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On Generalized Algebraic Cone Metric Spaces and Fixed Point Theorems

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Abstract

In this paper, the author first introduces the concept of generalized algebraic cone metric spaces and some elementary results concerning generalized algebraic cone metric spaces. Next, by using these results, some new fixed point theorems on generalized (complete) algebraic cone metric spaces are proved and an example is given. As a consequence, the main results generalize the corresponding results in complete algebraic cone metric spaces and generalized complete metric spaces.

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Acknowledgement

The author appreciates the valuable comments made by the anonymous referee.

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Authors and Affiliations

  1. School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, Shandong, China

    Qing Meng

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  1. Qing Meng
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Correspondence to Qing Meng.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 11871303, 11371222, 11271224), the China Postdoctoral Science Foundation (No. 2018M642633) and A Project of Shandong Province Higher Educational Science and Technology Program (No. J18KA238).

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Meng, Q. On Generalized Algebraic Cone Metric Spaces and Fixed Point Theorems. Chin. Ann. Math. Ser. B 40, 429–438 (2019). https://doi.org/10.1007/s11401-019-0142-8

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  • DOI: https://doi.org/10.1007/s11401-019-0142-8

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