FIXED POINT THEOREMS FOR MAPPINGS WHICH SATISFY (HRSC)-CONDITION
Nurcan Bilgili Güngör1*
1Amasya University, Amasya, Turkey
* Corresponding author: bilgilinurcan@gmail.com
Presented at the 4th International Symposium on Innovative Approaches in Engineering and Natural Sciences (ISAS WINTER-2019 (ENS)), Samsun, Turkey, Nov 22, 2019
SETSCI Conference Proceedings, 2019, 9, Page (s): 532-538 , https://doi.org/10.36287/setsci.4.6.151
Published Date: 22 December 2019
In 2008 Suzuki introduced C-condition for mappings which defined on a subset of a Banach space and presented fixed point theorems. And in 2010 Khan and Suzuki gave a reich type convergence theorem for generalized nonexpansive mappings in uniformly convex Banach space. Also in 2013 Karapinar introduced generalized C-conditions for mappings which defined on a subset of a Banach space and proved related fixed point theorems. And then in 2015 Thakur, Singh Thahur and Postolache proved fixed point theorems for mapping which satisfy RCSC-condition. In this paper fixed point theorems for mappings spaces which satisfy (HRSC)-condition are proved.
Keywords - fixed point , C-condition, nonexpansive mappings, uniformly convex Banach space
[1] F. E. Browder, Nonexpansive nonlinear operators in Banach space, Proc. Nat. Acad. Sci. USA 54 (1965)
1041-1044. MR0187120.
[2] D. Ghde, Zum Prinzip def kontraktiven Abbildung, Math. Nachr. 30 (1965) 251-258. MR0190718.
[3] E. Karapınar, K. Tas, Generalized (C)- conditions and related fixed point theorems, Computers and
Mathematics with Applications (2011), doi: 10.1016/j.camwa. 2011.04.035.
[4] E. Karapınar, Remarks on Suzuki (C)- condition, In: Dynamical Systems and Methods (2012), 227-243,
Springer.
[5] S. H. Khan, T. Suzuki, A Reich-type convergence theorem for generalized nonexpansive mappings in
uniformly convex Banach spaces, Nonlinear Analysis (2012), doi: 10.1016/ j.na. 2012.09.005.
[6] W. A. Kirk, A fixed point theorem for mappings which do not increase distances, Amer. Math. Monthly
72 (1965) 1004-1006. MR0189009.
[7] Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings,
Bull. Amer. Math. Soc. 73 (1967) 591-597.
[8] S. Reich, Weak convergence theorems for nonexpansive mappings in Banach space, Proc. Amer. Math.
Soc. 59 (1976) 65-71. MR0412909.
[9] T. Suzuki, Fixed point theorems and converges theorems and convergence theorems for some generalized
nonexpansive mappings, J. Math. Anal. Appl. 340 (2008) 1088-1095. MR2390912.
[10] D. Thakur, B. S. Thakur and M. Postolache, Convergence theorems for generalized nonexpansive mappings
in uniformly convex Banach spaces, Fixed Point Theory and Applications, (2015) 2015(1), 144.
|
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |