Strong convergence theorems of one-step iterative scheme for a countable family of multivalued mappings in a Banach space

• Autorzy: Bunyawat A. , Suantai S.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we introduce a new one-step iterative scheme for finding a common fixed point of a countable family of multivalued mappings in a real uniformly convex Banach space. By using the best approximation operators, a necessary and sufficient condition for strong convergence of the proposed method is given. Moreover, we establish some strong convergence theorems of the proposed iterative scheme under some control conditions

Słowa kluczowe

EN

multivalued mappings; common fixed point; best approximation operators

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2014
• Tom: Nr 53
• Strony: 31--38
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Bunyawat A.

• Department of Mathematics Faculty of Science Chiang Mai University Chiang Mai 50200, Thailand

autor

Suantai S.

• Department of Mathematics Faculty of Science Chiang Mai University Chiang Mai 50200, Thailand

Bibliografia

• [1] Abbas M., Khan S.H., Khan A.R., Agarwal R.P., Common fixed points of two multivalued nonexpansive mappings by one-step iterative scheme, Applied Mathematics Letters, 24(2011), 97-102.
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• [3] Cholamjiak P., Cholamjiak W., Cho Y.J., Suantai S., Weak and strong convergence to common fixed points of a countable family of multi-valued mappings in Banach spaces, Thai Journal of Mathematics, 9(2011) 505-520.
• [4] Cholamjiak W., Suantai S., Approximation of common fixed points of two quasi-nonexpansive multi-valued maps in Banach spaces, Computers and Mathematics with Applications, 61(2011), 941-949.
• [5] Eslamian M., Abkar A., One-step iterative process for a finite family of multivalued mappings, Math. Comp. Model., 54(2011), 105-111.
• [6] Hussain N., Khan A.R., Applications of the best approximation operator to *-nonexpansive maps in Hilbert spaces, Numer. Funct. Anal. Optim., 24(2003), 327-338.
• [7] Nadler, Jr. S.B., Multi-valued contraction mappings, Pacific J. Mathematics, 30(1969), 475-488.
• [8] Schu J., Weak and strong convergence to fixed points of asymptotically non-expansive mappings, Bull. Austral. Math. Soc., 43(1991), 153-159.
• [9] Shahzad N., Zegeye H., On Mann and Ishikawa iteration schemes for multi-valued maps in Banach spaces, Nonlinear Analysis, 71(2009), 838-844.