SavedAdd your journal

Journals / Results in Nonlinear Analysis / 2026 / Cilt: 2 Sayı: 2

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

Chi-ming Chen(National Tsing Hua University, Taiwan)
Chao-chung Kuo(National Tsing Hua University, Taiwan)
Pages
83–91
Publication Date
2019-08-30
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Our results generalize or improve many recent best proximity point theorems in the literature.

📌 3 Key Takeaways

🎯
Objective & Hypothesis: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.
📊
Key Findings & Data: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.
💡
Conclusion & Impact:Our results generalize or improve many recent best proximity point theorems in the literature.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Best proximity points · Cyclic Meir-Keeler-Kannan-Chatterjea contraction · Cyclic Meir-Keeler-Kannan-Chatterjea contractive pair

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.

🔖

Cite This Article

Chen, C., Kuo, C. (2019). Best proximity point theorems of cyclic Meir-Keeler-Kannan-Chatterjea contractions. Results in Nonlinear Analysis, Cilt: 2 Sayı: 2, 83–91. https://ajindex.com/articles/1537760

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (14)

  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.