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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 73, 2024 - Issue 7
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Research Article

A contribution to best proximity point theory and an application to partial differential equation

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Pages 2187-2219 | Received 18 Aug 2022, Accepted 11 Mar 2023, Published online: 22 Mar 2023

References

  • Al-Thagafi MA, Shahzad N. Best proximity pairs and equilibrium pairs for Kakutani multimaps. Nonlinear Anal. 2009;70(3):1209–1216.
  • Al-Thagafi MA, Shahzad N. Convergence and existence results for best proximity points. Nonlinear Anal. 2009;70(10):3665–3671.
  • Di Bari C, Suzuki T, Vetro C. Best proximity points for cyclic Meir–Keeler contractions. Nonlinear Anal. 2008;69(11):3790–3794.
  • Eldred AA, Veeramani P. Existence and convergence of best proximity points. J Math Anal Appl. 2006;323(2):1001–1006.
  • Sadiq Basha S. Extensions of Banach's contraction principle. Numer Funct Anal Optim. 2010;31(4–6):569–576.
  • Raj VS. A best proximity point theorem for weakly contractive non-self-mappings. Nonlinear Anal. 2011;74(14):4804–4808.
  • Suzuki T, Kikkawa M, Vetro C. The existence of best proximity points in metric spaces with the property UC. Nonlinear Anal. 2009;71(7–8):2918–2926.
  • Vetro C. Best proximity points: convergence and existence theorems for p-cyclic mappings. Nonlinear Anal. 2010;73(7):2283–2291.
  • Sadiq Basha S, Veeramani P. Best proximity pairs and best approximations. Acta Sci Math (Szeged). 1997;63(1–2):289–300.
  • Kirk WA, Reich S, Veeramani P. Proximinal retracts and best proximity pair theorems. Numer Funct Anal Optim. 2003;24(7–8):851–862.
  • Hussain N, Latif A, Salimi P. Best proximity point results for modified Suzuki α-ψ-proximal contractions. Fixed Point Theory Appl. 2014;Article ID 2014:10, 16.
  • Hussain N, Kutbi MA, Salimi P. Best proximity point results for modified α−ψ-proximal rational contractions. Abstr Appl Anal. 2013;Article ID 927457, 14.
  • Hussain N, Kutbi MA, Salimi P. Global optimal solutions for proximal fuzzy contractions. Physica A. 2020;551:Article ID 123925, 16.
  • Komal S, Gopal D, Khojasteh F, et al. The approximate solution for generalized proximal contractions in complete metric spaces. Thai J Math. 2019;17(Special issue):200–212.
  • Komal S, Kumam P, Gopal D. Best proximity point for Z-contraction and Suzuki type Z-contraction mappings with an application to fractional calculus. Appl Gen Topol. 2016;17(2):185–198.
  • Abkar A, Gabeleh M. Best proximity points for cyclic mappings in ordered metric spaces. J Optim Theory Appl. 2011;151(2):418–424.
  • Aslantas M. Best proximity point theorems for proximal b-cyclic contractions on b-metric spaces. Commun Fac Sci Univ Ank Ser A1 Math Stat. 2021;70(1):483–496.
  • Jain SK, Meena G, Singh D, et al. Best proximity point results with their consequences and applications. J Inequal Appl. 2022;Paper No. 73, 16.
  • Aslantas M. A new contribution to best proximity point theory on quasi metric spaces and an application to nonlinear integral equations. Optimization. 2022;1–14.
  • Padcharoen A, Kumam P, Gopal D. Coincidence and periodic point results in a modular metric space endowed with a graph and applications. Creat Math Inform. 2017;26(1):95–104.
  • Deshmukh A, Gopal D. Topology of non-triangular metric spaces and related fixed point results. Filomat. 2021;35(11):3557–3570.
  • Banach S. Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fund Math. 1922;3:133–181.
  • Jleli M, Samet B. Best proximity points for α−ψ-proximal contractive type mappings and applications. Bull Sci Math. 2013;137(8):977–995.
  • Samet B, Turinici M. Fixed point theorems on a metric space endowed with an arbitrary binary relation and applications. Commun Math Anal. 2012;13(2):82–97.
  • Kirk WA, Srinivasan PS, Veeramani P. Fixed points for mappings satisfying cyclical contractive conditions. Fixed Point Theory. 2003;4(1):79–89.
  • Padcharoen A, Gopal D, Chaipunya P, et al. Fixed point and periodic point results for α-type F-contractions in modular metric spaces. Fixed Point Theory Appl. 2016; Paper No. 39, 12.

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