Fixed point theorems for (p, q)-quasi-contraction mappings in cone metric spaces

In this work, we give a partial positive answer to the question concerning the set-valued quasicontraction proposed by Amini-Harandi (Appl. Math. Lett. 24:1791-1794 2011). By a useful lemma, we prove a fixed point theorem for the set-valued quasi-contraction, which extends the range of contraction constant in result of Amini-Harandi from [0, 1/2) to [0, 1/3? 3). Also, we give a new simple proof for the result of quasi-contraction type proposed by Haghi et al. (Appl. Math. Lett. 25:843-846 2012). Finally, a counterexample and a theorem concerning cyclic set-valued mapping are given, which improve some recent results.

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Fixed point theorems for (p, q)-quasi-contraction mappings in cone metric spaces

Cited by 3 publications

References 13 publications

On Generalized Algebraic Cone Metric Spaces and Fixed Point Theorems

On Generalized Algebraic Cone Metric Spaces and Fixed Point Theorems

Equivalence of some properties in the theory of Banach algebras and applications

Fixed point theorem for question of set-valued quasi-contraction

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