Fixed Point Results for Cyclic Contractions in Partial Symmetric Spaces
DOI:
https://doi.org/10.26713/cma.v12i4.1631Keywords:
Partial symmetric spaces, Fixed point theorems, Cyclic contractionsAbstract
In this paper, we prove fixed point results for various cyclic contractions in partial symmetric spaces. Our results generalize the fixed point results of Asim et al. (Fixed point results in partial symmetric spaces with an application, Axioms 8(13) (2019), 1 – 15) proved for the class of partial symmetric spaces for various contractions. Also, we provide an example in the support of proved result.
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S. Alshehri, I. Arand¯elovic´ and N. Shahzad, Symmetric spaces and fixed points of generalized contractions, Abstract and Applied Analysis 2014 (2014), Article ID 763547, 8 pages, DOI: 10.1155/2014/763547.
A. Ammini-Harandi, Metric-like spaces, partial metric spaces and fixed points, Fixed Point Theory and Applications 2012 (2012), Article number: 204, DOI: 10.1186/1687-1812-2012-204.
M. Asim, A. R. Khan and M. Imdad, Fixed point results in partial symmetric spaces with an application, Axioms 8(1) (2019), 13, DOI: 10.3390/axioms8010013.
S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fundamenta Mathematicae 3 (1922), 133 – 181, URL: http://matwbn.icm.edu.pl/ksiazki/fm/fm3/fm3120.pdf.
S. Czerwik, Contraction mappings in b-metric spaces, Acta Mathematica et Informatica Universitatis Ostraviensis 1 (1993), 5 – 11, URL: http://dml.cz/dmlcz/120469.
T. L. Hicks and B. E. Rhoades, Fixed point theory in symmetric spaces with applications to probabilistic spaces, Nonlinear Analysis: Theory, Methods & Applications 36 (1999), 331 – 344, DOI: 10.1016/S0362-546X(98)00002-9.
M. Imdad and J. Ali, Common fixed point theorems in symmetric spaces employing a new implicit function and common property (EA), Bulletin of the Belgian Mathematical Society, Simon Stevin 16(2009), 421 – 433, DOI: 10.36045/bbms/1251832369.
E. Karapınar, Fixed point theory for cyclic weak Á contraction, Applied Mathematics Letters 24 (2011), 822 – 825, DOI: 10.1016/j.aml.2010.12.016.
E. Karapınar, I. M. Erhan and A. Y. Ulus, Fixed point theorem for cyclic maps on partial metric spaces, Applied Mathematics & Information Sciences 6 (2012), 239 – 244, URL: https://dc.naturalspublishing.com/amis/vol06/iss2/9.
W. A. Kirk, P. S. Srinavasan and P. Veeramani, Fixed points for mapping satisfying cyclical contractive conditions, Fixed Point Theory 4 (2003), 79 – 89, URL: http://www.math.ubbcluj.ro/~nodeacj/download.php?f=031Kirk.pdf.
P. S. Kumari and D. Panthi, Connecting various types of cyclic contractions and contractive self mappings with Hardy Rogers self mappings, Fixed Point Theory and Applications 2016 (2016), Article number: 15, DOI: 10.1186/s13663-016-0498-3.
P. S. Kumari and D. Panthi, Cyclic compatible contractions and related fixed point theorems, Fixed Point Theory and Applications 2016 (2016), Article number: 28, DOI: 10.1186/s13663-016-0521-8.
S. G. Matthews, Partial metric topology, Annals of the New York Academy of Sciences 728 (1994), 183 – 197, DOI: 10.1111/j.1749-6632.1994.tb44144.x.
Z. Mustafa, J. R. Roshan, V. Parvaneh and Z. Kadelburg, Some common fixed point results in ordered partial b-metric spaces, Journal of Inequalities and Applications 2013 (2013), Article number: 562, DOI: 10.1186/1029-242X-2013-562.
Y. Shen and M. Lu, Fixed point theorems in symmetric spaces and applications to probabilistic spaces, Nonlinear Analysis: Theory, Methods & Applications 72 (2010), 527 – 532, DOI: 10.1016/J.NA.2009.06.102.
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