Research article

Generalized $ (\alpha_s, \xi, \hbar, \tau) $-Geraghty contractive mappings and common fixed point results in partial $ b $-metric spaces

  • Received: 26 March 2023 Revised: 23 May 2024 Accepted: 27 May 2024 Published: 11 June 2024
  • MSC : 47H09, 47H10, 54H25

  • In this paper, we introduce two new classes of mixed $ (\mathcal{S, T}) $-$ \alpha $-admissible mappings and interspersed $ (\mathcal{S}, \mathfrak{g}, \mathcal{T}) $-$ \alpha $-admissible mappings and study the sufficient conditions for the existence and uniqueness of a common fixed point of generalized $ (\alpha_s, \xi, \hbar, \tau) $-Geraghty contractive mapping in the framework of partial $ b $-metric spaces. We also provide two examples to show the applicability and validity of our results. Moreover, we present an application to the existence of solutions to an integral equation by means of one of our results.

    Citation: Ying Chang, Hongyan Guan. Generalized $ (\alpha_s, \xi, \hbar, \tau) $-Geraghty contractive mappings and common fixed point results in partial $ b $-metric spaces[J]. AIMS Mathematics, 2024, 9(7): 19299-19331. doi: 10.3934/math.2024940

    Related Papers:

  • In this paper, we introduce two new classes of mixed $ (\mathcal{S, T}) $-$ \alpha $-admissible mappings and interspersed $ (\mathcal{S}, \mathfrak{g}, \mathcal{T}) $-$ \alpha $-admissible mappings and study the sufficient conditions for the existence and uniqueness of a common fixed point of generalized $ (\alpha_s, \xi, \hbar, \tau) $-Geraghty contractive mapping in the framework of partial $ b $-metric spaces. We also provide two examples to show the applicability and validity of our results. Moreover, we present an application to the existence of solutions to an integral equation by means of one of our results.



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