Geraghty–Pata–Suzuki-Type Proximal Contractions and Related Coincidence Best Proximity Point Results

Naeem Saleem*, Maneesha Tur Raazzia, Nawab Hussain, Asim Asiri

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


The objective of this research paper is to establish the existence and uniqueness of the best proximity and coincidence with best proximity point results, specifically focusing on Geraghty–Pata–Suzuki-type proximal mappings. To achieve this, we introduce three types of mappings, all within the context of a complete metric space: an (Formula presented.) Geraghty–Pata–Suzuki-type proximal contraction; an (Formula presented.) generalized Geraghty–Pata–Suzuki-type proximal contraction; and an (Formula presented.) modified Geraghty–Pata–Suzuki-type proximal contraction. These new results generalize, extend, and unify various results from the existing literature. Symmetry plays a crucial role in solving nonlinear problems in operator theory, and the variables involved in the metric space are symmetric. Several illustrative examples are provided to showcase the superiority of our results over existing approaches.

Original languageEnglish
Article number1572
Issue number8
Publication statusPublished - Aug 2023
Externally publishedYes


  • best proximity point
  • the coincidence of best proximity point
  • α-θ-Geraghty–Pata–Suzuki-type proximal contraction
  • α-θ-generalized Geraghty–Pata–Suzuki-type proximal contraction
  • α-θ-modified Geraghty–Pata–Suzuki-type proximal contraction
  • α-θ-proximal admissible Picard sequence


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