Fixed Point Theorems Under New Caristi Type Contraction in Bipolar Metric Space with Applications

Authors

  • B Srinuvasa Rao

  • G N.V.Kishore

  • S Ramalingeswara Rao

How to Cite

Srinuvasa Rao, B., N.V.Kishore, G., & Ramalingeswara Rao, S. (2018). Fixed Point Theorems Under New Caristi Type Contraction in Bipolar Metric Space with Applications. International Journal of Engineering and Technology, 7(3.31), 106-110. https://doi.org/10.14419/ijet.v7i3.31.18276

Received date: August 25, 2018

Accepted date: August 25, 2018

Published date: August 24, 2018

DOI:

https://doi.org/10.14419/ijet.v7i3.31.18276

Keywords:

Bipolar metric space, covariant map, fixed point, lower semi continuous function, new caristi type contraction.

Abstract

In this paper, the existence of fixed-point results in a complete bipolar metric spaces under new caristi type contraction is well established. Some attention gaining consequences are attained through our results. Finally, it presented an illustration which present applicability of the obtained results.

 

References

  1. [1] Ali Mutlu, Utku Gürdal., Bipolar metric spaces and some fixed point theorems, J. Nonlinear Sci. Appl. 9(9), 2016, 5362-5373.

    [2] Ali Mutlu, Kübra Özkan, Utku Gürdal., Coupled fixed point
    theorems on bipolar metric spaces    , European journal of pure and applied mathematics. Vol. 10, No. 4, 2017, 655-667.

    [3] J. Caristi, Fixed point Theorems for mappings satisfying inwardness condition, Trans. Amer. Math. Soc.215 (1976), 241-251. http://dx.doi.org/10.1090/s0002-9947-1976-0394329-4.

    [4] Banach S., Sur les operations dans les ensembles abstraits
    etleur applications aux equations integrals    , Fund. Math.3. 133-181(1922).

    [5] Farshid Khojasteh, et. al., Some applications of Caristis´ fixed
    point theorem in metric spaces    . Fixed point theory and Applications (2016), 2016:16.

    [6] I. Ekeland., On the variational principle, J. Math. Anal. Appl.
    47(2), 324-353 (1974).

    [7] I. Ekeland., Sur les problems variationnels, C. R. Acad. Sci.
    Paris, 275(1972), 1057-1059. 1.

    [8] Lazaiz, Samih; Chaira, Karim; Aamri, Mohamed; Marhrani,
    EL Miloudi; Related point theorems of caristi type for two setvalued mappings, Bulletin of Mathematical Analysis and Applications. 2017, Vol. 9 Issue 1, p123-133. 11p.

    [9] M. A. Khamsi, W. A. Kirk, An Introduction to metric spaces
    and fixed point theory    , Wiley-Inter science, New York, (2001), http://dx.doi.org/10.1002/9781118033074.

    [10] MA. Khamsi, Remarks on Caristis´ fixed point theorem, Nonlinear Anal. TMA 71, 227-231(2009).

    [11] M. R. Alfuraidan; Remarks on Caristis fixed point theorem in
    metric spaces with a graph    , Fixed Point Theory and Applications, vol. 2014, no. 1, article no. 240, 2014.

    [12] RP. Agarwal, MA. Khamsi, Extension of Caristi’s fixed point
    theorem to vector valued metric space    , Nonlinear Anal. TMA
    74, 141-145(2011) doi: 10.1016/ j. na.2010.08.025.

    [13] Tomonari Suzuki; Characterization of -Semi completeness via
    Caristis Fixed Point Theorem in Semi metric Spaces    , Hindawi
    Journal of Function Spaces. Volume 2018, Article ID 9435470,
    7 pages, https://doi.org/10.1155/2018/9435470

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How to Cite

Srinuvasa Rao, B., N.V.Kishore, G., & Ramalingeswara Rao, S. (2018). Fixed Point Theorems Under New Caristi Type Contraction in Bipolar Metric Space with Applications. International Journal of Engineering and Technology, 7(3.31), 106-110. https://doi.org/10.14419/ijet.v7i3.31.18276

Received date: August 25, 2018

Accepted date: August 25, 2018

Published date: August 24, 2018