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Year 2014, Volume: 27 Issue: 1, 653 - 658, 28.03.2014

Abstract

References

  • Aamri, M., Bennani, S., El Moutawakil, D., “Fixed points and variational principle in uniform spaces”, Siberian Electronic Mathematical Reports, 3: 137– 142 (2006).
  • Aamri, M., El Moutawakil, D., “Common Fixed Point Theorems for E-contractive or E-expansive Maps in Uniform Spaces”, Acta Math. Acad. Paedagog. Nyh´azi (N.S.), 20(1): 83-91(2004).
  • Berinde, V., “Iterative Approximation of Fixed Points”, Editura Efemeride, Baia Mare, (2002).
  • Berinde, V., “Contractii Generalizate si Aplicatii”, vol. 22, Editura Cub Press, Baia Mare, (1997).
  • Bourbaki, N., “´E l´ements de math´ematique. Fasc. II. Livre III: Topologie g´en´erale. Chapitre 1: Structures topologiques. Chapitre 2: Structures uni- formes”, Scientifiques et Industrielles, No. 1142, Hermann, Paris, (1965). ´edition., Actualit´es
  • Jachymski, J., “Fixed Point Theorems for Expansive Mappings”, Math. Japon., 42(1):131-136(1995).
  • Kada, O., Suzuki, T., Takahashi, W., “Nonconvex Minimization Theorems and Fixed Point Theorems in Complete Metric Spaces”, Math. Japon., 44(2): 381-391(1996).
  • Karapnar, E., “Fixed point theory for cyclic weak φ-contraction”, Appl.Math. Lett., 24(6): 822-825 (2011).
  • Karap nar, E., Sadarangani, K., “Fixed point theory for cyclic (φ−
  • ψ)-contractions”, Fixed Point Theory
  • 1186/1687-1812-2011-69. 69, (2011) doi:
  • Kirk, W.A., Srinivasan, P.S., Veeramani, P., “Fixed points for mappings satisfying cyclical weak contractive conditions”, Fixed Point Theory, 4(1): 79–89(2003).
  • Pacurar, M., Rus, I.A., “Fixed point theory for cyclic ϕ-contractions”, Nonlinear Amal., 72: 1181- 1187(2010).
  • Rhoades, B.E., “A Comparison of Various Definitions of Contractive Mappings”, Trans. Amer. Math. Soc., 226: 257-290 (1977). [13] Rus, I.A., “Generalized Contractions and Applications”, Cluj University Press, Cluj-Napoca, (2001).
  • Rus, I.A., “Cyclic representations and fixed points”, Ann. T. Popoviciu, Seminar Funct. Eq. Approx. Convexity, 3: 171-178(2005).
  • De La Sen, M., “Linking contractive self-mappings and cyclic Meir-Keeler contractions with Kannan self-mappings”, Applications, Article ID 572057(2010). Point Theory and
  • Wang, S.Z., Li, B. Y., Gao, Z. M., Is´eki, K., “Some Fixed Point Theorems on Expansion Mappings”, Math. Japon., 29(4): 631-636(1984).
  • Zeidler, E., “Nonlinear Functional Analysis and its Applications”, Vol. 1, Springer- Verlag, New York, (1986).

Fixed Point Theory for Cyclic(φ ) - Contractions in Uniform Spaces

Year 2014, Volume: 27 Issue: 1, 653 - 658, 28.03.2014

Abstract

In this paper, we apply the concept of cyclic(φ ) -contraction for presenting a fixed point theorem on Hausdorff uniform space. Some more general results are also obtained in Hausdorff uniform space.

