Convergence analysis of Agarwal et al. iterative scheme for Lipschitzian hemicontractive mappings

Springer Science and Business Media LLC - Tập 2013 - Trang 1-6 - 2013
Shin Min Kang1, Arif Rafiq2, Faisal Ali3, Young Chel Kwun4
1Department of Mathematics and RINS, Gyeongsang National University, Jinju, Korea
2Department of Mathematics, Lahore Leads University, Lahore, Pakistan
3Centre for advanced studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, Pakistan
4Department of Mathematics, Dong-A University, Pusan, Korea

Tóm tắt

In this paper, we establish strong convergence for the Agarwal et al. iterative scheme associated with Lipschitzian hemicontractive mappings in Hilbert spaces. MSC:47H10, 47J25.

Tài liệu tham khảo

Browder FE: Nonlinear Operators and Nonlinear Equations of Evolution in Banach Spaces, Nonlinear Functional Analysis. Am. Math. Soc., Providence; 1976. Browder FE, Petryshyn WV: Construction of fixed points of nonlinear mappings in Hilbert spaces. J. Math. Anal. Appl. 1967, 20: 197–228. 10.1016/0022-247X(67)90085-6 Ishikawa S: Fixed point by a new iteration method. Proc. Am. Math. Soc. 1974, 4: 147–150. 10.2307/2039245 Agarwal RP, O’Regan D, Sahu DR: Iterative construction of fixed points of nearly asymptotically nonexpansive mappings. J. Nonlinear Convex Anal. 2007, 8: 61–79. Xu HK: Inequalities in Banach spaces with applications. Nonlinear Anal. 1991, 16: 1127–1138. 10.1016/0362-546X(91)90200-K Liu Z, Feng C, Ume JS, Kang SM: Weak and strong convergence for common fixed points of a pair of nonexpansive and asymptotically nonexpansive mappings. Taiwan. J. Math. 2007, 11: 27–42.