Ansari’s method in generalizations of some results in the fixed point theory: Survey
Abstract
The aim of this paper is to show that the C-class function introduced by A. H. Ansari is a powerful weapon for the generalization of many important results in the theory of fixed points.
References
Abbas, M., & Jungck, G. 2008. Common fixed point results for noncommuting mappings without continuity in cone metric spaces. Journal of Mathematical Analysis and Applications, 341(1), pp.416-420. Available at: http://dx.doi.org/10.1016/j.jmaa.2007.09.070.
Ansari, A.H. 2014a. Note on "α - admissible mappings and related fixed point theorems", pp.373-376. In: The 2nd Regional Conference on Mathematics And Applications, PNU, September.
Ansari, A.H. 2014b. Note on "φ-ψ - contractive type mappings and related fixed point", pp.377-38. In: The 2nd Regional Conference on Mathematics And Applications, PNU, September.
Ansari, A.H., & Chandok, S. 2016. Make unification on α - admissible mappings and related fixed point theorems. Scientific Publications of the State University of Novi Pazar Series A: Applied Mathematics, Informatics and mechanics, 8(1), pp.65-71. Available at: http://dx.doi.org/10.5937/spsunp1601065a.
Ansari, A.H., Dolićanin-Djekić, D., Došenović, T., & Radenović, S. 2017. Coupled coincidence point theorems for (α-μ-ψ-H-F) two sided-contractive type mappings in partially ordered metric spaces using compatible mappings. Filomat, 31(9), pp.2657-2673. Available at: http://journal.pmf.ni.ac.rs/filomat/index.php/filomat/article/view/3628/2113.
Altun, I., Damjanović, B., & Djorić, D. 2010. Fixed point and common fixed point theorems on ordered cone metric spaces. Applied Mathematics Letters, 23(3), pp.310-316. Available at: http://dx.doi.org/10.1016/j.aml.2009.09.016.
Amini-Harandi, A., & Emami, H. 2010. A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations. Nonlinear Analysis: Theory, Methods and Applications, 72(5), pp.2238-2242. Available at: http://dx.doi.org/10.1016/j.na.2009.10.023.
Banach, S. 1922. Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fundamenta Mathematicae, 3, pp.133-181. Available at: http://eudml.org/doc/213289.
Boyd, D.W., & Wong, J.S.W. 1969. On nonlinear contractions. Proceedings of the American Mathematical Society, 20(2), pp.458-464. Available at: http://dx.doi.org/10.1090/s0002-9939-1969-0239559-9.
Đorić, D. 2009. Common fixed point for generalized (ψ,φ) - weak contractions. Applied Mathematics Letters, 22(12), pp.1896-1990. Available at: https://doi.org/10.1016/j.aml.2009.08.001.
Geraghty, M.A. 1973. On contractive mappings. Proceedings of the American Mathematical Society, 40(2), pp.604-608. Available at: http://dx.doi.org/10.1090/s0002-9939-1973-0334176-5.
Harjani, J., & Sadarangani, K. 2009. Fixed point theorems for weakly contractive mappings in partially ordered sets. Nonlinear Analysis: Theory, Methods and Applications, 71(7-8), pp.3403-3410. Available at: http://dx.doi.org/10.1016/j.na.2009.01.240.
Hussain, N., Karapinar, E., Salimi, P., & Akbar, F. 2013. α - admissible mappings and related fixed point theorems. Journal of Inequalities and Applications, 2013(1), p.114. Available at: http://dx.doi.org/10.1186/1029-242x-2013-114.
Jachymski, J. 2011. Equivalent conditions for generalized contractions on (ordered) metric spaces. Nonlinear Analysis: Theory, Methods and Applications, 74(3), pp.768-774. Available at: http://dx.doi.org/10.1016/j.na.2010.09.025.
Jungck, G. 1976. Commuting Mappings and Fixed Points. The American Mathematical Monthly, 83(4), pp.261-263. Available at: http://dx.doi.org/10.2307/2318216.
Karapinar, E., & Salimi, P. 2012. Fixed Point Theorems via Auxiliary Functions. Journal of Applied Mathematics, 2012, pp.1-9. Available at: http://dx.doi.org/10.1155/2012/792174.
Khan, M.S., Swaleh, M., & Sessa, S. 1984. Fixed point theorems by altering distances between the points. Bulletin of the Australian Mathematical Society, 30(1), pp.1-9. Available at: http://dx.doi.org/10.1017/s0004972700001659.
Liu, Z., Zhang, X., Ume, J.S., & Kang, S.M. 2015. Common fixed point theorems for four mappings satisfying ψ-weakly contractive conditions. Fixed Point Theory and Applications, 20(1). Available at: http://dx.doi.org/10.1186/s13663-015-0271-z.
Radenović, S., & Kadelburg, Z. 2010. Generalized weak contractions in partially ordered metric spaces. Computers & Mathematics with Applications, 60(6), pp.1776-1783. Available at: http://dx.doi.org/10.1016/j.camwa.2010.07.008.
Radenović, S., Kadelburg, Z., Jandrlić, D., & Jandrlić, A. 2012. Some results on weakly contractive maps. Bull. Iran. Math. Soc, 38(3), pp.625-645. Available at: http://bims.iranjournals.ir/article_229.html.
Rhoades, B.E. 1977. A comparison of various definitions of contractive mappings. Transactions of the American Mathematical Society, 226, pp.257-290. Available at: http://dx.doi.org/10.1090/s0002-9947-1977-0433430-4.
Rhoades, B.E. 2001. Some theorems on weakly contractive maps. Nonlinear Analysis: Theory, Methods and Applications, 47(4), pp.2683-2693. Available at: http://dx.doi.org/10.1016/s0362-546x(01)00388-1.
Salimi, P., Latif, A., & Hussain, N. 2013. Modified α-ψ-contractive mappings with applications. Fixed Point Theory and Applications, 1, p.151. Available at: http://dx.doi.org/10.1186/1687-1812-2013-151.
Samet, B., Vetro, C., & Vetro, P. 2012. Fixed point theorems for α-ψ contractive type mappings. Nonlinear Analysis: Theory, Methods and Applications, 75(4), pp.2154-2165. Available at: http://dx.doi.org/10.1016/j.na.2011.10.014.
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