Αβ – contractive mappings and upclass of type II function

Authors: Ansari A.H., Chandok S., Došenović T., Radenović S.

Keywords: complete metric space; altering distance function; αβ -contractive mapping; fixed point

Abstract:

Inspired by the recent result of N. Hussain et al. [N. Hussain, E. Karapinar, P. Salimi, F. Akbar, α-admissible mappings and related fixed point theorems, Journal of Ineaqualities and Applications 2013, 2013:114] we introduced two new type functions, which we denoted as upclass of type II and αβ -contractive mappings. Specifically, all results of the mentioned paper is possible to generalize using this two types of functions.

References:

[1] 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 & Applications, 72(5): 2238-2242 [2] Banach, S. (1922) Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fund. Math, 3, 133-181 [3] Geraghty, M.A. (1973) On contractive mappings. Proceedings of the American Mathematical Society, 40(2): 604-604 [4] Harjani, J., Sadarangani, K. (2009) Fixed point theorems for weakly contractive mappings in partially ordered sets. Nonlinear Analysis: Theory, Methods & Applications, 71(7-8): 3403-3410 [5] Hussain, N., Karapinar, E., Salimi, P., Akbar, F. (2013) alpha-Admissible mappings and related Fixed point Theorems. Journal of Inequalities and Applications, 2013(1): 114 [6] Jachymski, J. (2011) Equivalent conditions for generalized contractions on (ordered) metric spaces. Nonlinear Analysis: Theory, Methods & Applications, 74(3): 768-774 [7] Samet, B., Vetro, C., Vetro, P. (2012) Fixed point theorems for -contractive type mappings. Nonlinear Analysis: Theory, Methods & Applications, 75(4): 2154-2165