... t>0.Proof. Putting y x in 3.20,weobtainμf3x−6f 2x15fxt≥ ρx,xt3.23Hindawi Publishing CorporationJournal of Inequalities and ApplicationsVolume 2009, Article ID 868423, ... mappings,” InformationSciences, vol. 178, no. 19, pp. 3791–3798, 2008.27 S. S. Chang, Y. J. Cho, and S. M. Kang, Nonlinear Operator Theory in Probabilistic Metric Spaces, NovaScience, Huntington, ... mappings g : X → Y defined by gx : f2x −16fx and h : X →Y defined by hx : f2x − 4fx are quadratic and quartic, respectively.Letting x y 0in 1.9, we have f00. Putting x 0in 1.9,wegetf−yfy.Thus...