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Some Common Fixed Point Results in Cone Metric Spaces for Rational Contractions

Received: 21 February 2022     Accepted: 15 March 2022     Published: 23 March 2022
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Abstract

A very engrossing technique in theory of contractive mapping fixed point. A number of authors have defined contractive type mappings on a cone metric spaces X which are generalization of the well -known Banach contraction, and have the property that each of such mapping has a unique fixed point. The fixed point can always be found by using Picard Iteration, opening with initial choice x0∈X. In this manuscript, we generalize, extend and improve the result under the assumption of normality of cone for rational expression type contraction mapping in cone metric spaces. The present article is to provide a new alternative proof for two and three mapping and obtain the entity and exclusiveness of common fixed point. The concernment of the present paper to open a new direction of proof to be extended based on the methods of rational type contraction mapping in cone metric spaces of fixed-point theory. The assistance of this article is organized as follows. In section 2, preliminary notes. In this section we recall some standard notations and definitions which we needed. In section 3, the main results of the author are given. In this section we evidence of new results for two and three maps. In section 4, gives brief concluding note of the paper.

Published in Mathematics Letters (Volume 8, Issue 1)
DOI 10.11648/j.ml.20220801.11
Page(s) 1-10
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2022. Published by Science Publishing Group

Keywords

Fixed Point, Common Fixed Point, Cone Metric Space, Rational Expression

References
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[2] Kumar, P. and Ansar, Z. K. (2017). Some Fixed Point Results in Cone Metric Spaces for Rational Contractions. South East Asian j. of Math. & Math. Sci., 13 (2), (2017), 125-132.
[3] Das, B. K. and Gupta, S. (1975). An Extension of Banach Contraction Principle Through Rational Expressions, Indian J. Pure Appl. Math. 6, 1455-1458.
[4] Jaggi, D. S. (1977). Some Unique Fixed Point Theorems, Indian J. Pure Appl. Math., 8 223-230.
[5] Fisher, B. (1978). Common Fixed Points and Constant Mappings Satisfying Rational Inequality, Math. Sem. Notes (Univ Kobe) (1978).
[6] Fisher, B. and Khan, M. S. (1978). Common Fixed Points and Constant Mappings, Studia Sci. Math. Hungar. 11, 467-470.
[7] Huang and Zhang (2007). Cone Metric Spaces and Fixed Point Theorems of Contractive, J. Math. Appl., 332, 1468-1476.
[8] Abbas, M. and Jungck, G. (2008). Common Fixed Point Results for Non-Commuting Mappings Without Continuity in Cone metric spaces, J. Math. Anal. Appl. 344, 16-420.
[9] Arshad, M., Azam A. and Vetro, P. (2009). Some Common Fixed Point Results in Cone Metric Spaces. Fixed Point Theory Appl., 2009, Article ID 493965, 11 pages.
[10] Radenovic, S. (2009). Common Fixed Points Under Contractive Conditions in Cone Metric Spaces. Compute. Mat. Appl., Doi: 10.1016/j.camwa.2009.07.035.
[11] Radenovic, S. and. Rhoades, B. E. (2009), Fixed Point Theorem for Two non-self-Mappings in Cone Metric Sspaces, Comput. Math. Appl., 57, 1701-1707.
[12] Jankovic, S. Kadelburg Z. and Radenovic, S. (2011). On Cone Metric Spaces: a survey, Non-linear Anal., 74, 2591-2601.
[13] Vetro, P. (2007). Common Fixed Points in Cone Metric Spaces, Rendiconti del Circolo Matematico di Palermo, 56 (3), 464-468.
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[15] Xiaoyan Sun, Yian Zhao, Guotao Wang, (2010), New Common Fixed Point Theorems for Maps on Cone Metric Spaces, Applied Mathematics Letters. 23. 1033-1037.
[16] Asadi, M. Vaezpour, S. M Rakocevic, V. and Rhoades, B. E. (2011). Fixed Point Theorem for Contractive Mapping in Cone Metric Spaces, Math. Commun. 16, 147-155.
[17] Ozturk, O. Basarr, M. (2012). Some Common Fixed Point Theorems with Rational Expressions on Cone Metric Spaces over a Banach Algebra, Hacettepe Journal of Mathematics and Statistics. 41 (2), 211-222.
[18] Rezapour, S. and Hamlbarani, R. (2008). Some note on the paper cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 345, 719-724.
[19] Uthaya, R and Prabhakar, G. A. (2012). Common Fixed Point Theorems in Cone Metric Space for Rational Contractions, international journal of anal. And appl., 3 (2), 112-118.
[20] Arshad, M. Karapinar, E. and Ahmad, J. (2013), Some Unique Fixed Point Theorems for Rational Contractions in Partially Ordered Metric Spaces, Journal of inequalities and applications, 2003: 248. doi: 10.1186/1029-242x-2013-248.
[21] Tiwari, S. K., Dubey, R. P. and Dubey, A. K. (2013). Cone Metric Spaces and Common Fixed Point Theorems for Generalized Jaggi and Das–Gupta Contractive Mapping. Int. j. of Mathematical Archive, 4 (10), 93-100.
[22] Kannan, (1968). Some Results on Fixed Point, Bull. Calc. Math. Soc., 60, 71-76.
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[25] Zamfirescu, T. (1972), Fixed Point Theorem in Metric Spaces, Arch. Math., 23, 292-298.
[26] Tiwari, S. K. and Dewangan, S. (2020). Cone Metric Spaces and Fixed Point Theorem for Generalized T-Contractive mappings under C- Distance, J. of Appl. Sci. and Comp., Vol. VII (I), 22-27.
[27] Tiwari, S. K. and Dewangan, S. (2020). Common Fixed Point Theorem for T- Contraction with C-Distance on Cone Metric Space, Trad Research, Vol. 7 (60), 297-304.
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  • APA Style

