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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 57 | Number 2 | Year 2018 | Article Id. IJMTT-V57P514 | DOI : https://doi.org/10.14445/22315373/IJMTT-V57P514

Fixed Point Theorems in Dislocated Quasi-b-Metric Space for Two Self Maps


Venkatesh Bhatt, Giniswamy, Jeyanthi C
Abstract

The purpose of this paper is to establish a common fixed point result for two self-maps, using generalised contraction condition in dislocated quasi-b-metric space. This result is an extension and generalisation of the result of Mujeeb Ur Rahman[8].

Keywords
fixed point, b-metric spaces, quasi-b-metric spaces.
References

[1] Bakhtin, IA: The contraction principle in quasimetric spaces. In: Functional Analysis, vol. 30, pp. 26-37 (1989)
[2] Banach S.,Surles operations dans les ensembles abstraites et leurs applications, Fund. Math., 3 (1922), 133-187.
[3] Brouwer L.E.S., Uber Abbildungen Von Mannigfaltigkeiten, Math. Ann., 77 (1912), 97-115.
[4] Hitzler P. and Seda A.K., Dislocated Topologies, J. Electr. Engg., 51 (12/s), (2000), 3-7.
[5] Imoru C.O. and Olatinwo M.O., On The Stability Of Picard And Mann Iteration Processes, Carpathian J. Math., 19 (2) (2003), 155-160.
[6] Kannan R., Some results on fixed points, Bull. Cal. Math. Soc., 60 (1968), 71-76.
[7] Mujeeb Ur Rahman,”New Fixed Point Theorems in Dislocated Quasi-b-Metric Space”,Appl. Math. Inf. Sci. Lett. 5, No. 1, 7-11 (2017).
[8] M.U.Rahman and M.Sarwar,”Dislocated Quasi-b-metric and fixed point theorem”,Electronic Journal of Mathematical Analysis and Applications,4 (2016)
[9] Osilike M.O., Stability Results For Fixed Point Iteration Procedures, J. The Nigerian Math. Society, 14 (15) (1995), 17-29.
[10] Rhoades B.E., A fixed point theorem for generalized metric spaces, Internat. J. Math. and Math. Sci., 19 (3) (1996), 457-460.
[11] Schauder J., Fixed point theorem in continuous mapping, Math. Ann., 174 (1930), 285-290.
[12] Wilson, WA: On quasi-metric spaces. Am. J. Math. 53(3), 675-684 (1931).
[13] Zamfirescu T., Fixed Point Theorems In Metric Spaces, Arch. Math., 23 (1972), 292-298.

Citation :

Venkatesh Bhatt, Giniswamy, Jeyanthi C, "Fixed Point Theorems in Dislocated Quasi-b-Metric Space for Two Self Maps," International Journal of Mathematics Trends and Technology (IJMTT), vol. 57, no. 2, pp. 95-98, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V57P514

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