Common Fixed Point Theorems of Compatible Maps in Complex Valued <i>b</i>-Metric Spaces

Authors

  • G. Yadav Institute of Engineering and Technology, Devi Ahilya University, Khandwa Road, Indore-452017 (M.P.), India
  • R. K. Sharma Department of Mathematics, Govt. (Model, Autonomous) Holkar Science College, Indore -452001 (M.P.), India
  • G. L. Prajapati Department of Computer Engineering, Institute of Engineering and Technology, Devi Ahilya University, Khandwa Road, Indore-452017 (M.P.), India

DOI:

https://doi.org/10.3329/jsr.v12i4.44374

Abstract

In a paper Mukheimer established some results regarding common fixed point of two self mappings in a complex valued b-metric space satisfying a rational type contractive condition. In this paper we have established a common fixed point theorem by making use of compatibility and weak compatibility of self mappings satisfying generalized rational inequality of four mappings as opposed to two self mappings in a complex valued b – metric space. Some concrete examples have also been presented to verify the effectiveness and applicability of established results. Towards the end, an application to solution of Urysohn’s integral equations has also been presented to substantiate the usability of the obtained results. Results of this paper generalize the results of Mukheimer and some other earlier results. Theorems approved in this article will be supportable for researchers to work on rational contractions with more than two pair of self mappings.  

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Published

2020-09-01

How to Cite

Yadav, G., Sharma, R. K., & Prajapati, G. L. (2020). Common Fixed Point Theorems of Compatible Maps in Complex Valued <i>b</i>-Metric Spaces. Journal of Scientific Research, 12(4), 431–446. https://doi.org/10.3329/jsr.v12i4.44374

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Section

Section A: Physical and Mathematical Sciences