Best proximity and coupled best proximity results for Suzuki type proximal multivalued mappings

Volume 9, Issue 6, pp 4754--4771 http://dx.doi.org/10.22436/jnsa.009.06.113

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 1673 Downloads
• 2903 Views

Authors

Xuelian Xu - School of Mathematical Sciences, Harbin Normal University, Harbin, 150025, P. R. China. Xiaoming Fan - School of Mathematical Sciences, Harbin Normal University, Harbin, 150025, P. R. China. Haiming Liu - School of Mathematics, Mudanjiang Normal University, Mudanjiang, 157011, P. R. China.

Abstract

We extend and generalize the best proximity results for Suzuki type \(\alpha^+-\psi\)-proximal single valued mappings given by Hussain et al. Some novel best proximity results and coupled best proximity results are presented for Suzuki type \(\alpha^+-\psi\)-proximal multivalued mappings satisfying generalized conditions of existence.

Share and Cite

Keywords

• Suzuki type \(\alpha^+-\psi\)-proximal multivalued mappings
• coupled best proximity point
• best proximity point.

MSC

•  47H09
•  54H25

References

• [1] A. Abkar, M. Gabeleh, Best proximity points for cyclic mappings in ordered metric spaces, J. Optim. Theory Appl., 151 (2011), 418--424


• [2] C. E. Chidume, H. Zegeye, Approximate fixed point sequences and convergence theorems for Lipschitz pseudocontractive maps, Proc. Amer. Math. Soc., 132 (2004), 834--840


• [3] C. Di Bari, T. Suzuki, C. Vetro, Best proximity points for cyclic Meir-Keeler contractions, Nonlinear Anal., 69 (2008), 3790--3794


• [4] A. A. Eldred, W. A. Kirk, P. Veeramani, Proximal normal structure and relatively nonexpansive mappings, Studia Math., 171 (2005), 283--293


• [5] A. A. Eldred, P. Veeramani, Existence and convergence of best proximity points, J. Math. Anal. Appl., 323 (2006), 1001--1006


• [6] K. Fan, Extensions of two fixed point theorems of F. E. Browder, Math. Z., 112 (1969), 234--240


• [7] N. Hussain, M. Hezarjaribi, M. A. Kutbi, P. Salimi, Best proximity results for Suzuki and convex type contractions, Fixed Point Theory and Appl., 2016 (2016), 20 pages


• [8] N. Hussain, M. A. Kutbi, P. Salimi, Best proximity point results for modified \(\alpha-\psi\)-proximal rational contractions, Abstr. Appl. Anal., 2013 (2013), 14 pages


• [9] N. Hussain, A. Latif, P. Salimi, Best proximity point results for modified Suzuki \(\alpha-\psi\)-proximal contractions, Fixed Point Theory and Appl., 2014 (2014), 16 pages


• [10] M. S. Khan, M. Swaleh, S. Sessa, Fixed point theorems by altering distances between the points, Bull. Austral. Math. Soc., 30 (1984), 1--9


• [11] A. Latif, M. Eshaghi Gordji, E. Karapınar, W. Sintunavarat, Fixed point results for generalized (\(\alpha,\psi\) )-Meir-Keeler contractive mappings and applications, J. Inequal. Appl., 2014 (2014), 10 pages


• [12] A. Latif, M. Hezarjaribi, P. Salimi, N. Hussain, Best proximity point theorems for \(\alpha-\psi\)-proximal contractions in intuitionistic fuzzy metric spaces, J. Inequal. Appl., 2014 (2014), 19 pages


• [13] C. Mongkolkeha, P. Kumam, Best proximity point theorems for generalized cyclic contractions in ordered metric spaces, J. Optim. Theory Appl., 155 (2012), 215--226


• [14] J. Nantadilok, Coupled best proximity point theorems for \(\alpha-\psi\)-proximal contractive multimaps, Fixed Point Theory and Appl., 2015 (2015), 14 pages


• [15] V. S. Raj, A best proximity point theorem for weakly contractive non-self-mappings, Nonlinear Anal., 74 (2011), 4804--4808


• [16] S. Reich, Approximate selections, best approximations, fixed points, and invariant sets, J. Math. Anal. Appl., 62 (1978), 104--113


• [17] N. Redjel, A. Dehici, E. Karapınar, I. M. Erhan, Fixed point theorems for (\(\alpha,\psi\))-Meir-Keeler-Khan mappings, J. Nonlinear Sci. Appl., 8 (2015), 955--964


• [18] B. Samet, C. Vetro, P. Vetro, Fixed point theorems for \(\alpha\psi\)-contractive type mappings, Nonlinear Anal., 75 (2012), 2154--2165


• [19] V. M. Sehgal, S. P. Singh, A generalization to multifunctions of Fan's best approximation theorem, Proc. Amer. Math. Soc., 102 (1988), 534--537


• [20] V. M. Sehgal, S. P. Singh, A theorem on best approximations, Numer. Funct. Anal. Optim., 10 (1989), 181--184


• [21] W. Sintunavarat, P. Kumam, Coupled best proximity point theorem in metric spaces, Fixed Point Theory and Appl., 2012 (2012), 16 pages


• [22] T. Suzuki, The existence of best proximity points with the weak P-property, Fixed Point Theory and Appl., 2013 (2013), 6 pages


• [23] Z. Wang, H. Li, Fixed point theorems and endpoint theorems for (\(\alpha,\psi\))-Meir-Keeler-Khan multivalued mappings, Fixed Point Theory and Appl., 2016 (2016), 18 pages


• [24] K. Wodarczyk, R. Plebaniak, A. Banach, Best proximity points for cyclic and noncyclic set-valued relatively quasi-asymptotic contractions in uniform spaces, Nonlinear Anal., 70 (2009), 3332--3342