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Best proximity point theorems of cyclic Meir-Keeler-Kannan-Chatterjea contractions

Year 2019, Volume: 2 Issue: 2, 83 - 91, 30.08.2019

Abstract

In this study, by using the Meir-Keeler mapping, cyclic Kannan contraction and cyclic Chatterjee contraction, we establish the notions of cyclic Meir-Keeler-Kannan-Chatterjea contraction T from (A union B) to  (A union B) and cyclic Meir-Keeler-Kannan-Chatterjea contractive pair (T,S) of mappings T from A to  B  and S from B to A , and then we prove some best proximity point theorems for these various types of cyclic contractions. Our results generalize or improve many recent best proximity point theorems in the literature.

References

  • [1] M.A. Al-Thagafi, N. Shahzad, Convergence and existence results for best proximity points, Nonlinear Anal., 70 (10) (2009)3665–3671.
  • [2] A. Anthony Eldred, P. Veeramani, Existence and convergence of best proximity points, J. Math. Anal. Appl., 323 (2006)1001–1006.
  • [3] M.A. Al-Thagafi, N. Shahzad, Best proximity pairs and equilibrium pairs for Kakutani multimaps, Nonlinear Anal., 70(3) (2009) 1209–1216.
  • [4] M.A. Al-Thagafi, N. Shahzad, Best proximity sets and equilibrium pairs for a finite family of multimaps, Fixed PointTheory Appl., 3 (2008).
  • [5] C. Di Bari, T. Suzuki, C. Vetro, Best proximity points for cyclic Meir-Keeler contractions, Nonlinear Anal., 69 (11) (2008)3790–3794.
  • [6] W.-S. Du, On coincidence point and fixed point theorems for nonlinear multivalued maps, Topology, and Applications,159(2012), 49–56.
  • [7] A. Anthony Eldred, P. Veeramani, Existence and convergence of best proximity points, J. Math. Anal. Appl., 323 (2006)1001–1006.
  • [8] S. Karpagam, S. Agrawal, Best proximity point theorems for p-cyclic Meir-Keeler contractions, Fixed Point Theory Appl.,(2009), ID 197308.
  • [9] A. Meir, E. Keeler, A theorem on contraction mappings, J. Math. Anal. Appl., 28(1969), 326–329.
  • [10] S. Sadiq Basha, P. Veeramani, Best approximations and best proximity pairs, Acta Sci. Math. (Szeged) 63(1997), 289–300.
  • [11] S. Sadiq Basha, P. Veeramani, Best proximity pair theorems for multifunctions with open fibers, 103 (2000) 119--129. J.Approx. Theory 103(2000), 119–129.
  • [12] S. Sadiq Basha, N. Shahzad, and R. Jeyaraj, Optimal approximate solutions of fixed point equations,h Abstract andApplied Analysis, (2011), Article ID 174560, 9 pages.
  • [13] S. Sadiq Basha, gBest proximity points: global optimal approximate solutions, Journal of Global Optimization, 49(2011),no. 1, pp. 15--21.
  • [14] K. Wlodarczyk, R. Plebaniak, A. Banach, Best proximity points for cyclic and noncyclic set-valued relatively quasi-asymptotic contractions in uniform spaces, Nonlinear Anal., 70 (9) (2009) 3332–3341.
Year 2019, Volume: 2 Issue: 2, 83 - 91, 30.08.2019

