Fixed Point and Common Fixed Point Results of \(D_F\)-Contractions via Measure of Non-compactness with Applications
non-compactness. As an application, we prove some results on the existence of solutions for a system of an infinite fractional order differential equations in the space \(c\), where space \(c\) consists of real sequences having the finite limits.
R.P. Agarwal, D. O’Regan and N. Shahzad, Fixed point theorems for generalized contractive maps of Mei-Keeler type, Mathematische Nachrichten 276 (2004), 3 – 12.
R. Agarwal, M. Maheen and D. O’Regan, Fixed Point Theory and Applications, Cambridge University Press (2004).
A. Aghajani, R. Allahyari and M. Mursaleen, A generalization of Darbo’s theorem with application to the solvability of systems of integral equations, Journal of Computational and Applied Mathematics 260 (2014), 68 – 77, doi:10.1016/j.cam.2013.09.039.
J. Banas and M. Mursaleen, Sequence spaces and measure of noncompactness with applications to differential and integral equations, Springer India, doi:10.1007/978-81-322-1886-9.
S. Banach, Sur les opérations dens les énsembles abstraits et leur applications aux équations integrales, Fund. Math. 3 (1922), 133 – 181.
V. Berinde, Iterative Approximation of Fixed Points, Springer-Verlag, Berlin — Heidelberg (2007).
V. Berinde, On the approximation of fixed points of weak contractive mappings, Carpathian Journal of Mathematics 19 (1) (2003), 7 – 22.
D.W.Boyd and J.S.W. Wong, On nonlinear contractions, Proceedings of the American Mathematical Society 20 (1969), 458 – 464.
Lj.B. Ciric, A generalization of Banach’s contraction principle, Proceedings of the American Mathematical Society 45 (1974), 267 – 273.
G. Darbo, Punti uniti in transformazioni a condominio non compatto, Rendiconti del Seminario Mathematico della Universita di Padova 24 (1955), 84 – 92.
L.S. Goldenstein and A.S. Markus, On a measure of non-compactness of bounded sets and linear operators, in: Studies in Algebra and Mathematical Analysis, Kishinev, pp. 45 – 54 (1964).
L.S. Goldenstein, I.T. Gohberg and A. Markus, Investigation of some properties of bounded linear operators with their q-norms, Ucen. Zap. Kishinevsk. Univ. 29 (1957), 29 – 36.
V.I. Istratescu, On a measure of non-compactness, Bull. Math. Soc. Sci. Math. R.S. Roumanie (1972), 195 – 197.
R.Khalil, M.A. Horani, A. Yousef and M. Sababheh, A new definition of fractional derivative, Journal of Computational and Applied Mathematics 264 (2014), 65 – 70.
K. Kuratowski, Sur les espaces completes, Fund. Math. 5 (1930), 301 – 309.
J. Matkowski, Fixed point theorems for mappings with a contractive iterate at a point, Proceedings of the American Mathematical Society 62 (1977), 344 – 348.
S. Reich, Kannan’s fixed point theorem, Bollettino della Unione Matematica Italiana 4 (4) (1971), 1 – 11.
B.E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Analysis 47 (4) (2001), 2683 – 2693.
T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proceedings of the American Mathematical Society 136 (5) (2008), 1861 – 1869.
D. Wardowski, Fixed Points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory and Applications 94 (2012), 1 – 6, doi:10.1186/1687-1812-2012-94.
- There are currently no refbacks.
eISSN 0975-8607; pISSN 0976-5905