ABSORBING PAIRS FACILITATING COMMON FIXED POINT THEOREMS FOR LIPSCHITZIAN TYPE MAPPINGS IN SYMMETRIC SPACES Gopal, Dhananjay; Hasan, Mohammad; Imdad, Mohammad;
The purpose of this paper is to improve certain results proved in a recent paper of Soliman et al. . These results are the outcome of utilizing the idea of absorbing pairs due to Gopal et al.  as opposed to two conditions namely: weak compatibility and the peculiar condition initiated by Pant  to ascertain the common fixed points of Lipschitzian mappings. Some illustrative examples are also furnished to highlight the realized improvements.
Some Integral Type Fixed Point Theorems for Non-Self-Mappings Satisfying Generalized(ψ,φ)-Weak Contractive Conditions in Symmetric Spaces, Abstract and Applied Analysis, 2014, 2014, 1
Fixed point theorems for non-self mappings in symmetric spaces under φ-weak contractive conditions and an application to functional equations in dynamic programming, Applied Mathematics and Computation, 2014, 227, 469
Some Nonunique Common Fixed Point Theorems in Symmetric Spaces through Property, International Journal of Mathematics and Mathematical Sciences, 2013, 2013, 1
M. Aamri and D. El Moutawakil, Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl. 270 (2002), no. 1, 181-188.
A. Aliouche, A common fixed point theorem for weakly compatible mappings in symmet- ric spaces satisfying a contractive condition of integral type, J. Math. Anal. Appl. 322 (2006), no. 2, 796-802.
D. K. Burke, Cauchy sequences in semimetric spaces, Proc. Amer. Math. Soc. 33 (1972), 161-164.
S. H. Cho, G. Y. Lee, and J. S. Bae, On coincidence and fixed point theorems in symmetric spaces, Fixed Point Theory Appl. 2008 (2008), Art. ID 562130, 9 pp.
F. Galvin and S. D. Shore, Completeness in semimetric spaces, Pacific. J. Math. 113 (1984), no. 1, 67-75.
D. Gopal, R. P. Pant, and A. S. Ranadive, Common fixed point of absorbing maps, Bull. Marathwada Math. Soc. 9 (2008), no. 1, 43-48.
T. L. Hicks and B. E. Rhoades, Fixed point theory in symmetric spaces with applications to probabilistic spaces, Nonlinear Anal. 36 (1999), no. 3, Ser. A: Theory Methods, 331- 344.
M. Imdad, J. Ali, and L. Khan, Coincidence and fixed points in symmetric spaces under strict contractions, J. Math. Anal. Appl. 320 (2006), no. 1, 352-360.
M. Imdad and A. H. Soliman, Some Common fixed point theorems for a pair of tangen- tial mappings in symmetric spaces, Appl. Math. Lett. 23 (2010), no. 4, 351-355.
G. Jungck, Compatible mappings and common fixed points, Internat. J. Math. Math. Sci. 9 (1986), no. 4, 771-779.
G. Jungck, Common fixed points for noncontinuous nonself maps on non-metric spaces, Far East J. Math. Sci. 4 (1996), no. 2, 199-215.
G. Jungck and B. E. Rhoades, Fixed point theorems for occasionally weakly compatible mappings, Fixed Point Theory 7 (2006), no. 2, 287-296.
Y. Liu, Jun Wu and Z. Li, Common fixed points of singlevalued and multivalued maps, Int. J. Math. Math. Sci. 2005 (2005), no. 19, 3045-3055.
R. P. Pant, Common fixed points of noncommuting mappings, J. Math. Anal. Appl. 188 (1994), no. 2, 436-440.
R. P. Pant, Common fixed points of Lipschitz type mapping pairs, J. Math. Anal. Appl. 248 (1999), no. 1, 280-283.
R. P. Pant and V. Pant, Common fixed points under strict contractive conditions, J. Math. Anal. Appl. 248 (2000), no. 1, 327-332.
V. Pant, Common fixed points under Lipschitz type conditions, Bull. Korean Math. Soc. 45 (2008), no. 3, 467-475.
K. P. R. Sastry and I. S. R. Krishna Murthy, Common fixed points of two partially commuting tangential selfmaps on a metric space, J. Math. Anal. Appl. 250 (2000), no. 2, 731-734.
S. L. Singh and A. Kumar, Fixed point theorems for Lipschitz type maps, Riv. Math. Univ. Parma, (7) 3 (2004), 25-34.
A. H. Soliman, M. Imdad, and M. Hasan, Proving unified common fixed point theorems via common property (E-A) in symmetric spaces, Commun. Korean Math. Soc. 25 (2010), no. 4, 629-645.
W. A. Wilson, On semi-metric spaces, Amer. J. Math. 53 (1931), no. 2, 361-373.