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Fixed Points of Almost Generalized ( a , y) - Contractions with Rational Expressions



GVR Babu, KKM Sarma and VA Kumari


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].


α-admissible; ( a, y) -contraction mapping; generalized ( a, y) - contraction mapping; almost Jaggi contraction; almost generalized ( a, y) - contraction map with rational expression.


  • 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 (, ) αψ -contractive type mappings. Non-linear Analysis, (75), 2154–2165. doi: 10.1016/
  • Karapinar, E. and Samet, B. (2012). Generalized (, ) αψ -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.
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