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GENERALISED COMMON FIXED POINT THEOREM FOR WEAKLY COMPATIBLE MAPPINGS VIA IMPLICIT CONTRACTIVE RELATION IN QUASI-PARTIAL Sb-METRIC SPACE WITH SOME APPLICATIONS

  • Lucas Wangwe (Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam) ;
  • Santosh Kumar (Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam)
  • Received : 2021.08.02
  • Accepted : 2022.09.27
  • Published : 2023.03.25
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Abstract

In the present paper, we prove common fixed point theorems for a pair of weakly compatible mappings under implicit contractive relation in quasi-partial Sb-metric spaces. We also provide an illustrative example to support our results. Furthermore, we will use the results obtained for application to two boundary value problems for the second-order differential equation. Also, we prove a common solution for the nonlinear fractional differential equation.

Keywords

Acknowledgement

The authors are thankful to the learned reviewer for his valuable comments.

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