In 2012, Samet, Vetro and Vetro introduced α-ψ-contractive mappings and gave some results on a fixed point of the mappings (Samet et al. in Nonlinear Anal. 75:2154-2165. In fact, their technique generalized some ordered fixed point results (see (Alikhani et al. in Filomat, 2012, to appear) and (Samet et al. in Nonlinear Anal. 75:2154-2165). By using the main idea of (Samet et al. in Nonlinear Anal. 75:2154-2165, we give some new results for α-ψ-Ciric generalized multifunctions and some related self-maps. Also, we give an affirmative answer to a recent open problem which was raised by Haghi, Rezapour and Shahzad in 2012.

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The goal of this work is to introduce an extended interpolativeĆirić-Reich-Rus type contraction by the approach of Wardowski. We establish some related fixed point results (for single and multivalued-mappings). Some examples are presented to illustrate the main result. Moreover, we give an application to integral equations. MSC: Primary 47H10; secondary 54H25

A novel and simple synthesis of 3-aryl-2,6-dicyano-5-methylanilines is described. Reactions between nitrostyrenes and excess malononitrile in the presence of sodium carbonate in 80% ethanol proceeded at room temperature to afford the aromatic products in good yields. A mechanism for the formation of the products is proposed.

SUMMARYA new approach for optimal shape design based on a CAD-free framework for shape and unstructured mesh deformations, automatic differentiation for the gradient computation and mesh adaption by metric control in 2D is presented. The CAD-free framework is shown to be particularly convenient for optimization when the mesh connectivities and control space size are variable during optimization. Constrained optimization for a transonic regime has been investigated in both 2D and 3D. Copyright