Fixed Points of Almost Generalized (a, y)-Contractions with Rational Expressions

Authors

  • GVR Babu Department of Mathematics, Andhra University, Visakapatnam-530 003, India.
  • KKM Sarma Department of Mathematics, Andhra University, Visakapatnam-530 003, India.
  • VA Kumari Department of Mathematics, Andhra University, Visakapatnam-530 003, India.

DOI:

https://doi.org/10.15415/mjis.2017.52008

Keywords:

α-admissible, (a, y)-contraction mapping, generalized (a, y)-contraction mapping, almost Jaggi contraction, almost generalized (a, y)-contraction map with rational expression

Abstract

In this paper, we introduce almost generalized (a, y)-contractions with rational expression type mappings and establish the existence of fixed points for such mappings in complete partially ordered metric spaces. Further, we define `Condition (H)’ and prove the existence of unique fixed point under the additional assumption `Condition (H)’. Our results generalize the results of Arshad, Karapinar and Ahmad [1] and Harjani, Lopez and Sadarangani [2].

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References

Arshad, M. Karapinar, E. and Ahmad, J. (2013). Some unique fixed point theorem for rational contractions in partially ordered metric spaces. Journal Of Inequalities and Applcations, Article ID 307234.

Harjani, J., Lopez, B. and Sadarangani, K. (2010). A fixed point theorem for mappings satisfying a contractive condition of rational type on a partially ordered metric space. Abstract and Applied Analysis, 1–8.

Jaggi, D.S. (1977). Some unique fixed point theorems. Indian Journal of Pure and Applied Mathematics, (8), 223–230.

Samet, B., Vetro, C. and Vetro, P. (2012). Fixed point theorem for (α, ψ)-contractive type mappings. Non-linear Analysis, (75), 2154–2165.doi: 10.1016/j.na.2011.10.014.

Karapinar, E. and Samet, B.(2012). Generalized (α, ψ) -contractive type mappings and related fixed point theorems with applications. Abstract and Applied Analysis, Article ID 793486, 17 pages. doi: 10.1155/2012/793486.

Bhaskar, T.G. and Lakshmikantham, V. (2006). Fixed point theorems in partially ordered metric spaces and applications. Non-linear Analysis, (65), 1379–1393.

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Published

2017-03-05

How to Cite

GVR Babu, KKM Sarma, and VA Kumari. 2017. “Fixed Points of Almost Generalized (a, Y)-Contractions With Rational Expressions”. Mathematical Journal of Interdisciplinary Sciences 5 (2):101-20. https://doi.org/10.15415/mjis.2017.52008.

Issue

Vol. 5 No. 2 (2017)

Section

Articles

License

 

Articles in Mathematical Journal of Interdisciplinary Sciences (Math. J. Interdiscip. Sci.) by Chitkara University Publications are Open Access articles that are published with licensed under a Creative Commons Attribution- CC-BY 4.0 International License. Based on a work at https://mjis.chitkara.edu.in. This license permits one to use, remix, tweak and reproduction in any medium, even commercially provided one give credit for the original creation.

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Creative Commons License Mathematical Journal of Interdisciplinary Sciences by Chitkara University Publications is licensed under a Creative Commons Attribution 4.0 International License. Based on a work at https://mjis.chitkara.edu.in
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