The purpose of this paper is to study solvability of two classes of functional equations and a class of system of functional equations arising in dynamic programming of multistage decision processes. By using fixed point theorems, a few existence and uniqueness theorems of solutions and iterative approximation for solving these classes of functional equations are established. Under certain conditions, some existence theorems of coincidence solutions for the class of system of functional equations are shown. Some examples are given to demonstrate the advantage of our results than existing ones in the literature.  2004 Elsevier Inc. All rights reserved.

Transition metal (Fe, Co and Ni) doped carbon xerogels (CXs) were synthesised by one-pot pyrolysis of the sol-gel polymer of resorcinol and formaldehyde in the presence of the corresponding metal nitrates. N 2 adsorption-desorption and scanning and transmission electron microscopies proved that the addition of different metals could exert a remarkable influence on the textural properties. From X-ray diffraction, the phase of the metallic species was confirmed. Scanning electron microscopy images revealed that the surface morphologies of the resultant metal-CXs were composed of carbon microspheres. Transmission electron microscopy observations illustrated that Ni-CX was made of uniform carbon nanotubes that differed from the core/shell structures of Fe-and Co-xerogels. Measurements on the magnetic properties indicated that the Fe-, Co-and Ni-CXs exhibited typical ferromagnetic characteristics at room temperature.

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