Fixed Points of Almost Generalized (a, y)-Contractions with Rational Expressions
Abstract:
In this paper, we introduce almost generalized (a, y)-contractions with rational expression type mappings and establish the existence of fixed points for such mappings in complete partially ordered metric spaces. Further, we define `Condition (H)’ and prove the existence of unique fixed point under the additional assumption `Condition (H)’. Our results generalize the results of Arshad, Karapinar and Ahmad [1] and Harjani, Lopez and Sadarangani [2].
Author(s):
GVR Babu, KKM Sarma and VA Kumari, Department of Mathematics, Andhra University, Visakapatnam-530 003, India.
DOI:
Keywords:
References:
Arshad, M. Karapinar, E. and Ahmad, J. (2013). Some unique fixed point theorem for rational contractions in partially ordered metric spaces. Journal Of Inequalities and Applcations, Article ID 307234.
Harjani, J., Lopez, B. and Sadarangani, K. (2010). A fixed point theorem for mappings satisfying a contractive condition of rational type on a partially ordered metric space. Abstract and Applied Analysis, 1–8.
Jaggi, D.S. (1977). Some unique fixed point theorems. Indian Journal of Pure and Applied Mathematics, (8), 223–230.
Samet, B., Vetro, C. and Vetro, P. (2012). Fixed point theorem for (α, ψ)-contractive type mappings. Non-linear Analysis, (75), 2154–2165.doi: 10.1016/j.na.2011.10.014.
Karapinar, E. and Samet, B.(2012). Generalized (α, ψ) -contractive type mappings and related fixed point theorems with applications. Abstract and Applied Analysis, Article ID 793486, 17 pages. doi: 10.1155/2012/793486.
Bhaskar, T.G. and Lakshmikantham, V. (2006). Fixed point theorems in partially ordered metric spaces and applications. Non-linear Analysis, (65), 1379–1393.
