Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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On the Hyers-Ulam Stability of Polynomial Equations in Dislocated Quasi-metric Spaces

  • Liu, Yishi (Department of Mathematics, Sun Yat-sen University) ;
  • Li, Yongjin (Department of Mathematics, Sun Yat-sen University)
  • Received : 2019.07.13
  • Accepted : 2020.07.28
  • Published : 2020.12.31
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Abstract

This paper primarily discusses and proves the Hyers-Ulam stability of three types of polynomial equations: xn+a1x+a0 = 0, anxn+⋯+a1x+a0 = 0, and the infinite series equation: ${\sum\limits_{i=0}^{\infty}}\;a_ix^i=0$, in dislocated quasi-metric spaces under certain conditions by constructing contraction mappings and using fixed-point methods. We present an example to illustrate that the Hyers-Ulam stability of polynomial equations in dislocated quasi-metric spaces do not work when the constant term is not equal to zero.

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Acknowledgement

This work was supported by the National Natural Science Foundation of China (11971493).

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