    Devnarayan Yadav, Surendra Kumar Tiwari. (2022). Some Common Fixed Point Results in Cone Metric Spaces for Rational Contractions. Mathematics Letters, 8(1), 1-10. https://doi.org/10.11648/j.ml.20220801.11

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    ACS Style

    Devnarayan Yadav; Surendra Kumar Tiwari. Some Common Fixed Point Results in Cone Metric Spaces for Rational Contractions. Math. Lett. 2022, 8(1), 1-10. doi: 10.11648/j.ml.20220801.11

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    AMA Style

    Devnarayan Yadav, Surendra Kumar Tiwari. Some Common Fixed Point Results in Cone Metric Spaces for Rational Contractions. Math Lett. 2022;8(1):1-10. doi: 10.11648/j.ml.20220801.11

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  • @article{10.11648/j.ml.20220801.11,
      author = {Devnarayan Yadav and Surendra Kumar Tiwari},
      title = {Some Common Fixed Point Results in Cone Metric Spaces for Rational Contractions},
      journal = {Mathematics Letters},
      volume = {8},
      number = {1},
      pages = {1-10},
      doi = {10.11648/j.ml.20220801.11},
      url = {https://doi.org/10.11648/j.ml.20220801.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20220801.11},
      abstract = {A very engrossing technique in theory of contractive mapping fixed point. A number of authors have defined contractive type mappings on a cone metric spaces X which are generalization of the well -known Banach contraction, and have the property that each of such mapping has a unique fixed point. The fixed point can always be found by using Picard Iteration, opening with initial choice x0∈X. In this manuscript, we generalize, extend and improve the result under the assumption of normality of cone for rational expression type contraction mapping in cone metric spaces. The present article is to provide a new alternative proof for two and three mapping and obtain the entity and exclusiveness of common fixed point. The concernment of the present paper to open a new direction of proof to be extended based on the methods of rational type contraction mapping in cone metric spaces of fixed-point theory. The assistance of this article is organized as follows. In section 2, preliminary notes. In this section we recall some standard notations and definitions which we needed. In section 3, the main results of the author are given. In this section we evidence of new results for two and three maps. In section 4, gives brief concluding note of the paper.},
     year = {2022}
    }
    

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    T1  - Some Common Fixed Point Results in Cone Metric Spaces for Rational Contractions
    AU  - Devnarayan Yadav
    AU  - Surendra Kumar Tiwari
    Y1  - 2022/03/23
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    N1  - https://doi.org/10.11648/j.ml.20220801.11
    DO  - 10.11648/j.ml.20220801.11
    T2  - Mathematics Letters
    JF  - Mathematics Letters
    JO  - Mathematics Letters
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    PB  - Science Publishing Group
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    UR  - https://doi.org/10.11648/j.ml.20220801.11
    AB  - A very engrossing technique in theory of contractive mapping fixed point. A number of authors have defined contractive type mappings on a cone metric spaces X which are generalization of the well -known Banach contraction, and have the property that each of such mapping has a unique fixed point. The fixed point can always be found by using Picard Iteration, opening with initial choice x0∈X. In this manuscript, we generalize, extend and improve the result under the assumption of normality of cone for rational expression type contraction mapping in cone metric spaces. The present article is to provide a new alternative proof for two and three mapping and obtain the entity and exclusiveness of common fixed point. The concernment of the present paper to open a new direction of proof to be extended based on the methods of rational type contraction mapping in cone metric spaces of fixed-point theory. The assistance of this article is organized as follows. In section 2, preliminary notes. In this section we recall some standard notations and definitions which we needed. In section 3, the main results of the author are given. In this section we evidence of new results for two and three maps. In section 4, gives brief concluding note of the paper.
    VL  - 8
    IS  - 1
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Author Information
  • Department of Mathematics, Govt. H. School Shilpari, Bilaspur, India

  • Department of Mathematics, Dr. C. V. Raman University Kota, Bilaspur, India

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