On the existence of coupled best proximity point and best proximity point for Suzuki type \(\alpha^+-\theta-\)proximal multivalued mappings
-
1962
Downloads
-
3786
Views
Authors
Haiming Liu
- School of Mathematics, Mudanjiang Normal University, Mudanjiang, 157011, P. R. China.
Xiaoming Fan
- School of Mathematical Sciences, Harbin Normal University, Harbin, 150025, P. R. China.
Lixu Yan
- Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, P. R. China.
Zhigang Wang
- School of Mathematical Sciences, Harbin Normal University, Harbin, 150025, P. R. China.
Abstract
Following the study for the best proximity points of the Suzuki type \(\alpha^+-\theta\)-proximal single-valued mappings given by
Hussain et al., we deal with the Suzuki type \(\alpha^+-\theta\)-proximal multivalued mappings satisfying generalized conditions of existence,
some novel existence results of best proximity point and coupled best proximity points are established. Our results improve and
extend some recent results in the previous work.
Share and Cite
ISRP Style
Haiming Liu, Xiaoming Fan, Lixu Yan, Zhigang Wang, On the existence of coupled best proximity point and best proximity point for Suzuki type \(\alpha^+-\theta-\)proximal multivalued mappings, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 4, 1801--1819
AMA Style
Liu Haiming, Fan Xiaoming, Yan Lixu, Wang Zhigang, On the existence of coupled best proximity point and best proximity point for Suzuki type \(\alpha^+-\theta-\)proximal multivalued mappings. J. Nonlinear Sci. Appl. (2017); 10(4):1801--1819
Chicago/Turabian Style
Liu, Haiming, Fan, Xiaoming, Yan, Lixu, Wang, Zhigang. "On the existence of coupled best proximity point and best proximity point for Suzuki type \(\alpha^+-\theta-\)proximal multivalued mappings." Journal of Nonlinear Sciences and Applications, 10, no. 4 (2017): 1801--1819
Keywords
- Suzuki type \(\alpha^+-\theta\)-proximal multivalued mappings
- coupled best proximity point
- best proximity point.
MSC
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. Di Bari, T. Suzuki, C. Vetro, Best proximity points for cyclic Meir-Keeler contractions, Nonlinear Anal., 69 (2008), 3790–3794.
-
[3]
A. A. Eldred, W. A. Kirk, P. Veeramani, Proximal normal structure and relatively nonexpansive mappings, Studia Math., 171 (2005), 283–293.
-
[4]
A. A. Eldred, P. Veeramani, Existence and convergence of best proximity points, J. Math. Anal. Appl., 323 (2006), 1001–1006.
-
[5]
K. Fan,/ , Extensions of two fixed point theorems of F. E. Browder, Math. Z., 112 (1969), 234–240.
-
[6]
N. Hussain, M. Hezarjaribi, M. A. Kutbi, P. Salimi, Best proximity results for Suzuki and convex type contractions, Fixed Point Theory Appl., 2016 (2016), 20 pages.
-
[7]
M. Jleli, B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl., 2014 (2014), 8 pages.
-
[8]
M. Jleli, B. Samet, Remarks on the paper: Best proximity point theorems: an exploration of a common solution to approximation and optimization problems, Appl. Math. Comput., 228 (2014), 366–370.
-
[9]
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), 11 pages.
-
[10]
C. Mongkolkeha, P. Kumam, Best proximity point theorems for generalized cyclic contractions in ordered metric spaces, J. Optim. Theory Appl., 155 (2012), 215–226.
-
[11]
J. Nantadilok, Coupled best proximity point theorems for \(\alpha-\psi\)-proximal contractive multimaps, Fixed Point Theory Appl., 2015 (2015), 14 pages.
-
[12]
V. S. Raj, A best proximity point theorem for weakly contractive non-self-mappings, Nonlinear Anal., 74 (2011), 4804– 4808.
-
[13]
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.
-
[14]
S. Reich, Approximate selections, best approximations, fixed points, and invariant sets, J. Math. Anal. Appl., 62 (1978), 104–113.
-
[15]
S. Sadiq Basha, Best proximity points: global optimal approximate solutions, J. Global Optim., 49 (2011), 15–21.
-
[16]
S. Sadiq Basha, Best proximity point theorems, J. Approx. Theory, 163 (2011), 1772–1781.
-
[17]
S. Sadiq Basha, Best proximity point theorems: an exploration of a common solution to approximation and optimization problems, Appl. Math. Comput., 218 (2012), 9773–9780.
-
[18]
S. Sadiq Basha, N. Shahzad, R. Jeyaraj, Common best proximity points: global optimization of multi-objective functions, Appl. Math. Lett., 24 (2011), 883–886.
-
[19]
S. Sadiq Basha, P. Veeramani, Best proximity pair theorems for multifunctions with open fibres, J. Approx. Theory, 103 (2000), 119–129.
-
[20]
B. Samet, C. Vetro, P. Vetro, Fixed point theorems for \(\alpha\psi\)-contractive type mappings, Nonlinear Anal., 75 (2012), 2154–2165.
-
[21]
V. M. Sehgal, S. P. Singh, A generalization to multifunctions of Fan’s best approximation theorem, Proc. Amer. Math. Soc., 102 (1988), 534–537.
-
[22]
V. M. Sehgal, S. P. Singh, A theorem on best approximations, Numer. Funct. Anal. Optim., 10 (1989), 181–184.
-
[23]
W. Sintunavarat, P. Kumam, Coupled best proximity point theorem in metric spaces, Fixed Point Theory Appl., 2012 (2012), 16 pages.
-
[24]
T. Suzuki, The existence of best proximity points with the weak P-property, Fixed Point Theory Appl., 2013 (2013), 6 pages.
-
[25]
Z.-G. Wang, H.-L. Li, Fixed point theorems and endpoint theorems for (\(\alpha,\psi\))-Meir-Keeler-Khan multivalued mappings, Fixed Point Theory Appl., 2016 (2016), 18 pages.
-
[26]
K. Włodarczyk, R. Plebaniak, A. Banach, Best proximity points for cyclic and noncyclic set-valued relatively quasiasymptotic contractions in uniform spaces, Nonlinear Anal., 70 (2009), 3332–3341.