Some Best Proximity Point Results for \(\mathcal{MT}\)-Rational Cyclic Contractions in \(S\)-Metric Space

Authors

  • Somkiat Chaipornjareansri Department of Mathematics, Faculty of Science, Lampang Rajabhat University, Lampang 52100

DOI:

https://doi.org/10.26713/cma.v11i4.1413

Keywords:

cyclic mapping, best proximity point, \(\mathcal{MT}\)-function (\(\mathcal{R}\)-function), \(S\)-metric space

Abstract

In this paper, we use the concept of \(\mathcal{MT}\)-function to establish the best proximity point results for a certain class of proximal cyclic contractive mappings in \(S\)-metric spaces. Our results extend and improve some known results in the literature. We give an example to analyze and support our main results.

Downloads

Download data is not yet available.

References

A. Abkar and M. Gabeleh, Best proximity points for cyclic mappings in ordered metric spaces, Journal of Optimization Theory and Applications 151(2) (2011), 418 – 424, DOI: 10.1007/s10957-011-9818-2.

M. A. Al-Thagafi and N. Shahzad, Convergence and existence results for best proximity points, Nonlinear Analysis: Theory, Methods & Applications 70(10) (2009), 3665 – 3671, DOI: 10.1016/j.na.2008.07.022.

C. Di Bari, T. Suzuki and C. Vetro, Best proximity points for cyclic Meir-Keeler contractions, Nonlinear Analysis: Theory, Methods & Applications 69(11) (2008), 3790 – 3794, DOI: 10.1016/j.na.2007.10.014.

S. S. Basha, Best proximity point theorems generalizing the contraction principle, Nonlinear Analysis: Theory, Methods & Applications 74 (2011), 5844 – 5850, DOI: 10.1016/j.na.2011.04.017.

J. Caballero, J. Harjani and K. Sadarangani, A best proximity point theorem for Geraghtycontractions, Fixed Point Theory and Applications 2012 (2012), Article number: 231, DOI: 10.1186/1687-1812-2012-231.

S. Chaipornjareansri, Fixed point theorems for Fw-contractions in complete S-metric spaces, Thai Journal of Mathematics 14 (2016), 98 – 109, URL: http://thaijmath.in.cmu.ac.th/index.php/thaijmath/article/view/2201.

W.-S. Du and H. Lakzian, Nonlinear conditions for the existence of best proximity points, Journal of Inequalities and Application 2012 (2012), Article number: 206, DOI: 10.1186/1029-242X-2012-206.

W.-S. Du, On coincidence point and fixed point theorems for nonlinear multivalued maps, Topology and its Applications 159 (2012), 49 – 56, DOI: 10.1016/j.topol.2011.07.021.

A. A. Eldered and P. Veeramani, Existence and convergence of best proximity points, Journal of Mathematical Analysis Applications 323(2) (2006), 1001 – 1006, DOI: 10.1016/j.jmaa.2005.10.081.

K. Fan, Extensions of two fixed point theorems of F.E. Browder, Mathematische Zeitschrift 112 (1969), 234 – 240, DOI: 10.1007/BF01110225.

N. Hussain, A. Latif and P. Salimi, Best proximity point results for modified Suzuki (alpha)-(psi) proximal contractions, Fixed Point Theory and Applications 2014 (2014), Article number: 10, DOI: 10.1186/1687-1812-2014-10.

N. Hussain, M. A. Kutbi and P. Salimi, Best proximity point results for modified (alpha)-(psi) proximal rational contractions, Abstract and Applied Analysis 2013 (2013), Article ID 927457, 14 pages, DOI: 10.1155/2013/927457.

M. Jleli and B. Samet, A new generalization of the Banach contraction principle, Journal of Inequalities and Applications 2014 (2014), Article number: 38, 8 pages, DOI: 10.1186/1029-242X-2014-38.

S. Karpagam and S. Agrawal, Best proximity point theorems for p-cyclic Meir-Keeler contractions, Fixed Point Theory and Applications 2009 (2009), Article number: 197308, DOI: 10.1155/2009/197308.

W. A. Kirk, P. S. Srinavasan and P. Veeramani, Fixed points for mapping satisfying cyclical contractive conditions, Fixed Point Theory 1(4) (2003), 79 – 89, URL: http://www.math.ubbcluj.ro/~nodeacj/download.php?f=031Kirk.pdf.

Z. Mustafa and B. Sims, A new approach to generalized metric spaces, Journal of Nonlinear and Convex Analysis 7(2) (2006), 289 – 297, URL: https://carma.newcastle.edu.au/brailey/Research_papers/A%20new%20Approach%20to%20Generalized%20Metric%20Spaces.pdf.

N. Y. Ozgur and N. Tas, Some fixed point theorems on S-metric spaces, Matematicki Vesnik 69(1) (2017), 39 – 52, URL: https://www.emis.de/journals/MV/171/mv17104.pdf.

S. Sedghi, N. Shobkolaei, M. Shahraki and T. Dosenovic, Common fixed point of four maps in S-metric spaces, Mathematical Sciences 12 (2018), 137 – 143, DOI: 10.1007/s40096-018-0252-6.

S. Sedghi, N. Shobe and A. Aliouche, A generalization of fixed point theorems in S-metric spaces, Matematicki Vesnik 64(3) (2012), 258 – 266, URL: http://emis.um.ac.ir/journals/MV/123/mv12309.pdf.

S. Sedghi, N. Shobe and H. Zhou, A common fixed point theorem in (D^*)-metric spaces, Fixed Point Theory and Applications 2007 (2007), Article number: 027906, 1 – 13, DOI: 10.1155/2007/27906.

Downloads

Published

31-12-2020
CITATION

How to Cite

Chaipornjareansri, S. (2020). Some Best Proximity Point Results for \(\mathcal{MT}\)-Rational Cyclic Contractions in \(S\)-Metric Space. Communications in Mathematics and Applications, 11(4), 587–600. https://doi.org/10.26713/cma.v11i4.1413

Issue

Section

Research Article