Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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FIXED POINT THEOREMS IN COMPLEX VALUED CONVEX METRIC SPACES

  • Okeke, G.A. (Department of Mathematics, School of Physical Sciences Federal University of Technology Owerri) ;
  • Khan, S.H. (Department of Mathematics, Statistics and Physics Qatar University) ;
  • Kim, J.K. (Department of Mathematics, Statistics and Physics Qatar University)
  • Received : 2020.08.04
  • Accepted : 2020.10.06
  • Published : 2021.03.15
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Abstract

Our purpose in this paper is to introduce the concept of complex valued convex metric spaces and introduce an analogue of the Picard-Ishikawa hybrid iterative scheme, recently proposed by Okeke [24] in this new setting. We approximate (common) fixed points of certain contractive conditions through these two new concepts and obtain several corollaries. We prove that the Picard-Ishikawa hybrid iterative scheme [24] converges faster than all of Mann, Ishikawa and Noor [23] iterative schemes in complex valued convex metric spaces. Also, we give some numerical examples to validate our results.

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References

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