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FIXED POINTS THEOREMS FOR GENERALISED WEAKLY CONTRACTIVE MAPPINGS

Part of: Connections with other structures, applications Nonlinear operators and their properties

Published online by Cambridge University Press:ย  04 September 2015

ZHIQUN XUE
ZHIQUN XUE*
Affiliation:
Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043, PR China email xuezhiqun@126.com
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Abstract

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In this paper, we establish a convergence theorem for fixed points of generalised weak contractions in complete metric spaces under some new control conditions on the functions. An illustrative example of a generalised weak contraction is discussed to show how the new conditions extend known results.

Keywords

complete metric spacegeneralised weakly contractive mappingfixed point

MSC classification

Primary: 47H10: Fixed-point theorems
Secondary: 54H25: Fixed-point and coincidence theorems
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 93 , Issue 2 , April 2016 , pp. 321 - 329
Copyright
ยฉ 2015 Australian Mathematical Publishing Association Inc.ย 

References

Alber, Ya. I. and Guerre-Delabriere, S., โ€˜Principle of weakly contractive maps in Hilbert spacesโ€™, in: New Results in Operator Theory and its Applications, Operator Theory:ย Advances and Applications, 98 (eds. Gohberg, I. and Lyubich, Yu.) (Birkhรคuser, Basel, 1997), 7โ€“22.Google Scholar
Boyd, D. W. and Wong, J. S. W., โ€˜On nonlinear contractionsโ€™, Proc. Amer. Math. Soc. 20(2) (1969), 458โ€“464.CrossRefGoogle Scholar
Choudhury, B. C., Konar, P., Rhoades, B. E. and Metiya, N., โ€˜Fixed point theorems for generalized weakly contractive mappingsโ€™, Nonlinear Anal. 74 (2011), 2116โ€“2126.CrossRefGoogle Scholar
Doriฤ‡, D., โ€˜Common fixed point for generalized (๐œ“, ๐œ™)-weak contractionsโ€™, Appl. Math. Lett. 223 (2009), 1896โ€“1900.CrossRefGoogle Scholar
Dutta, P. N. and Choudhury, B.ย S., โ€˜A generalisation of contraction principle in metric spacesโ€™, Fixed Point Theory Appl. (2008), ID: 406368, 8 pages, doi:10.1155/2008/406368.Google Scholar
Moradi, S. and Farajzadeh, A., โ€˜On the fixed point of (๐œ“โˆ’๐œ™)-weak and generalized (๐œ“โˆ’๐œ™)-weak contraction mappingsโ€™, Appl. Math. Lett. 25 (2012), 1257โ€“1262.Google Scholar
Popescu, O., โ€˜Fixed points for (๐œ“, ๐œ™)-weak contractionsโ€™, Appl. Math. Lett. 24 (2011), 1โ€“4.CrossRefGoogle Scholar
Rhoades, B. E., โ€˜Some theorems on weakly contractive mapsโ€™, Nonlinear Anal. 47 (2001), 2683โ€“2693.CrossRefGoogle Scholar
Zhang, Q. N. and Song, Y. S., โ€˜Fixed point theory for generalized ๐œ™-weak contractionsโ€™, Appl. Math. Lett. 22 (2009), 75โ€“78.Google Scholar