한국수학교육학회지시리즈B:순수및응용수학 (The Pure and Applied Mathematics)

  • 제31권3호
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  • Pages.337-354
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  • 2024
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  • 1226-0657(pISSN)
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  • 2287-6081(eISSN)
한국수학교육학회 (Korean Society of Mathematical Education)
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BEST PROXIMITY POINT THEOREMS FOR 𝜓-𝜙-CONTRACTIONS IN METRIC SPACES

  • Shilpa Rahurikar (Department of Mathematics, Shri Vaishnav Vidyapeeth Vishwavidyalaya) ;
  • Varsha Pathak (Department of Mathematics, Shri Vaishnav Vidyapeeth Vishwavidyalaya) ;
  • Satish Shukla (Department of Mathematics, Shri Vaishnav Vidyapeeth Vishwavidyalaya)
  • 투고 : 2024.04.27
  • 심사 : 2024.05.25
  • 발행 : 2024.08.31
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초록

In this paper, some best proximity points results for 𝜓-𝜙-contractions on complete metric spaces are proved. These results extend and generalize some best proximity and fixed point results on complete metric spaces. An example and some corollaries are provided that demonstrate the results proved herein.

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과제정보

All the authors are thankful to the Reviewers and Editors for their suggestions and remarks on the first draft of the manuscript.

