Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations

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Some Coincidence Point Theorems for Nonlinear Contraction in Ordered Metric Spaces (2011, background): “Harjani and Sadarangani [7,8] obtained some fixed point theorems in a complete ordered metric space using altering distance functions.”
Fixed point theorem for generalized weak contractions satisfying rational expressions in ordered metric spaces (2011, background): “Afterward, coupled fixed point and common fixed point theorems and their applications to periodic boundary value problems and integral equations were given in [5-7,12-19].”
Common fixed-point results for nonlinear contractions in ordered partial metric spaces (2011, background): “Using this lemma, he proved that some very recent fixed-point theorems for generalized contractions on ordered metric spaces obtained by Harjani and Sadarangani [15] and Amini-Harandi and Emami [5] do follow from an earlier result of O’Regan and Petruşel [29, Theorem 3.6].”
Fixed point theorems on ordered metric spaces and applications to nonlinear elastic beam equations (2012, result): “The obtained result in [19] was further extended and refined by many authors (see, for example, [2, 3, 10, 12, 16, 17, 18] and the references cited therein).”
Coupled fixed points in partially ordered metric spaces and application (2011, unknown): “The existence of solutions for matrix equations or ordinary differential equations by applying fixed point theorems are presented in [8,2,9,3,4,1].”