Some Fixed Point Theorems Under Contractive Type Conditions in Complex Valued Metric Spaces

Authors

  • G. S. Saluja

DOI:

https://doi.org/10.18311/jims/2017/6122

Keywords:

Fixed Point, Common fixed Point, Contractive Type Condition, Complex Valued Metric Space

Abstract

The purpose of this paper is to establish some fixed point and common fixed point theorems under contractive type conditions involving rational expression in the setting of complex valued metric spaces. The results presented in this paper extend and generalize some previous works from the existing literature.

Downloads

Download data is not yet available.

References

R. P. Agarwal, D. O'Regan and D. R. Sahu, Fixed point theory for Lipschitzian type mappings with applications, Series: Topological Fixed Point Theorems and Applications, 6, Springer, New York, 2009.

M. A. Alghamdi, V. Berinde and N. Shahazad, Fixed points non-self almost contractions, Carpathian J. Math. 30(1) (2014), 7-11.

H. Aydi, M. Bota, E. Karapinar and S. Moradi, A common xed point for weak -contractions on b-metric spaces, Fixed Point Theory 13(2) (2012), 337-346.

A. Azam, B. Fisher and M. Khan, Common xed point theorems in complex valued metric spaces, Numer. Funct. Anal. Optim. 3(3) (2011), 243-253.

S. Banach, Surles operation dans les ensembles abstraits et leur application aux equation integrals, Fund. Math. 3 (1922), 133-181.

I. A. Bakhtin, The contraction mapping principle in almost metric spaces, Funct. Anal. Gos. Ped. Inst. Unianowsk 30 (1989), 26-37.

M. Boriceanu, M. Bota and A. Petrusel, A multivalued fractals in b-metric spaces, Cent. Eur. J. Math. 8(2) (2010), 367-377.

M. Bota, A. Moinar and V. Csaba, On Ekeland's variational principle in b-metric spaces, Fixed Point Theory 12 (2011), 21-28.

V. W. Bryant, A remark on a xed point theorem for iterated mappings, Amer. Math. Monthly 75 (1968), 399-400.

S. Czerwik, Nonlinear set-valued contraction mappings in b-metric spaces, Atti. Semin. Mat. Fis. Univ. Modena 46 (1998), 263-276.

B. K. Dass and S. Gupta, An extension of Banach contraction principle through rational expressions, Indian J. Pure Appl. Math. 6 (1975), 1455-1458.

B. Djafari-Rouhani and S. Moradi, Common xed point of multivalued generalized '- weak contractive mappings, Fixed Point Theory Appl. (2010), Art. ID 708984, 13 pages, doi:10.1155/2010/708984.

B. Fisher, Common xed points and constant mapping satisfying rational inequality, Math. Sem. Notes (Univ. Kobe), (1978).

B. Fisher and M. S. Khan, Fixed points, common xed points and constant mappings, Studia Sci. Math. Hungar. 11 (1978), 467-470.

D. S. Jaggi, Some unique xed point theorems, Indian J. Pure Appl. Math. 8 (1977), 223-230.

O. Hadzic and E. Pap, Fixed point theory in PM-spaces, Kluwer Academic Dordrecht, The Netherlands (2011).

H. Huang and S. Xu, Fixed point theorems of contractive mappings in cone b-metric spaces and applications, Fixed Point Theory Appl. 2013, 2013:112.

L. -G. Huang and X. Zhang, Cone metric spaces and xed point theorems of contractive mappings, J. Math. Anal. Appl. 332(2) (2007), 1468-1476.

N. Hussain and MH. Shah, KKM mappings in cone b-metric spaces, Comput. Math. Appl. 62 (2011), 1677-1684.

D. Ilic and V. Rakocevic, Common xed points for maps on cone metric space, J. Math. Anal. Appl. 341 (2008), 876-882.

M. Imdad, J. Ali and M. Tanveer, Coincedence and common xed point theorem for nonlinear contractions in Menger PM spaces, Chaos Solitones Fractals 42 (2009), 3121-3129.

S. Jankovic, Z. Kadelburg and S. Radenovicc, On cone metric spaces: a survey, Nonlinear Anal. 4(7) (2011), 2591-2601.

H. P. A. Kunzi, A note on sequentially compact quasi-pseudo metric spaces, Monatsheft Math. 95 (1983), 219-220.

S. Moradi, Z. Fathi and E. Analouee, The common xed point of single-valued generalized f-weakly contractive mappings, Appl. Math. Lett. 24(5) (2011), 771-776.

H. K. Nashine, M. Imdad and M. Hasan, Common xed point theorems under rational con- tractions in complvalued metric spaces, J. Nonlinear Sci. Appl. 7 (2014), 42-50.

Sh. Rezapour and R. Hamlbarani, Some notes on the paper "Cone metric spaces and xed point theorems of contractive mappings", J. Math. Anal. Appl. 345(2) (2008), 719-724.

M. Telei and B. Fisher, On a xed theorem for fuzzy mappings in quasi-metric spaces, Thai J. Math. 2 (2003), 1-8.

P. Vetro, Common xed points in cone metric spaces, Rend. Circ. Mat. Palermo, (2) 56(3) (2007), 464-468.

Published

2017-01-02

How to Cite

Saluja, G. S. (2017). Some Fixed Point Theorems Under Contractive Type Conditions in Complex Valued Metric Spaces. The Journal of the Indian Mathematical Society, 84(1-2), 96–108. https://doi.org/10.18311/jims/2017/6122