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Approximate best proximity pair results on metric spaces using contraction operators

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The aim of this paper is to prove some new approximate best proximity pair theorems on metric spaces using contraction mappings such as $P$-Bianchini contraction, $P-B$ contraction and so on. A few examples are provided to exemplify our findings. Finally, we discuss some applications that are related to the main results.

Abstract

The aim of this paper is to prove some new approximate best proximity pair theorems on metric spaces using contraction mappings such as $P$-Bianchini contraction, $P-B$ contraction and so on. A few examples are provided to exemplify our findings. Finally, we discuss some applications that are related to the main results.

참고문헌 (37)

  1. Balraj, D., "Existence of best proximity points satisfying two constraint inequalities", Electranic Research Archive, 28(1), pp.549~557 (2020)
  2. Banach, S., "Surles operations dans les ensembles abstract et leur application aux equation integrals", Fund. Math, 3, pp.133~181 (1922)
  3. Beer, G., "Proximal maps, prox maps and coincidence points", Numerical Functional Analysis and Optimization, 11(5-6), pp.429~448 (1990)
  4. Berinde, M., "Approximate fixed point theorems, Stud. Univ. ”Babes-Bolyai”", Mathematica LI, 1, pp.11~25 (2006)
  5. Berinde, V., "Iterative approximation of fixed points" (2002), Editura Efemeride
  6. Berinde, V., "On the approximation of fixed points of weak contractive mappings", Carpathian J. Math, 19(1), pp.7~22 (2003)
  7. Bianchini, R. M. T., "Su un problema di S. Reich riguardante la teoria dei punti fissi", Bolletino U. M. I, 4(5), pp.103~106 (1972)
  8. Chatterjea, S. K., "Fixed point theorems", C. R. Acad. Bulg. Sci, 25, pp.727~730 (1972)
  9. Ciric, L. B., "Generalized contractions and fixed point theorems", Publ. Inst. Math. (Bulgr), 12(26), pp.19~26 (1971)
  10. Dass, B. K., "An extension of Banach contraction principle through rational expression, Communicated by F.C. Auluck", FNA., ~ (1975)
  11. Dey, D.2, "Approximate fixed point of Reich operator, Acta Mathematica Universitatis Comenianae", ~ (2012)
  12. Eldred, A. A., "Existence and convergence of best proximity points", Journal of Mathematical Analysis and Applications, 323(2), pp.1001~1006 (2006)
  13. Fallahi, K., "Best proximity points for (φψ)-weak contractions and some applications", Filomat, 37(6) (2023)
  14. Gardasevic-Filipovic, M., "Some best proximity point results in the orthogonal O-complete b-metric-like spaces", Journal of Contemporary Mathematical Analysis(Armenian Academy of Sciences), 58, pp.105115~ (2023)
  15. Hardy, G. E., "A generalization of fixed point theorem of Reich", Can. Math. Bull, 16, pp.201~206 (1973)
  16. Iqbal, M., "Fixed point of generalized weak contraction in b-metric spaces", Journal of Function Spaces, pp.8~ (2021)
  17. Iqbal, M., "Fixed point of almost contraction in b-metric spaces", Journal of Mathematics, pp.1~6 (2020)
  18. Jaggi, D. S., "Some unique fixed point theorems", Indian Journal of Pure and Applied Mathematics, 8, pp.223~230 (1977)
  19. Kannan, R., "Some results on fixed points", Bull Calcutta Math. Soc, 60, pp.71~76 (1968)
  20. Kannan, R., "Some results on fixed points", II. Am. Math. Mon, 76, pp.405~408 (1969)
  21. Khan, M. S., "A fixed point theorems for metric spaces", Rendiconti Dell ’istituto di mathematica dell’ Universtia di tresti, 8, pp.69~72 (1976)
  22. Khuri, S. A., "A novel Ishikawa-Green’s fixed point scheme for the solution of BVPs", Appl. Math. Lett, 82, pp.50~57 (2018)
  23. Kim, W. K., "Corrigendum to existence of best proximity pairs and equilibrium pairs", J. Math. Anal. Appl, 316, pp.433~446 (2006)
  24. Kirk, W. A., "Proximinal retracts and best proximity pair theorems", Numerical Functional Analysis and Optimization, 24(7-8) (2003)
  25. Marudai, M., "Unique fixed point theorem weakly B-contractive mappings", Far East journal of Mathematical Sciences(FJMS), 98(7), pp.897~914 (2015)
  26. Mohsenalhosseini, S. A. M., "Approximate best proximate pairs in metric space for contraction maps", Fixed Point Theory, 4(2), pp.310~324 (2014)
  27. Mohsenalhosseini, S. A. M., "Some of family of contractive type maps and approximate common fixed point", J.Fixed Point Theory, 2 (2021)
  28. Mohsenalhosseini, S. A. M., "Approximate best proximity pairs in metric space", Abstr. Appl. Anal (2011)
  29. Nallaselli, G., "Solving integral equations via admissible contraction mappings", Filomat, 36(14), pp.4947~4961 (2022)
  30. Reich, S., "Some remarks connecting contraction mappings", Can. Math. Bull., 14, pp.121~124 (1971)
  31. Singer, I., "Die Grundlehren der mathematischen Wissenschaften, Band 171" (1970), Springer-Verlag
  32. Tis, S., "Approximate fixed point theorems", Libertas Mathematica, 23, pp.35~39 (2003)
  33. Vetrivel, V., "Some extensions of Fan’s best approximation theorem", Numerical Functional Analysis and Optimization, 13(3-4), pp.397~402 (1992)
  34. W lodarczyk, K., "Best proximity points for cyclic and noncyclic set-valued relatively quasi-asymptotic contractions in uniform spacand es", Nonlinear Analysis:Theory, Methods and Applications, pp.3332~3341 (2009)
  35. W lodarczyk, K., "Convergence theorems, best approximation and best proximity for set-valued dynamic systems of relatively quasi-asymptotic contractions in cone uniform spaces", Nonlinear Analysis: Theory, Methods and Applications, 72(2), pp.794~805 (2010)
  36. Xu, X. B., "A result on best proximity pair of two sets", Journal of Approximation Theory, 54(3), pp.322~325 (1988)
  37. Zamfirescu, T., "Fixed Point theorems in metric spaces", Arch. Math. (Basel), 23, pp.292~298 (1972)

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