×

A new approach for the approximations of solutions to a common fixed point problem in metric fixed point theory. (English) Zbl 1470.54038

Summary: We provide sufficient conditions for the existence of a unique common fixed point for a pair of mappings \(T, S : X \rightarrow X\), where \(X\) is a nonempty set endowed with a certain metric. Moreover, a numerical algorithm is presented in order to approximate such solution. Our approach is different to the usual used methods in the literature.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E40 Special maps on metric spaces
65J15 Numerical solutions to equations with nonlinear operators
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Ahmad, B.; Nieto, J. J., Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions, Computers & Mathematics with Applications, 58, 9, 1838-1843 (2009) · Zbl 1205.34003 · doi:10.1016/j.camwa.2009.07.091
[2] Goodrich, C. S., Existence of a positive solution to systems of differential equations of fractional order, Computers & Mathematics with Applications, 62, 3, 1251-1268 (2011) · Zbl 1253.34012 · doi:10.1016/j.camwa.2011.02.039
[3] Jleli, M.; Samet, B., Existence of positive solutions to a coupled system of fractional differential equations, Mathematical Methods in the Applied Sciences, 38, 6, 1014-1031 (2015) · Zbl 1311.34015 · doi:10.1002/mma.3124
[4] Liu, S.; Wang, G.; Zhang, L., Existence results for a coupled system of nonlinear neutral fractional differential equations, Applied Mathematics Letters, 26, 12, 1120-1124 (2013) · Zbl 1308.34103 · doi:10.1016/j.aml.2013.06.003
[5] Su, X., Boundary value problem for a coupled system of nonlinear fractional differential equations, Applied Mathematics Letters, 22, 1, 64-69 (2009) · Zbl 1163.34321 · doi:10.1016/j.aml.2008.03.001
[6] Jungck, G., Compatible mappings and common fixed points, International Journal of Mathematics and Mathematical Sciences, 9, 4, 771-779 (1986) · Zbl 0613.54029 · doi:10.1155/S0161171286000935
[7] Cirić, L.; Samet, B.; Vetro, C., Common fixed point theorems for families of occasionally weakly compatible mappings, Mathematical and Computer Modelling, 53, 5-6, 631-636 (2011) · Zbl 1217.54042 · doi:10.1016/j.mcm.2010.09.015
[8] Damjanović, B.; Samet, B.; Vetro, C., Common fixed point theorems for multi-valued maps, Acta Mathematica Scientia. Series B. English Edition, 32, 2, 818-824 (2012) · Zbl 1265.54166 · doi:10.1016/s0252-9602(12)60063-0
[9] Nashine, H. K.; Samet, B.; Vetro, C., Fixed point theorems in partially ordered metric spaces and existence results for integral equations, Numerical Functional Analysis and Optimization, 33, 11, 1304-1320 (2012) · Zbl 1272.54039 · doi:10.1080/01630563.2012.675395
[10] Berinde, V., Contracţii Generalizate şi Aplicaţii, 22 (1997), Baia Mare, Romania: Editura Cub Press, Baia Mare, Romania
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.