# 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

#### 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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