Common Fixed Point Theorems of Integral Type Contraction on Cone Metric Spaces and Applications

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DOI:

https://doi.org/10.26713/cma.v14i2.2142

Keywords:

Common fixed point, Cone metric space, Property (EA), Contractive mappings of integral type, Weakly compatible mappings

Abstract

In this paper, we establish the existence and uniqueness of a common fixed point for two pairs of weakly compatible mappings satisfying integral type contractive condition and property (EA) on cone metric spaces, and we prove the existence and uniqueness of a solution for an ordinary differential equation with periodic boundary conditions. The derived results generalized some well-known results that exist in the literature

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References

M. Aamri and D. El Moutawakil, Some new common fixed point theorems under strict contractive conditions, Journal of Mathematical Analysis and Applications 270 (2002), 181 – 188, URL: https://core.ac.uk/download/pdf/82144867.pdf.

M. Abbas and G. Jungck, Common fixed point results for noncommuting mappings without continuity in cone metric spaces, Journal of Mathematical Analysis and Applications 341(1) (2008), 416 – 420, DOI: 10.1016/j.jmaa.2007.09.070.

M. Arshad, A. Azam and P. Vetro, Some common fixed point results in cone metric spaces, Fixed Point Theory and Applications 2009 (2009), Article ID 493965, 11 pages, DOI: 10.1155/2009/493965.

A. Azam and M. Arshad, Common fixed points of generalized contractive maps in cone metric spaces, Bulletin of the Iranian Mathematical Society 35(2) (2009), 255 – 264, URL: http://bims.iranjournals.ir/article_43_b1cb0ec796a649d02106074e7f6aac94.pdf.

S. M. A. A. Bakr, Theta cone metric spaces and some fixed point theorems, Journal of Mathematics 2020 (2020), Article ID 8895568, 7 pages, DOI: 10.1155/2020/8895568.

S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fundamenta Mathematicae 3(1) (1922), 133 – 181, URL: https://eudml.org/doc/213289.

A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type, International Journal of Mathematics and Mathematical Sciences 29 (2002), Article ID 641824, 6 pages, DOI: 10.1155/S0161171202007524.

S.-H. Cho and J.-S. Bae, Common fixed point theorems for mappings satisfying property (E.A) on cone metric spaces, Mathematical and Computer Modelling 53(5-6) (2011), 945 – 951, DOI: 10.1016/j.mcm.2010.11.002.

R. H. Haghi and Sh. Rezapour, Fixed points of multifunctions on regular cone metric spaces, Expositiones Mathematicae 28(1) (2010), 71 – 77, DOI: 10.1016/j.exmath.2009.04.001.

D. Ilic and V. Rakocevic, Common fixed points for maps on cone metric space, Journal of Mathematical Analysis and Applications 341(2) (2008), 876 – 882, DOI: 10.1016/j.jmaa.2007.10.065.

H. Long-Guang and Z. Xian, Cone metric spaces and fixed point theorems of contractive mappings, Journal of Mathematical Analysis and Applications 332(2) (2007), 1468 – 1476, DOI: 10.1016/j.jmaa.2005.03.087.

Q. Meng, On generalized algebraic cone metric spaces and fixed point theorems, Chinese Annals of Mathematics, Series B 40 (2019), 429 – 438, DOI: 10.1007/s11401-019-0142-8.

R. P. Pant, Common fixed point theorems for contractive maps, Journal of Mathematical Analysis and Applications 226 (1998), 251 – 258, URL: https://core.ac.uk/download/pdf/82474413.pdf.

Sh. Rezapour and R. Hamlbarani, Some notes on the paper “Cone metric spaces and fixed point theorems of contractive mappings”, Journal of Mathematical Analysis and Applications 345(2) (2008), 719 – 724, DOI: 10.1016/j.jmaa.2008.04.049.

G. Song, X. Sun, Y. Zhao and G. Wang, New common fixed point theorems for maps on cone metric spaces, Applied Mathematics Letters 23(9) (2010), 1033 – 1037, DOI: 10.1016/j.aml.2010.04.032.

P. P. Zabrejko, K-metric and K-normed linear spaces: survey, Collectanea Mathematica 48 (1997), 825 – 859, URL: http://dmle.icmat.es/pdf/COLLECTANEAMATHEMATICA_1997_48_04_37.pdf.

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Published

18-09-2023
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How to Cite

Kumar, S., Singhal, A., & Sharma, M. (2023). Common Fixed Point Theorems of Integral Type Contraction on Cone Metric Spaces and Applications. Communications in Mathematics and Applications, 14(2), 503–510. https://doi.org/10.26713/cma.v14i2.2142

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Research Article