Surveys in Mathematics and its Applications


ISSN 1842-6298 (electronic), 1843-7265 (print)
Volume 11 (2016), 21 -- 31

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This work is licensed under a Creative Commons Attribution 4.0 International License.

COINCIDENCE AND COMMON FIXED POINT OF F-CONTRACTIONS VIA CLRST PROPERTY

Anita Tomar, Giniswamy, C. Jeyanthi, P. G. Maheshwari

Abstract. The aim of this paper is to establish the existence of coincidence and common fixed point of F-contractions via CLRST property. Our results generalize, extend and improve the results of Wardowski [D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory and Applications (2012) 2012:94, 6 pages, doi: 10.1186/1687-1812-2012-94], Batra et al. [Coincidence Point Theorem for a New Type of Contraction on Metric Spaces, Int. Journal of Math. Analysis, Vol. 8(27) 2014, 1315-1320] and others existing in literature. Examples are also given in support of our results.

2010 Mathematics Subject Classification: 47H10; 54H25
Keywords: Common fixed point, common limit range property, F-contraction, weakly compatible maps.

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References

  1. S. Banach, Sur les ope'rations dansles ensembles abstraits et leur application aux e'quationsint e'grales, Fundamenta Mathematicae, 3 (1922), 133-181. JFM 48.0201.01.

  2. S. K. Chatterjea, Fixed point theorems, Comptes Rendus de l'Academie Bulgare des Sciences, 25(1972), 727-730. MR0324493. Zbl 0274.54033.

  3. L. B. Ciric, A generalization of Banach's contraction principle, Proc. Am. Math. Soc. 45(2)(1974), 267-273. MR0356011. Zbl 0291.54056.

  4. M. Imdad, B. O. Pant, S. Chauhan, Fixed point theorems in Menger spaces using the (CLRST) property and applications, J. Nonlinear Anal. Optim., 3(2) (2012), 225-237. MR2982410.

  5. Monica Cosentino and Pasquale Vetro, Fixed point results for F-contractive mappings of Hardy-Rogers-type, Filomat, 28:4 (2014), 715-722, DOI 10.2298/ FIL1404715C. MR3360064.

  6. G. E. Hardy and T. D. Rogers, A generalization of a fixed point theorem of Reich, Canad. Math. Bull., 16(1973), 201-206. MR0324495. Zbl 0266.54015.

  7. G. Jungck, Compatible mappings and common fixed points, Inter. J. Math. Math. Sci., 9 (1986), 771-779. MR0870534. Zbl 0613.54029.

  8. G. Jungck and B. E. Rhoades, Fixed point for set valued functions without continuity, Indian J. Pure Appl. Math., 29 (1998), 227-238. MR1617919. Zbl 0904.54034.

  9. R. Kannan, Some results on fixed points, Bull. Cal. Math. Soc., 60(1968), 71-76. MR0257837. Zbl 0209.27104.

  10. S.K. Malhotra, Stojan Radenovic and Satish Shukla, Some fixed point results without monotone property in partially ordered metric-like spaces, J. Egyptian Math. Soc., 22 (2014), 83-89. MR3168597. Zbl 1293.54029.

  11. G. Minak, A. Helvac, and I. Altun, Ciric type generalized F- contractions on complete metric spaces and fixed point results, Filomat 28:6 (2014), 1143-1151, DOI.10.2298/FIL1406143M. MR3360088.

  12. Hossein Piri and Poom Kumam, Some fixed point theorems concerning F-contraction in complete metric spaces, Fixed Point Theory and Appl. 2014, (2014) 210. MR3357360.

  13. Rakesh Batra, Sachin Vashistha and Rajesh Kumar, Coincidence Point Theorem for a New Type of Contraction on Metric Spaces, Int. J. Math. Anal., 8( 2014) no. 27, 1315-1320 http://dx.doi.org/10.12988/ijma.2014.45147.

  14. S. Reich, Some remarks concerning contraction mappings, Canad. Math. Bull. 14(1) (1971), 121-124. 878730. MR0292057. Zbl 0211.26002.

  15. Satish Shukla and Stojan Radenovic, Some common fixed point theorems for F-contraction type mappings in 0-complete partial metric spaces, J. Math., 2013(2013), Article ID 878730, 7 pages, doi: 10.1155/ 2013/ 878730. MR3100741. Zbl 1268.54035.

  16. W. Sintunavarat and P. Kumam, Common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces, J. Appl. Math., (2011), 1-14. MR2822403. Zbl 1226.54061.

  17. D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory and Appl., 94(2012), 6 pages, doi: 10.1186/1687-1812-2012-94. MR2949666. Zbl 1310.54074.

  18. D. Wardowski and N. Van Dung, Fixed points of F-weak contractions on complete metric spaces, Demons. Math., 47(1) (2014), 146-155. MR3200192. Zbl 1287.54046.



Anita Tomar,
Government P.G. College, Dakpathar(Dehradun), India.
e-mail: anitatmr@yahoo.com


Giniswamy,
P. E. S College of Science, Arts and Commerce, Mandya, India.
e-mail: gswamypes@gmail.com


C. Jeyanthi,
Teresian College, Mysore.
e-mail: jaiprab@yahoo.co.in


P. G. Maheshwari,
Government First Grade College, Vijayanagara, Bangalore.
e-mail: maheshwari616@yahoo.com


http://www.utgjiu.ro/math/sma