Abstract

References

  • [1] M.A. Al-Thagafi, N. Shahzad, Convergence and existence results for best proximity points, Nonlinear Anal., 70 (10) (2009)3665–3671.
  • [2] A. Anthony Eldred, P. Veeramani, Existence and convergence of best proximity points, J. Math. Anal. Appl., 323 (2006)1001–1006.
  • [3] M.A. Al-Thagafi, N. Shahzad, Best proximity pairs and equilibrium pairs for Kakutani multimaps, Nonlinear Anal., 70(3) (2009) 1209–1216.
  • [4] M.A. Al-Thagafi, N. Shahzad, Best proximity sets and equilibrium pairs for a finite family of multimaps, Fixed PointTheory Appl., 3 (2008).
  • [5] C. Di Bari, T. Suzuki, C. Vetro, Best proximity points for cyclic Meir-Keeler contractions, Nonlinear Anal., 69 (11) (2008)3790–3794.
  • [6] W.-S. Du, On coincidence point and fixed point theorems for nonlinear multivalued maps, Topology, and Applications,159(2012), 49–56.
  • [7] A. Anthony Eldred, P. Veeramani, Existence and convergence of best proximity points, J. Math. Anal. Appl., 323 (2006)1001–1006.
  • [8] S. Karpagam, S. Agrawal, Best proximity point theorems for p-cyclic Meir-Keeler contractions, Fixed Point Theory Appl.,(2009), ID 197308.
  • [9] A. Meir, E. Keeler, A theorem on contraction mappings, J. Math. Anal. Appl., 28(1969), 326–329.
  • [10] S. Sadiq Basha, P. Veeramani, Best approximations and best proximity pairs, Acta Sci. Math. (Szeged) 63(1997), 289–300.
  • [11] S. Sadiq Basha, P. Veeramani, Best proximity pair theorems for multifunctions with open fibers, 103 (2000) 119--129. J.Approx. Theory 103(2000), 119–129.
  • [12] S. Sadiq Basha, N. Shahzad, and R. Jeyaraj, Optimal approximate solutions of fixed point equations,h Abstract andApplied Analysis, (2011), Article ID 174560, 9 pages.
  • [13] S. Sadiq Basha, gBest proximity points: global optimal approximate solutions, Journal of Global Optimization, 49(2011),no. 1, pp. 15--21.
  • [14] K. Wlodarczyk, R. Plebaniak, A. Banach, Best proximity points for cyclic and noncyclic set-valued relatively quasi-asymptotic contractions in uniform spaces, Nonlinear Anal., 70 (9) (2009) 3332–3341.
There are 14 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Chi-ming Chen

Chao-chung Kuo This is me

Publication Date August 30, 2019
Published in Issue Year 2019 Volume: 2 Issue: 2

Cite

APA Chen, C.-m., & Kuo, C.-c. (2019). Best proximity point theorems of cyclic Meir-Keeler-Kannan-Chatterjea contractions. Results in Nonlinear Analysis, 2(2), 83-91.
AMA Chen Cm, Kuo Cc. Best proximity point theorems of cyclic Meir-Keeler-Kannan-Chatterjea contractions. RNA. August 2019;2(2):83-91.
Chicago Chen, Chi-ming, and Chao-chung Kuo. “Best Proximity Point Theorems of Cyclic Meir-Keeler-Kannan-Chatterjea Contractions”. Results in Nonlinear Analysis 2, no. 2 (August 2019): 83-91.
EndNote Chen C-m, Kuo C-c (August 1, 2019) Best proximity point theorems of cyclic Meir-Keeler-Kannan-Chatterjea contractions. Results in Nonlinear Analysis 2 2 83–91.
IEEE C.-m. Chen and C.-c. Kuo, “Best proximity point theorems of cyclic Meir-Keeler-Kannan-Chatterjea contractions”, RNA, vol. 2, no. 2, pp. 83–91, 2019.
ISNAD Chen, Chi-ming - Kuo, Chao-chung. “Best Proximity Point Theorems of Cyclic Meir-Keeler-Kannan-Chatterjea Contractions”. Results in Nonlinear Analysis 2/2 (August 2019), 83-91.
JAMA Chen C-m, Kuo C-c. Best proximity point theorems of cyclic Meir-Keeler-Kannan-Chatterjea contractions. RNA. 2019;2:83–91.
MLA Chen, Chi-ming and Chao-chung Kuo. “Best Proximity Point Theorems of Cyclic Meir-Keeler-Kannan-Chatterjea Contractions”. Results in Nonlinear Analysis, vol. 2, no. 2, 2019, pp. 83-91.
Vancouver Chen C-m, Kuo C-c. Best proximity point theorems of cyclic Meir-Keeler-Kannan-Chatterjea contractions. RNA. 2019;2(2):83-91.