Research Article
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Year 2019, Volume: 4 Issue: 1, 11 - 18, 15.04.2019
https://doi.org/10.30931/jetas.510813

Abstract

References

  • Nadler, S.B., “Multi-valued contraction mappings”, Pac. J. Math. 30(2) (1969) : 475–488.
  • Czerwik, S., “Contraction mappings in b-metric spaces”, Acta Math Inf Univ Ostraviensis 1(1) (1993) : 5–11.
  • Huang, L.G., Zhang, X., “Cone metric spaces and fixed point theorems of contractive mappings”, J. Math. Anal. Appl. 332(2) (2007) : 1468–1476.
  • Du, W.-S., “A note on cone metric fixed point theory and its equivalence”, Nonlinear Anal. 72(5) (2010) : 2259–2261.
  • Liu, H., Xu, S., “Cone metric spaces with Banach algebras and fixed point theorems of generalized Lipschitz mappings”, Fixed Point Theory Appl. 2013(1) (2013) : 320.
  • Wardowski, D., “On set-valued contractions of Nadler type in cone metric spaces”, Appl. Math. Lett. 24(3) (2011) : 275–278.
  • Ozavsar, M., “Nadler mappings in cone b-metric spaces over Banach algebras”, Rendiconti del Seminario Matematico (2018).
  • Suzuki, T., “Basic inequality on a b-metric space and its applications”, Journal of inequalities and applications 2017(1) 2017 : 256.
  • Huang, H., Radenovic, S., “Common fixed point theorems of generalized Lipschitz mappings in cone b-metric spaces over Banach algebras and applications”, J. Non. Sci. Appl. 8(5) (2015) : 787–799.
  • Rezapour, S., Hamlbarani, R., “Some notes on the paper “Cone metric spaces and fixed point theorems of contractive mappings””, J. Math. Anal. Appl. 345(2) (2008) : 719-724.
  • Radenovic, S., Rhoades, B.E., “Fixed point theorem for two non-self mappings in cone metric spaces”, Comput. Math. Appl. 57(10) (2009) : 1701-1707.
  • Xu, S., Radenovic, S., “Fixed point theorems of generalized Lipschitz mappings on cone metric spaces over Banach algebras without assumption of normality”, Fixed Point Theory Appl. 2014(1) (2014) : 102.
  • Rudin, W., Functional Analysis, 2nd edn. McGraw-Hill, New York (1991).
  • Kadelburg, Z., Radenovic, S., “A note on various types of cones and fixed point results in cone metric spaces”, Asian J. Math. Appl. (2013).

A Proper Generalization of Banach Principle for Nadler Type Mappings in Cone b-Metric Spaces Over Banach Algebras

Year 2019, Volume: 4 Issue: 1, 11 - 18, 15.04.2019
https://doi.org/10.30931/jetas.510813

Abstract

In this paper, we first consider Nadler type contractions with the
generalized Lipschitz constant k holding r(k)<1 instead of r(sk)<1
where r(k) is the spectral radius of k and s≥1 is the coefficient
of the underlying cone b-metric spaces over Banach algebras. Then, we
prove the corresponding fixed point theorem for such mappings. Finally, we
compare our result with one obtained by the case r(sk)<1 by introducing
some proper examples.

