Best proximity point theorems for $ \alpha^{+} F, (\theta-\phi )$-proximal contraction

Authors

  • Mohamed Rossafi Faculty of Sciences, Dhar El Mahraz University Sidi Mohamed Ben Abdellah, Fes,
  • Abdelkarim Kari

DOI:

https://doi.org/10.20956/j.v18i2.17994

Keywords:

proximity point, $ \alpha^{ } F$-proximal contraction, $ \alpha^{ } (\theta-\phi )$-proximal contraction

Abstract

In this paper, inspired by the idea of Suzuki type $ \alpha^{+} F$-proximal contraction in metric spaces, we prove a new existence of best proximity point for Suzuki type $ \alpha^{+} F$-proximal contraction and $ \alpha^{+} (\theta-\phi )$-proximal contraction defined on a closed subset of a complete metric space. Our theorems extend, generalize, and improve many existing results.

Downloads

Download data is not yet available.

References

bibitem{KI} A. A. Eldred, W. A. Kirk, P. Veeramani, Proximal normal structure and relatively nonexpansive mappings. Stud. Math. 171, 283–293 (2005).

bibitem{HS} N. Hussain, M. Hezarjaribi, M. Kutbi, P. Salimi, Best proximity results for Suzuki and convex type contractions. Fixed Point Theory Appl 2016, 14 (2016). https://doi.org/10.1186/s13663-016-0499-2

bibitem{JK} M. Jleli, B. Samet : A new generalization of the Banach contraction principale. J. Inequal. Appl.$2014$. Article ID $38$. Appl. Anal., $2014(2014),11$ pages.

bibitem{RJ} V. S. Raj, A best proximity point theorem for weakly contractive non-self-mappings. Nonlinear Anal. 74, 4804–4808 (2011).

bibitem{ZHN} J. Zhang, Y. Su, Q. Cheng, A note on ‘A best proximity point theorem for Geraghty-contractions’. Fixed Point Theory Appl 2013, 99 (2013). https://doi.org/10.1186/1687-1812-2013-99

bibitem{ZH} D. Zheng, Z. Cai, P. Wang, New fixed point theorems for ($theta-phi $)-contraction in complete metric spaces. J. Nonlinear Sci. Appl. (2017); 10(5):2662-2670.

bibitem{WR} D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces.

Fixed Point Theory Appl 2012, 94 (2012).

Downloads

Published

2022-01-01

How to Cite

Rossafi, M., & Kari, A. (2022). Best proximity point theorems for $ \alpha^{+} F, (\theta-\phi )$-proximal contraction. Jurnal Matematika, Statistika Dan Komputasi, 18(2), 181-197. https://doi.org/10.20956/j.v18i2.17994

Issue

Section

Research Articles

Most read articles by the same author(s)