A note on the theorem of V. Berinde

• Autorzy: Rafiq A.
• Języki publikacji: EN

Abstrakty

EN

V. Berinde presented convergence theorem [1] in normed spaces for Ishikawa iterations associated with Zamfirescue operators, which is an extension of the theorem of Rhoades [11]. In this note, we point out some misprints in the calculations and established new inequalities involved in the proof of the theorem. Consequently we give better estimation in proving the convergence theorem.

Słowa kluczowe

EN

contractive condition; strong convergence; iteration process

PL

warunek przeciwny; silna zbieżność; proces iteracji

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2006
• Tom: Vol. 39, nr 4
• Strony: 863--867
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Rafiq A.

• Comsats Institute of Information Technology Islamabad, Pakistan,

Bibliografia

• [1] V. Berinde, A convergence theorem for some mean value fixed point iteration procedures, Demonstratio Math. 38 (1) (2005), 177–184.
• [2] S. K. Chatterjea, Fixed point theorems, C.R. Acad. Bulgare Sci. 25 (1972), 727–730.
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• [4] R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc. 10 (1968), 71–76.
• [5] R. Kannan, Some results on fixed points III , Fund. Math. 70 (1971), 169–177.
• [6] R. Kannan, Construction of fixed points of class of nonlinear mappings, J. Math. Anal. Appl. 41 (1973), 430–438.
• [7] L. S. Liu, Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces, J. Math. Anal. Appl. 194 (1) (1995), 114–125.
• [8] W. R. Mann, Mean value methods in iterations, Proc. Amer. Math. Soc. 4 (1953), 506-510.
• [9] M. O. Osilike, Short proofs of stability results for fixed point iteration procedures for a class of contractive-type mappings, Indian J. Pure and Appl.Math. 30 (12) (1999), 1229–1234.
• [10] M. O. Osilike, Stability results for fixed point iteration procedures, J. Nigerian Math. Soc. 14/15 (1995/1996), 17–29.
• [11] B. E. Rhoades, Fixed point iteration using infinite matrices, Trans. Amer. Math. Soc. 196 (1974), 161–176.
• [12] B. E. Rhoades, Comments on two fixed point iteration method, J. Math. Anal. Appl. 56 (2) (1976), 741–750.
• [13] W. Takahashi, Iterative methods for approximation of fixed points and thier applications, J. Oper. Res. Soc. Jpn., 43 (1) (2000), 87–108.
• [14] W. Takahashi and T. Tamura, Convergence theorems for a pair of nonexpansive mappings, J. Convex Analysis, 5(1) (1995), 45–58.
• [15] Y. Xu, Ishikawa and Mann iteration process with errors for nonlinear strongly accretive operator equations, J. Math. Anal. Appl. 224 (1998), 91–101.
• [16] T. Zamfirescu, Fix point theorems in metric spaces, Arch. Math.(Basel) 23 (1972), 292–298.