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Integral Type Contractions in Partially Ordered Metric Spaces and Best Proximity Point

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In this paper, we introduce Banach and Kannan integral type contractions in partially ordered metric spaces and investigate the existence and uniqueness of best proximity points for them. Additionally, we pose two non-trivial examples for our main results.

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  1. Aghanians A, Nourouzi K (2015) Fixed points of integral type contractions in uniform spaces. Filomat 29(7):1613–1621

  2. Banach S (1922) Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fund Math J 3:133–181

  3. Branciari A (2002) A fixed point theorem for mappings satisfying a general contractive condition of integral type. Int J Math Sci 29(9):531–536

  4. Gabeleh M, Shahzad N (2016) Best proximity points, cyclic Kannan maps and geodesic metric spaces. J Fixed Point Theory Appl 18(1):167–188

  5. Kannan R (1969) Some results on fixed points-II. Am Math Mon 76:405–408

  6. Nieto JJ, Rodriguez-Lopez R (2005) Contractive mappings theorems in partially ordered sets and applications to ordinary differential equations. Order 22(3):223–239

  7. Petrusel A, Rus IA (2019) Fixed point theory in terms of a metric and of an order relation. Fixed Point Theory 20(2):601–622

  8. Raj VS (2011) A best proximity point theorem for weakly contractive non-self-mappings. Nonlinear Anal 74:4804–4808

  9. Raj VS (2013) Best proximity point theorems for non-self mappings. Fixed Point Theory 14:447–454

  10. Ran ACM, Reurings MCB (2004) A fixed point theorem in partially ordered sets and some applications to matrix equations. Proc Am Math Soc 132(5):1435–1443

  11. Sadiq Basha S (2012) Discrete optimization in partially ordered sets. J Glob Optim 54:511–517

  12. Sadiq Basha S (2017) Best proximity point theorems in the frameworks of fairly and proximally complete spaces. J Fixed Point Theory Appl 19(3):1939–1951

  13. Sadiq Basha S, Shahzad N, Vetro C (2017) Best proximity point theorems for proximal cyclic contractions. J Fixed Point Theory Appl 19(4):2647–2661

  14. Samet B, Vetro C (2012) An integral version of Ćirić’s fixed point theorem. Mediterr J Math 9(1):225–238

  15. Suzuki T (2013) The existence of best proximity points with the weak P-property. Fixed Point Theory Appl 2013:259

  16. Zhang J, Su Y, Cheng Q (2013) A note on ‘A best proximity point theorem for Geraghty-contractions’. Fixed Point Theory Appl 2013:99

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Correspondence to Kamal Fallahi.

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Fallahi, K., Ghahramani, H. & Soleimani Rad, G. Integral Type Contractions in Partially Ordered Metric Spaces and Best Proximity Point. Iran J Sci Technol Trans Sci 44, 177–183 (2020). https://doi.org/10.1007/s40995-019-00807-0

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  • Proximal mapping
  • Banach integral type contraction
  • Kannan integral type contraction
  • Best proximity point

Mathematics Subject Classification

  • 47H10
  • 54H25