References

  • Nadler, S.B., “Multi-valued contraction mappings”, Pac. J. Math. 30(2) (1969) : 475–488.
  • Czerwik, S., “Contraction mappings in b-metric spaces”, Acta Math Inf Univ Ostraviensis 1(1) (1993) : 5–11.
  • Huang, L.G., Zhang, X., “Cone metric spaces and fixed point theorems of contractive mappings”, J. Math. Anal. Appl. 332(2) (2007) : 1468–1476.
  • Du, W.-S., “A note on cone metric fixed point theory and its equivalence”, Nonlinear Anal. 72(5) (2010) : 2259–2261.
  • Liu, H., Xu, S., “Cone metric spaces with Banach algebras and fixed point theorems of generalized Lipschitz mappings”, Fixed Point Theory Appl. 2013(1) (2013) : 320.
  • Wardowski, D., “On set-valued contractions of Nadler type in cone metric spaces”, Appl. Math. Lett. 24(3) (2011) : 275–278.
  • Ozavsar, M., “Nadler mappings in cone b-metric spaces over Banach algebras”, Rendiconti del Seminario Matematico (2018).
  • Suzuki, T., “Basic inequality on a b-metric space and its applications”, Journal of inequalities and applications 2017(1) 2017 : 256.
  • Huang, H., Radenovic, S., “Common fixed point theorems of generalized Lipschitz mappings in cone b-metric spaces over Banach algebras and applications”, J. Non. Sci. Appl. 8(5) (2015) : 787–799.
  • Rezapour, S., Hamlbarani, R., “Some notes on the paper “Cone metric spaces and fixed point theorems of contractive mappings””, J. Math. Anal. Appl. 345(2) (2008) : 719-724.
  • Radenovic, S., Rhoades, B.E., “Fixed point theorem for two non-self mappings in cone metric spaces”, Comput. Math. Appl. 57(10) (2009) : 1701-1707.
  • Xu, S., Radenovic, S., “Fixed point theorems of generalized Lipschitz mappings on cone metric spaces over Banach algebras without assumption of normality”, Fixed Point Theory Appl. 2014(1) (2014) : 102.
  • Rudin, W., Functional Analysis, 2nd edn. McGraw-Hill, New York (1991).
  • Kadelburg, Z., Radenovic, S., “A note on various types of cones and fixed point results in cone metric spaces”, Asian J. Math. Appl. (2013).
There are 14 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Faruk Develi

Muttalip Özavşar This is me

Stojan Radenovic

Publication Date April 15, 2019
Published in Issue Year 2019 Volume: 4 Issue: 1

Cite

APA Develi, F., Özavşar, M., & Radenovic, S. (2019). A Proper Generalization of Banach Principle for Nadler Type Mappings in Cone b-Metric Spaces Over Banach Algebras. Journal of Engineering Technology and Applied Sciences, 4(1), 11-18. https://doi.org/10.30931/jetas.510813
AMA Develi F, Özavşar M, Radenovic S. A Proper Generalization of Banach Principle for Nadler Type Mappings in Cone b-Metric Spaces Over Banach Algebras. JETAS. April 2019;4(1):11-18. doi:10.30931/jetas.510813
Chicago Develi, Faruk, Muttalip Özavşar, and Stojan Radenovic. “A Proper Generalization of Banach Principle for Nadler Type Mappings in Cone B-Metric Spaces Over Banach Algebras”. Journal of Engineering Technology and Applied Sciences 4, no. 1 (April 2019): 11-18. https://doi.org/10.30931/jetas.510813.
EndNote Develi F, Özavşar M, Radenovic S (April 1, 2019) A Proper Generalization of Banach Principle for Nadler Type Mappings in Cone b-Metric Spaces Over Banach Algebras. Journal of Engineering Technology and Applied Sciences 4 1 11–18.
IEEE F. Develi, M. Özavşar, and S. Radenovic, “A Proper Generalization of Banach Principle for Nadler Type Mappings in Cone b-Metric Spaces Over Banach Algebras”, JETAS, vol. 4, no. 1, pp. 11–18, 2019, doi: 10.30931/jetas.510813.
ISNAD Develi, Faruk et al. “A Proper Generalization of Banach Principle for Nadler Type Mappings in Cone B-Metric Spaces Over Banach Algebras”. Journal of Engineering Technology and Applied Sciences 4/1 (April 2019), 11-18. https://doi.org/10.30931/jetas.510813.
JAMA Develi F, Özavşar M, Radenovic S. A Proper Generalization of Banach Principle for Nadler Type Mappings in Cone b-Metric Spaces Over Banach Algebras. JETAS. 2019;4:11–18.
MLA Develi, Faruk et al. “A Proper Generalization of Banach Principle for Nadler Type Mappings in Cone B-Metric Spaces Over Banach Algebras”. Journal of Engineering Technology and Applied Sciences, vol. 4, no. 1, 2019, pp. 11-18, doi:10.30931/jetas.510813.
Vancouver Develi F, Özavşar M, Radenovic S. A Proper Generalization of Banach Principle for Nadler Type Mappings in Cone b-Metric Spaces Over Banach Algebras. JETAS. 2019;4(1):11-8.