Abstract
Abstract In this paper, we generalize some coupled fixed point theorems for the mixed monotone operators F : X × X → X obtained in (Choudhury and Maity in Math. Comput. Model., 2011, doi:10.1016/j.mcm.2011.01.036) by significantly weakening the contractive condition involved and by replacing the mixed monotone property with another property which is automatically satisfied in the case of a totally ordered space. The proof follows a different and more natural new technique recently introduced by Berinde (Nonlinear Anal. 74:7347-7355, 2011). The example demonstrates that our main result is an actual improvement over the results which are generalized. MSC:47H10, 54H25.
Highlights
One of the authors (Yeol Je Cho) found mistakes during the proofreading
*Correspondence: yjcho@gnu.ac.kr 2Gyeongsang National University, Chinju, Korea Full list of author information is available at the end of the article
One of the authors (Yeol Je Cho) found mistakes during the proofreading. He was advised to retract his paper [ ] and resubmit the corrected version later for consideration
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