Proximal pairs and P-­KKM mappings

Document Type : Original Article

Authors

1 Department of Mathematics, Faculty of Science, Imam Khomeini International University, P. O. Box 34149-16818, Qazvin, Iran.

2 Department of Mathematics, College of Basic Science, Hamedan Branch, Islamic Azad University, Hamedan, Iran.

Abstract

We introduced a new class of multi-valued mappings, called P-KKM mappings, which generalized the notation
of R-KKM maps of Raj and Somasundaram [KKM-type theorem for best proximity points, Applied
Mathematics Letters, 25 (2012), 496-499] and appropriate to best proximity theory. An analog version of
KKM property and a common fixed point theorem is also proved.

Keywords

References

[1] M. A. Al-Thagha i, N. Shahzad, Best proximity sets and equilibrium pairs for a nite family of multimaps, Fixed
Point Theory Appl., 2008 (2008), 10 pages.
[2] M. A. Al-Thagha i, N. Shahzad, Best proximity pairs and equilibrium pairs for Kukutani multimaps, Nonlinear
Anal., 70 (2009), 1209-1216.
[3] A. Amini-Harandi, A. P. Farajzadeh, D. O'Regan, R. P. Agarwal, Best proximity pairs theorems for continuous
set-valued maps, Fixed Point Theory Appl., 2008 (2008), 9 pages.
[4] L. J. Lin, C. SH. Chuang and Z. T. Yu, Generalized KKM theorems and common fixed point theorems, Nonlinear
Anal., 74 (2011), 5591-5599.
[5] V. S. Raj, S. Somasundaram, KKM-type theorems for best proximity points, Appl. Math. Lett., 25 (2012), 496-
499.
[6] S. Sadiq Basha, Best proximity point theorems, J. Approx. Theory, 163 (2011), 1777-1781.
[7] S. Sadiq Basha, P. Veermani, Theorems for multifunctions with open ber, J. Approx. Theory, 103 (2000), 119-129.
Communications in Nonlinear Analysis
Volume 1, Issue 2
Winter and Spring 2016
Pages 37-41

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