Research Article

Best proximity points for weak $\mathcal{MT}$-cyclic Kannan contractions

Volume: 1 Number: 1 June 30, 2018
EN

Best proximity points for weak $\mathcal{MT}$-cyclic Kannan contractions

Abstract

In this paper, we introduce a notion of weak $% \mathcal{MT}$-cyclic Kannan contractions with respect to a $\mathcal{MT}$% -function $\varphi$ and then we shall prove some new convergent and existence theorems of best proximity point theorems for these contractions in uniformly Banach spaces.

Keywords

References

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  2. [2] A. Anthony Eldred, P. Veeramani, Existence and convergence of best proximity points , J. Math. Anal. Appl. 323 (2006) 1001-1006.
  3. [3] A. Anthony Eldred, J. Anuradha, P. Veeramani, On the equivalence of the Mizoguchi-Takahashi fixed point theorem to Nadler’s theorem, Appl. Math. Letters 22 (2009) 1539-1542.
  4. [4] M.A. Al-Thagafi, Naseer Shahzad, Convergence and existence results for best proximity points, Nonlinear Analysis 70 (2009) 3665-3671.
  5. [5] T. Suzuki, M. Kikkawa, C. Vetro, The existence of the best proximity points in metric spaces with the property UC, Nonlinear Anal. 71 (2009) 2918-2926.
  6. [6] W.-S. Du, Some new results and generalizations in metric fixed point theory, Nonlinear Anal. 73 (2010) 1439-1446.
  7. [7] W.-S. Du, Coupled fixed point theorems for nonlinear contractions satisfied Mizoguchi-Takahashi’s condition in quasi ordered metric spaces, Fixed Point Theory and Applications (2010), Article ID 876372, doi: 10.1155/2010/876372.
  8. [8] W.-S. Du, H. Lakzian, Nonlinear conditions and new inequalities for best proximity points, Journal of Inequalities and Applications, 2012 (2012), 206. https://doi.org/10.1186/1029-242x-2012-206.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Hossein Lakzian *
Department of Mathematics, Payame Noor University, 19395-4697 Tehran, I.R. of Iran
Iran

Ing-Jer Lin This is me
Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 824, Taiwan
Taiwan

Publication Date

June 30, 2018

Submission Date

March 14, 2018

Acceptance Date

March 27, 2018

Published in Issue

Year 2018 Volume: 1 Number: 1

APA
Lakzian, H., & Lin, I.-J. (2018). Best proximity points for weak $\mathcal{MT}$-cyclic Kannan contractions. Fundamental Journal of Mathematics and Applications, 1(1), 43-48. https://doi.org/10.33401/fujma.405536
AMA
1.Lakzian H, Lin IJ. Best proximity points for weak $\mathcal{MT}$-cyclic Kannan contractions. Fundam. J. Math. Appl. 2018;1(1):43-48. doi:10.33401/fujma.405536
Chicago
Lakzian, Hossein, and Ing-Jer Lin. 2018. “Best Proximity Points for Weak $\mathcal{MT}$-Cyclic Kannan Contractions”. Fundamental Journal of Mathematics and Applications 1 (1): 43-48. https://doi.org/10.33401/fujma.405536.
EndNote
Lakzian H, Lin I-J (June 1, 2018) Best proximity points for weak $\mathcal{MT}$-cyclic Kannan contractions. Fundamental Journal of Mathematics and Applications 1 1 43–48.
IEEE
[1]H. Lakzian and I.-J. Lin, “Best proximity points for weak $\mathcal{MT}$-cyclic Kannan contractions”, Fundam. J. Math. Appl., vol. 1, no. 1, pp. 43–48, June 2018, doi: 10.33401/fujma.405536.
ISNAD
Lakzian, Hossein - Lin, Ing-Jer. “Best Proximity Points for Weak $\mathcal{MT}$-Cyclic Kannan Contractions”. Fundamental Journal of Mathematics and Applications 1/1 (June 1, 2018): 43-48. https://doi.org/10.33401/fujma.405536.
JAMA
1.Lakzian H, Lin I-J. Best proximity points for weak $\mathcal{MT}$-cyclic Kannan contractions. Fundam. J. Math. Appl. 2018;1:43–48.
MLA
Lakzian, Hossein, and Ing-Jer Lin. “Best Proximity Points for Weak $\mathcal{MT}$-Cyclic Kannan Contractions”. Fundamental Journal of Mathematics and Applications, vol. 1, no. 1, June 2018, pp. 43-48, doi:10.33401/fujma.405536.
Vancouver
1.Hossein Lakzian, Ing-Jer Lin. Best proximity points for weak $\mathcal{MT}$-cyclic Kannan contractions. Fundam. J. Math. Appl. 2018 Jun. 1;1(1):43-8. doi:10.33401/fujma.405536

Cited By

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