Some stability theorems for some iteration processes

C. O. Imoru; Memudu Olaposi Olatinwo

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2006)

  • Volume: 45, Issue: 1, page 81-88
  • ISSN: 0231-9721

Abstract

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In this paper, we obtain some stability results for Picard and Mann iteration processes in metric space and normed linear space respectively, using two different contractive definitions which are more general than those of Harder and Hicks [4], Rhoades [10, 11], Osilike [8], Osilike and Udomene [9], Berinde [1, 2], Imoru and Olatinwo [5] and Imoru et al [6].Our results are generalizations of some results of Harder and Hicks [4], Rhoades [10, 11], Osilike [8], Osilike and Udomene [9], Berinde [1, 2], Imoru and Olatinwo [5] and Imoru et al [6].

How to cite

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Imoru, C. O., and Olatinwo, Memudu Olaposi. "Some stability theorems for some iteration processes." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 45.1 (2006): 81-88. <http://eudml.org/doc/32515>.

@article{Imoru2006,
abstract = {In this paper, we obtain some stability results for Picard and Mann iteration processes in metric space and normed linear space respectively, using two different contractive definitions which are more general than those of Harder and Hicks [4], Rhoades [10, 11], Osilike [8], Osilike and Udomene [9], Berinde [1, 2], Imoru and Olatinwo [5] and Imoru et al [6].Our results are generalizations of some results of Harder and Hicks [4], Rhoades [10, 11], Osilike [8], Osilike and Udomene [9], Berinde [1, 2], Imoru and Olatinwo [5] and Imoru et al [6].},
author = {Imoru, C. O., Olatinwo, Memudu Olaposi},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {stability results; Picard and Mann iteration processes; stability; Picard iteration process; Mann iteration process},
language = {eng},
number = {1},
pages = {81-88},
publisher = {Palacký University Olomouc},
title = {Some stability theorems for some iteration processes},
url = {http://eudml.org/doc/32515},
volume = {45},
year = {2006},
}

TY - JOUR
AU - Imoru, C. O.
AU - Olatinwo, Memudu Olaposi
TI - Some stability theorems for some iteration processes
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2006
PB - Palacký University Olomouc
VL - 45
IS - 1
SP - 81
EP - 88
AB - In this paper, we obtain some stability results for Picard and Mann iteration processes in metric space and normed linear space respectively, using two different contractive definitions which are more general than those of Harder and Hicks [4], Rhoades [10, 11], Osilike [8], Osilike and Udomene [9], Berinde [1, 2], Imoru and Olatinwo [5] and Imoru et al [6].Our results are generalizations of some results of Harder and Hicks [4], Rhoades [10, 11], Osilike [8], Osilike and Udomene [9], Berinde [1, 2], Imoru and Olatinwo [5] and Imoru et al [6].
LA - eng
KW - stability results; Picard and Mann iteration processes; stability; Picard iteration process; Mann iteration process
UR - http://eudml.org/doc/32515
ER -

References

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  1. Berinde V., On the Stability of Some Fixed Point Procedures, Bul. Stiint. Univ. Baia Mare, Ser. B, Matematica–Informatica 18, 1 (2002), 7–14. Zbl1031.47030MR2014277
  2. Berinde V., Iterative Approximation of Fixed Points, Editura Efemeride (2002). Zbl1212.26040MR1995230
  3. Berinde V., A priori and A posteriori Error Estimates for a class of ϕ -contractions, Bulletins for Applied & Computing Math. (1999), 183–192. (1999) 
  4. Harder A. M., Hicks T. L., Stability Results for Fixed Point Iteration Procedures, Math. Japonica 33, 5 (1988), 693–706. (1988) Zbl0655.47045MR0972379
  5. Imoru C. O., Olatinwo M. O., On the Stability of Picard and Mann Iteration Processes, Carpathian J. Math. 19, 2 (2003), 155–160. Zbl1086.47512MR2069844
  6. Imoru C. O., Olatinwo M. O., Owojori O. O., On the Stability Results for Picard and Mann Iteration Procedures, J. Appl. Funct. Diff. Eqns. 1, 1 (2006), 71–80. MR2293939
  7. Jachymski J. R., An Extension of A. Ostrowski’s Theorem On the Round-off Stability of Iterations, Aequationes Math. 53 (1997), 242–253. (1997) Zbl0885.47023MR1444177
  8. Osilike M. O., Some Stability Results for Fixed Point Iteration Procedures, J. Nigerian Math. Soc. 14/15 (1995), 17–29. (1995) MR1775011
  9. Osilike M. O., Udomene A., Short Proofs of Stability Results for Fixed Point Iteration Procedures for a Class of Contractive-type Mappings, Indian J. Pure Appl. Math. 30, 2 (1999), 1229–1234. (1999) Zbl0955.47038MR1729212
  10. Rhoades B. E., Fixed Point Theorems and Stability Results for Fixed Point Iteration Procedures, Indian J. Pure Appl. Math. 21, 1 (1990), 1–9. (1990) Zbl0692.54027MR1048010
  11. Rhoades B. E., Fixed Point Theorems and Stability Results for Fixed Point Iteration Procedures II, Indian J. Pure Appl. Math. 24, 11 (1993), 691–703. (1993) Zbl0794.54048MR1251180
  12. Rhoades B. E., Some Fixed Point Iteration Procedures, Internat. J. Math. and Math. Sci. 14, 1 (1991), 1–16. (1991) Zbl0716.47030MR1087396
  13. Zeidler E.: Nonlinear Functional Analysis, its Applications, Fixed-Point Theorems I., Springer-Verlag, New York, , 1986. (1986) MR0816732

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