References

  • Aamri, M., Bennani, S., El Moutawakil, D., “Fixed points and variational principle in uniform spaces”, Siberian Electronic Mathematical Reports, 3: 137– 142 (2006).
  • Aamri, M., El Moutawakil, D., “Common Fixed Point Theorems for E-contractive or E-expansive Maps in Uniform Spaces”, Acta Math. Acad. Paedagog. Nyh´azi (N.S.), 20(1): 83-91(2004).
  • Berinde, V., “Iterative Approximation of Fixed Points”, Editura Efemeride, Baia Mare, (2002).
  • Berinde, V., “Contractii Generalizate si Aplicatii”, vol. 22, Editura Cub Press, Baia Mare, (1997).
  • Bourbaki, N., “´E l´ements de math´ematique. Fasc. II. Livre III: Topologie g´en´erale. Chapitre 1: Structures topologiques. Chapitre 2: Structures uni- formes”, Scientifiques et Industrielles, No. 1142, Hermann, Paris, (1965). ´edition., Actualit´es
  • Jachymski, J., “Fixed Point Theorems for Expansive Mappings”, Math. Japon., 42(1):131-136(1995).
  • Kada, O., Suzuki, T., Takahashi, W., “Nonconvex Minimization Theorems and Fixed Point Theorems in Complete Metric Spaces”, Math. Japon., 44(2): 381-391(1996).
  • Karapnar, E., “Fixed point theory for cyclic weak φ-contraction”, Appl.Math. Lett., 24(6): 822-825 (2011).
  • Karap nar, E., Sadarangani, K., “Fixed point theory for cyclic (φ−
  • ψ)-contractions”, Fixed Point Theory
  • 1186/1687-1812-2011-69. 69, (2011) doi:
  • Kirk, W.A., Srinivasan, P.S., Veeramani, P., “Fixed points for mappings satisfying cyclical weak contractive conditions”, Fixed Point Theory, 4(1): 79–89(2003).
  • Pacurar, M., Rus, I.A., “Fixed point theory for cyclic ϕ-contractions”, Nonlinear Amal., 72: 1181- 1187(2010).
  • Rhoades, B.E., “A Comparison of Various Definitions of Contractive Mappings”, Trans. Amer. Math. Soc., 226: 257-290 (1977). [13] Rus, I.A., “Generalized Contractions and Applications”, Cluj University Press, Cluj-Napoca, (2001).
  • Rus, I.A., “Cyclic representations and fixed points”, Ann. T. Popoviciu, Seminar Funct. Eq. Approx. Convexity, 3: 171-178(2005).
  • De La Sen, M., “Linking contractive self-mappings and cyclic Meir-Keeler contractions with Kannan self-mappings”, Applications, Article ID 572057(2010). Point Theory and
  • Wang, S.Z., Li, B. Y., Gao, Z. M., Is´eki, K., “Some Fixed Point Theorems on Expansion Mappings”, Math. Japon., 29(4): 631-636(1984).
  • Zeidler, E., “Nonlinear Functional Analysis and its Applications”, Vol. 1, Springer- Verlag, New York, (1986).
There are 18 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Mathematics
Authors

Shaban Sedghı

Nabi Shobkolaeı

S. Fırouzıan

Publication Date March 28, 2014
Published in Issue Year 2014 Volume: 27 Issue: 1

Cite

APA Sedghı, S., Shobkolaeı, N., & Fırouzıan, S. (2014). Fixed Point Theory for Cyclic(φ ) - Contractions in Uniform Spaces. Gazi University Journal of Science, 27(1), 653-658.
AMA Sedghı S, Shobkolaeı N, Fırouzıan S. Fixed Point Theory for Cyclic(φ ) - Contractions in Uniform Spaces. Gazi University Journal of Science. March 2014;27(1):653-658.
Chicago Sedghı, Shaban, Nabi Shobkolaeı, and S. Fırouzıan. “Fixed Point Theory for Cyclic(φ ) - Contractions in Uniform Spaces”. Gazi University Journal of Science 27, no. 1 (March 2014): 653-58.
EndNote Sedghı S, Shobkolaeı N, Fırouzıan S (March 1, 2014) Fixed Point Theory for Cyclic(φ ) - Contractions in Uniform Spaces. Gazi University Journal of Science 27 1 653–658.
IEEE S. Sedghı, N. Shobkolaeı, and S. Fırouzıan, “Fixed Point Theory for Cyclic(φ ) - Contractions in Uniform Spaces”, Gazi University Journal of Science, vol. 27, no. 1, pp. 653–658, 2014.
ISNAD Sedghı, Shaban et al. “Fixed Point Theory for Cyclic(φ ) - Contractions in Uniform Spaces”. Gazi University Journal of Science 27/1 (March 2014), 653-658.
JAMA Sedghı S, Shobkolaeı N, Fırouzıan S. Fixed Point Theory for Cyclic(φ ) - Contractions in Uniform Spaces. Gazi University Journal of Science. 2014;27:653–658.
MLA Sedghı, Shaban et al. “Fixed Point Theory for Cyclic(φ ) - Contractions in Uniform Spaces”. Gazi University Journal of Science, vol. 27, no. 1, 2014, pp. 653-8.
Vancouver Sedghı S, Shobkolaeı N, Fırouzıan S. Fixed Point Theory for Cyclic(φ ) - Contractions in Uniform Spaces. Gazi University Journal of Science. 2014;27(1):653-8.