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Fixed point theorems for asymptotically regular semigroups equipped with generalized Lipschitzian conditions in metric spaces

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Abstract

In this paper, we prove some common fixed point theorems for one-parameter semigroups of asymptotically regular mappings which satisfy certain generalized Lipschitzian conditions in metric spaces. Our results do not assume the continuity of the mappings in the semigroups. The results extend some relevant common fixed point theorems in Górnicki (Colloq Math 64:55–57, 1993), Imdad and Soliman (Fixed Point Theory Appl 2010:692401, 2010), Imdad and Soliman (Bull Malays Math Sci Soc 2(35):687–694, 2012), Yao and Zeng (J Nonlinear Convex Anal 8:153–163, 2007).

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Acknowledgements

The authors would like to thank the anonymous referees for valuable comments and suggestions which lead to the improvement of the manuscript.

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Authors and Affiliations

  1. Department of Mathematics Education, Universitas Pekalongan, 51119, Pekalongan, Indonesia

    Muhamad Najibufahmi

  2. Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Sekip Utara, 55281, Yogyakarta, Indonesia

    Atok Zulijanto

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  1. Muhamad Najibufahmi
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  2. Atok Zulijanto
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Correspondence to Muhamad Najibufahmi.

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Najibufahmi, M., Zulijanto, A. Fixed point theorems for asymptotically regular semigroups equipped with generalized Lipschitzian conditions in metric spaces. J. Fixed Point Theory Appl. 23, 23 (2021). https://doi.org/10.1007/s11784-021-00861-5

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