of Mathematics, Informatics and Systems (LAMIS), Echahid Cheikh Larbi Tebessi University-Tebessa, Route de constantine, 12002, Tebessa, Algeria

    Radhowane Chaib & Fayçel Merghadi

  2. Department of Mathematics, Édouard-Montpetit College, Longueuil, Canada

    Zahir Mouhoubi

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  1. Radhowane Chaib
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  2. Fayçel Merghadi
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Chaib, R., Merghadi, F. & Mouhoubi, Z. Improvement of fixed point theorems for Hardy–Rogers contraction type in b-metric spaces without F-contraction assumption. Rend. Circ. Mat. Palermo, II. Ser 72, 4209–4237 (2023). https://doi.org/10.1007/s12215-023-00892-6

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