This article is aimed at proving the existence and uniqueness of common fixed point theorems for a pair of self maps satisfying a new rational type condition in complex valued metric spaces. Interpolation approach has been used in this work to get a common fixed point. We have proved some new common fixed point theorems on complex valued metric space for a new type of interpolative rational contractive condition by choosing a complex degree of freedom of power α with an additional degree of freedom of power β, which is also complex valued, on the right hand side of the condition. The results obtained generalize some theorems of Karapinar [1], Noorwali [2], Sarwar et al. [3], Pandey and Tiwari [4] and Gaba and Karapınar [5] in real valued metric spaces to complex valued metric spaces. Also, we have proved and generalized few fixed point theorems on complex valued metric space for a pair of mappings under various conditions. Moreover some applications and examples validating the results have been discussed.
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1 August 2024
MATHEMATICS AND ITS APPLICATIONS IN TECHNOLOGY
24–25 March 2023
Kumbakonam, India
Research Article|
August 01 2024
Fixed points for interpolative and rational type mappings on complex valued metric spaces
A. Murali;
A. Murali
a)
Division of Mathematics, Vellore Institute of Technology
, Chennai Campus, Chennai-600127, Tamil Nadu, India
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K. Muthunagai
K. Muthunagai
b)
Division of Mathematics, Vellore Institute of Technology
, Chennai Campus, Chennai-600127, Tamil Nadu, India
b)Corresponding author: [email protected]
Search for other works by this author on:
b)Corresponding author: [email protected]
AIP Conf. Proc. 3180, 020001 (2024)
Citation
A. Murali, K. Muthunagai; Fixed points for interpolative and rational type mappings on complex valued metric spaces. AIP Conf. Proc. 1 August 2024; 3180 (1): 020001. https://doi.org/10.1063/5.0224350
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