참고문헌

  1. J. Anuradha Eldered & P. Veeramani: Proximal pointwise contraction. Topol. Appl. 156 (2009), no. 18, 2942-2948. https://doi.org/10.1016/j.topol.2009.01.017
  2. A. Anthony Eldred & P. Veeramani: Existence and convergence of best proximity points. J. Math. Anal. Appl. 323 (2006), 1001-1006. https://doi.org/10.1016/j.jmaa.2005.10.081
  3. A.D. Arvanitakis: A proof of the generalized Banach contraction conjecture. Proc. Amer. Math. Soc. 131 (2003), no. 12, 3647-3656. https://doi.org/10.2307/1194510
  4. B.S. Choudhury & K.P. Das: A new contraction principle in Menger spaces. Acta Mathematica Sinica 24 (2008), no. 8, 1379-1386. https://doi.org/ 10.1007/s10114-007-6509-x
  5. C. Mongkolkeha & P. Kumam: Fixed point and common fixed-point theorems for generalized weak contraction mappings of integral type in modular spaces. Internat. J. Math. & Math. Sci. 2011 (2011), Article ID 705943, 12 pages.
  6. C. Mongkolkeha & P. Kumam: Fixed point theorems for generalized asymptotic pointwise ρ-contraction mappings involving orbits in modular function spaces. Applied Mathematics Letters 25 (2012), no. 10, 1285-1290. https://doi.org/ 10.1016/j.aml.2011.11.027
  7. D.W. Boyd & J.S.W. Wong: On nonlinear contractions. Proc. Amer. Math. Soc. 20 (1969), 458-464. https://doi.org/ 10.1090/S0002-9939-1969-0239559-9
  8. G. Prasad & D. Khantwal: Fixed points of JS-contractive mappings with applications. J. Anal. 31 (2023), 2687-2701. https://doi.org/10.1007/s41478-023-00598-z
  9. G. Prasad & R.C. Dimri: Fixed point theorems for weakly contractive mappings in relational metric spaces with an application. J. Anal. 26 (2018), 151-162. https://doi.org/10.1007/s41478-018-0076-7
  10. G. Prasad & R.C. Dimri: Coincidence theorems in new generalized metric spaces under locally g-transitive binary relation. J. Indian Math. Soc. 85 (2018), no. 3-4, 396-410. https://doi.org/10.18311/jims/2018/16383
  11. J.B. Prolla: Fixed point theorems for set valued mappings and existence of best approximations. Numer. Funct. Anal. Optim. 5 (1982-1983), 449-455. https://doi.org/10.1080/01630568308816149
  12. K. Fan: Extensions of two fixed point theorems of F. E. Browder. Mathematische Zeitschrift 112 (1969), no. 3, 234-240. https://api.semanticscholar.org/CorpusID:119627163 https://doi.org/10.1007/BF01110225
  13. K. Ungchittrakool: A Best Proximity Point Theorem for Generalized Non-Self-Kannan-Type and Chatterjea-Type Mappings and Lipschitzian Mappings in Complete Metric Spaces. Journal of Function Spaces 2016 (2016), no. 1-2, 1-11. https://doi.org/10.1155/2016/9321082
  14. N. Hussain, A.Latif & P. Salimi: Best Proximity Point Result in G-Metric Space. Abstract and Applied Analysis 2014 (2014) Artical ID 837943, 8. http://dx.doi.org/10.1155/2014/837943
  15. N. Dubey, S. Shukla & R. Shukla: On Graphical Symmetric Spaces, Fixed-Point Theorems and the Existence of Positive Solution of Fractional Periodic Boundary Value Problems. Symmetry 16 (2024), no. 2, 182. https://doi.org/10.3390/sym16020182
  16. S. Banach: Sur les operations dans les ensembles abstraits et leur application aux equations integrals. Fundam. Math. 3 (1922), 133-181. https://api.semanticscholar.org/CorpusID:118543265 https://doi.org/10.4064/fm-3-1-133-181
  17. S. Sadiq Basha: Best proximity point theorems. Journal of Approximation theory 163 (2011), no. 11, 1772-1781. https://doi.org/10.1016/j.jat.2011.06.012
  18. S. Reich: Approximate selections, best approximations, fixed points and invariant sets. J. Math. Anal. Appl. 62 (1978), 104-113. https://api.semanticscholar.org/CorpusID:21665412 https://doi.org/10.1016/0022-247X(78)90222-6
  19. S. Shukla, N. Dubey, J-J. Minana: Vector-Valued Fuzzy Metric Spaces and Fixed Point Theorems. Axioms 13 (2024), no. 4, 252. https://doi.org/10.3390/axioms13040252
  20. S. Shukla, S. Rai & R. Shukla: Some Fixed Point Theorems for α-Admissible Mappings in Complex-Valued Fuzzy Metric Spaces. Symmetry 15(9) (2023), 1797. https://doi.org/10.3390/sym15091797
  21. S. Shukla & S. Rai: Caristi type fixed point theorems in 1-M-complete fuzzy metric-like spaces. The Journal of Analysis 31 (2023), no. 3, 2247-2263. https://doi.org/10.1007/s41478-023-00562-x
  22. S. Shukla, N. Dubey, R. Shukla & I. Mezn'ik: Coincidence point of Edelstein type mappings in fuzzy metric spaces and application to the stability of dynamic markets. Axioms 12 (2023), no. 9, 854. https://doi.org/10.3390/axioms12090854
  23. V.M. Sehgal & S.P. Singh: A generalization to multifunctions of fans best approximation theorem. Proc. Amer. Math. Soc. 102 (1988), 534-537. https://doi.org/10.1090/S0002-9939-1988-0928974-5
  24. V.M. Sehgal & S.P. Singh: A theorem on best approximations. Numer. Funct. Anal. Optim. 10 (1988), 181-184. https://doi.org/10.1080/01630568908816298
  25. V. Vetrivel, P. Veeramani & P. Bhattacharyya: Some extensions of fans best approximation theorem. Numer. Funct. Anal. Optim. 13 (1992), 397-402. https://doi.org/10.1080/01630569208816486
  26. W.A. Kirk, P.S. Srinivasan & P. Veeramani: Fixed points for mappings satisfying cyclic contractive conditions. Fixed Point Theory 4 (2003), 79-89.
  27. W Sanhan, C. Mongkolkeha & P. Kumam: Generalized Proximalψ -Contraction Mappings and Best Proximity Points. Abstract and Applied Analysis 2012 (2012), Article ID 896912, 19. https://doi.org/10.1155/2012/896912
  28. W. Sintunavarat & P. Kumam: Gregus-type common fixed-point theorems for tangential multivalued mappings of integral type in metric spaces. Internat. J. Math. & Math. Sci. 2011 (2011), Article ID 923458, 12 pages. https://doi.org/10.1155/2011/923458
  29. W. Sintunavarat & P. Kumam: Weak condition for generalized multi-valued (f, α, β) weak contraction mappings. Applied Mathematics Letters 24 (2011), no. 4, 460-465. https://api.semanticscholar.org/CorpusID:31271775 https://doi.org/10.1016/j.aml.2010.10.042
  30. X. Zhang: Common fixed-point theorems for some new generalized contractive type mappings. J. Math. Anal. Appl. 333 (2007), no. 2, 780-786. https://doi.org/10.1016/j.jmaa.2006.11.028