Strong convergence and stability of Kirk-multistep-type iterative schemes for contractive-type operators
Tóm tắt
Từ khóa
Tài liệu tham khảo
Glowinski R, Le-Tallec P: Augmented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanics. SIAM, Philadelphia; 1989.
Haubruge S, Nguyen VH, Strodiot JJ: Convergence analysis and applications of the Glowinski-Le-Tallec splitting method for finding a zero of the sum of two maximal monotone operators. J. Optim. Theory Appl. 1998, 97: 645–673. 10.1023/A:1022646327085
Chugh R, Kumar V: Strong convergence of SP iterative scheme for quasi-contractive operators. Int. J. Comput. Appl. 2011, 31(5):21–27.
Chugh R: Stability of hybrid fixed point iterative algorithms of Kirk-Noor type in normed linear space for self and nonself operators. Int. J. Contemp. Math. Sci. 2012, 7(24):1165–1184.
Hussain N, Chugh R, Kumar V, Rafiq A: On the rate of convergence of Kirk-type iterative schemes. J. Appl. Math. 2012., 2012: Article ID 526503
Hussain N, Rafiq A, Damjanović B, Lazović R: On rate of convergence of various iterative schemes. Fixed Point Theory Appl. 2011., 2011: Article ID 45
Imoru CO, Olatinwo MO: On the stability of Picard and Mann iteration. Carpath. J. Math. 2003, 19: 155–160.
Ishikawa S: Fixed points by a new iteration method. Proc. Am. Math. Soc. 1974, 44: 147–150. 10.1090/S0002-9939-1974-0336469-5
Kirk WA: On successive approximations for nonexpansive mappings in Banach spaces. Glasg. Math. J. 1971, 12: 6–9. 10.1017/S0017089500001063
Noor MA: New approximation schemes for general variational inequalities. J. Math. Anal. Appl. 2000, 251: 217–229. 10.1006/jmaa.2000.7042
Phuengrattana W, Suantai S: On the rate of convergence of Mann, Ishikawa, Noor and SP-iterations for continuous functions on an arbitrary interval. J. Comput. Appl. Math. 2011, 235(9):3006–3014. 10.1016/j.cam.2010.12.022
Qing Y, Rhoades BE: Comments on the rate of convergence between Mann and Ishikawa iterations applied to Zamfirescu operators. Fixed Point Theory Appl. 2008., 2008: Article ID 387504
Rafiq A: On the convergence of the three-step iteration process in the class of quasi-contractive operators. Acta Math. Acad. Paedagog. Nyházi. 2006, 22: 305–309.
Rhoades BE, Soltuz SM: The equivalence between Mann-Ishikawa iterations and multi-step iteration. Nonlinear Anal. 2004, 58: 219–228. 10.1016/j.na.2003.11.013
Olatinwo MO: Some stability results for two hybrid fixed point iterative algorithms in normed linear space. Mat. Vesn. 2009, 61(4):247–256.
Berinde V: Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators. Fixed Point Theory Appl. 2004, 2: 97–105.
Chatterjea SK: Fixed point theorems. C. R. Acad. Bulgare Sci. 1972, 25(6):727–730.
Kannan R: Some results on fixed points. Bull. Calcutta Math. Soc. 1968, 10: 71–76.
Osilike MO: Stability results for Ishikawa fixed point iteration procedure. Indian J. Pure Appl. Math. 1995/1996, 26(10):937–941.
Zamfirescu T: Fixed point theorems in metric spaces. Arch. Math. 1972, 23: 292–298. 10.1007/BF01304884
Berinde V: On the stability of some fixed point procedures. Bul. Ştiinţ. - Univ. Baia Mare, Ser. B Fasc. Mat.-Inform. 2002, XVIII(1):7–14.
Berinde V: On the convergence of the Ishikawa iteration in the class of quasi-contractive operators. Acta Math. Univ. Comen. 2004, LXXIII(1):119–126.
Ostrowski AM: The round-off stability of iterations. Z. Angew. Math. Mech. 1967, 47: 77–81. 10.1002/zamm.19670470202
Harder AM, Hicks TL: Stability results for fixed point iteration procedures. Math. Jpn. 1988, 33(5):693–706.
Akewe, H: Approximation of fixed and common fixed points of generalized contractive-like operators. Ph.D. thesis, University of Lagos, Lagos, Nigeria (2010)
Berinde V: Iterative Approximation of Fixed Points. Editura Efemeride, Baia Mare; 2002.
Rhoades BE: Fixed point iteration using infinite matrices. Trans. Am. Math. Soc. 1974, 196: 161–176.
Rhoades BE: Comment on two fixed point iteration method. J. Math. Anal. Appl. 1976, 56: 741–750. 10.1016/0022-247X(76)90038-X
Rhoades BE: A comparison of various definition of contractive mapping. Trans. Am. Math. Soc. 1977, 226: 257–290.
Akewe H, Olaoluwa H: On the convergence of modified three-step iteration process for generalized contractive-like operators. Bull. Math. Anal. Appl. 2012, 4(3):78–86.
Rafiq A: A convergence theorem for Mann fixed point iteration procedure. Appl. Math. E-Notes 2006, 6: 289–293.
Olaleru JO, Akewe H: An extension of Gregus fixed point theorem. Fixed Point Theory Appl. 2007., 2007: Article ID 78628
Osilike MO, Udomene A: Short proofs of stability results for fixed point iteration procedures for a class of contractive-type mappings. Indian J. Pure Appl. Math. 1999, 30: 1229–1234.
Rhoades BE: Fixed point theorems and stability results for fixed point iteration procedures. Indian J. Pure Appl. Math. 1990, 21: 1–9.
Rhoades BE: Fixed point theorems and stability results for fixed point iteration procedures II. Indian J. Pure Appl. Math. 1993, 24(11):691–703.