Some stability results for Picard iterative process in uniform space

Some stability results for Picard iterative process in uniform space

Автор: Olatinwo M.O.

Журнал: Владикавказский математический журнал @vmj-ru

Статья в выпуске: 4 т.12, 2010 года.

Бесплатный доступ

We prove some stability results for Picard iteration in uniform space by introducing the concept of an M_e-distance as well as using some contractive conditions. Our results generalize, extend and improve some earlier results.

Picard iteration, uniform space, contractive conditions.

Короткий адрес: https://sciup.org/14318329

IDR: 14318329

Список литературы Some stability results for Picard iterative process in uniform space

  • Aamri M., Moutawakil D. E. Common fixed point theorems for E-contractive or E-expansive maps in uniform spaces//Acta Math. Acad. Paedagogicae Nyiregyhaziensis.-2004.-Vol. 20.-P. 83-91.
  • Banach S. Sur les operations dans les ensembles abstraits et leur applications aux equations integrales//Fund. Math.-1922.-Vol. 3.-P. 133-181.
  • Berinde V. On the stability of some fixed point procedures//Bul. Stiint. Univ. Baia Mare. Ser. B, Matematica-Informatica.-2002.-Vol. 18, № 1.-P. 7-14.
  • Berinde V. Iterative approximation of fixed points.-Berlin: Springer-Verlag, 2007.-325 p.
  • Bourbaki N. Elements de mathematique. Fas. II. Livre III: Topologie generale (Chapter 1: Structures topologiques), (Chapter 2: Structures uniformes). Quatrieme Edition. Actualites Scientifiques et Industrielles, № 1142, Hermann, Paris (1965).
  • Ciric Lj. B. A Generalization of Banach's contraction principle//Proc. Amer. Math. Soc.-1974.-Vol. 45.-P. 267-273.
  • Ciric Lj. B. Some recent results in metrical fixed point theory.-Beograd: University of Belgrade, 2003.
  • Harder A. M., Hicks T. L. Stability results for fixed point iteration procedures//Math. Japonica.-Vol. 33, № 5.-P. 693-706.
  • Imoru C. O., Olatinwo M. O. On the stability of Picard and Mann iteration processes//Carp. J. Math.-2003.-Vol. 19, № 2.-P. 155-160.
  • Imoru C. O., Olatinwo M. O., Owojori O. O. On the stability results for Picard and Mann iteration procedures//J. Appl. Funct. Differ. Equ.-2006.-Vol. 1, № 1.-P. 71-80.
  • Olatinwo M. O., Owojori O. O., Imoru C. O. Some stability results on Krasnoselskij and Ishikawa fixed point iteration procedures//J. Math. Stat.-2006.-Vol. 2, № 1.-P. 360-362.
  • Olatinwo M. O., Owojori O. O., Imoru C. O. Some stability results for fixed point iteration processes//Aus. J. Math. Anal. Appl.-2006.-Vol. 3, № 2.-P. 1-7.
  • Olatinwo M. O. Some stability and strong convergence results for the Jungck-Ishikawa iteration process//Creative Math. & Inf.-2008.-Vol. 17.-P. 33-42.
  • Olatinwo M. O. Some stability results for two hybrid fixed point iterative algorithms of Kirk-Ishikawa and Kirk-Mann type//J. Adv. Math. Studies.-2008.-Vol. 1, № 1-2.-P. 87-96.
  • Olatinwo M. O. Some unifying results on stability and strong convergence for some new iteration processes//Acta Math. Academiae Paedagogicae Nyiregyhaziensis.-2009.-Vol. 25, № 1.-P. 105-118.
  • Olatinwo M. O. An extension of some common fixed point theorems for selfmappings in uniform space//J. of Concrete and Appl. Math.-2009.-Vol. 7, № 2.-P. 179-186.
  • Jachymski J. R. An extension of A. Ostrowski's theorem on the round-off stability of iterations//Aequ. Math.-1997.-Vol. 53.-P. 242-253.
  • Osilike M. O. Some stability results for fixed point iteration procedures//J. Nigerian Math. Soc.-1995.-Vol. 14-15.-P. 17-29.
  • 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.-1999.-Vol. 30, № 12.-P. 1229-1234.
  • Ostrowski A. M. The round-off stability of iterations//Z. Angew. Math. Mech.-1967.-Vol. 47.-P. 77-81.
  • Rhoades B. E. Fixed point theorems and stability results for fixed point iteration procedures//Indian J. Pure Appl. Math.-1990.-Vol. 21, № 1.-P. 1-9.
  • Rhoades B. E. Some fixed point iteration procedures//Int. J. Math. Math. Sci.-1991.-Vol. 14, № 1.-P. 1-16.
  • Rhoades B. E. Fixed point theorems and stability results for fixed point iteration procedures II//Indian J. Pure Appl. Math.-1993.-Vol. 24, № 11.-P. 691-703.
  • Rhoades B. E. A comparison of various definitions of contractive mappings//Trans. Amer. Math. Soc.-1977.-Vol. 226.-P. 257-290.
  • Rus I. A. Generalized contractions and applications.-Cluj Napoca: Cluj Univ. Press, 2001.
  • Zamfirescu T. Fix point theorems in metric spaces//Arch. Math.-1972.-Vol. 23.-P. 292-298.}
  • Zeidler E. Nonlinear functional analysis and its applications, fixed-point theorems I.-New York: Springer-Verlag, 1986.
Еще
Статья научная
QR-код для установки приложения SciUp Наведите камеру и скачайте бесплатное приложение SciUp