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Wardowski [Fixed Point Theory Appl., 2012:94] introduced a new concept of contraction and proved a fixed point theorem which generalizes Banach contraction principle. Following this direction of research, we will present some fixed point results for closed multi-valued F-contractions or multi-valued mappings which satisfy an F-contractive condition of Hardy-Rogers-type, in the setting of complete metric spaces or complete ordered metric spaces. An example and two applications, for the solution of certain functional and integral equations, are given to illustrate the usability of the obtained results.

Very recently, Khojasteh, Shukla and Radenović [F. Khojasteh, S. Shukla, S. Radenović, Filomat, 29 (2015), [1189][1190][1191][1192][1193][1194] introduced the notion of Z-contraction, that is, a nonlinear contraction involving a new class of mappings namely simulation functions. This kind of contractions generalizes the Banach contraction and unifies several known types of nonlinear contractions. In this paper, we consider a pair of nonlinear operators satisfying a nonlinear contraction involving a simulation function in a metric space endowed with a partial order. For this pair of operators, we establish coincidence and common fixed point results. As applications, several related results in fixed point theory in a metric space with a partial order are deduced. c 2015 All rights reserved.

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Objective: GH replacement therapy in children with GH deficiency (GHD) mainly promotes linear growth. Not only have very few studies fully analyzed the metabolic consequences of GH therapy, but also the question as to whether GH may affect adipokine secretion has been insufficiently investigated. Our aim was to study the effects of GH replacement therapy on auxological data, lipid and glycemic profiles, insulin homeostasis (HOMA-IR) and serum adipokines in children.Methods: This was a 1-year prospective study. Thirty-four GHD children (11.6G2.6 years) and thirty healthy matched controls were enrolled. Children affected by GHD were studied both before beginning continuous GH replacement therapy and again at 12 months. Results: At the beginning of the study, total and LDL cholesterol were higher in GHD children than in controls (P!0.001), whereas HDL cholesterol, triglycerides, insulin, HOMA-IR, leptin, and adiponectin were similar. At 12 months of continuous GH replacement therapy in the GHD group, there was a significant increase in both auxological data and IGF-I (P!0.001); total cholesterol (P!0.001), LDL (P!0.001), triglycerides (P!0.005), and leptin (P!0.001) decreased significantly; HDL (P!0.003), insulin (P!0.001), HOMA-IR (P!0.001) increased while adiponectin was unmodified. Furthermore, IGF-ID showed an inverse correlation with leptin D (rZK0.398, PZ0.02). Conclusions: In GHD children, the evaluation of metabolic parameters proves to be a useful tool for the evaluation of auxological parameters during GH replacement therapy. In our study, GH replacement therapy in GHD children improved final height, restored IGF-I levels, reduced leptin levels, and improved the lipid profile, without producing any unfavorable effects on glucose metabolism. 156 353-360 European Journal of Endocrinology

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