Solvability and iterative approximations for a functional equation

This paper studies the existence, uniqueness and iterative approximations of solutions, bounded solutions and continuous bounded solutions for a functional equation arising in dynamic programming of multistage decision processes by using fixed point theorems and the iterative methods in complete metric spaces and Banach spaces, respectively. Four examples are given to illustrate the validity and applications of the results presented in this paper.     

Mechanism and Kinetics of Carbon Dioxide Capture Using Activated 2‐Amino‐2‐methyl‐1,3‐propanediol

The continued use of fossil fuels as primary sources of energy in industry and other applications stands the test of time, due to their availability and relatively lower cost than alternative sources of energy. In view of this perspective, obtaining an advanced bulk carbon dioxide (CO₂) capture medium becomes an urgent necessity so as to mitigate their effect, especially in global warming, as the use of fossil fuels produces a high rate of CO₂. In this work, the mechanism and kinetics of CO₂ capture using aqueous piperazine (PZ) as an activator to 2‐amino‐2‐methyl‐1,3‐propanediol (AMPD) were investigated. The termolecular mechanism was used to model the kinetics of the system. Reaction kinetics of the single pure amines was first obtained. The reaction rate constant, the k value of AMPD, was 77.2 m³/kmol·s, with a reaction order, n, of 1.25 at 298 K. while that of PZ was equal to 11,059 m³/kmol·s and n as 1.49 at 298 K. Blending of 0.05 kmol/m³ of PZ with 0.5 kmol/m³ of AMPD gave a rate constant, k, value of 23,319 m³/kmol·s and n equal to 1.23 at 298 K. The result obtained for the blended system is more than twice the value of the summation of the corresponding pure amines; in addition, it is comparably higher than the rate constant of monoethanolamine (MEA) in use as a commercial solvent for CO₂ capture. Therefore, an aqueous blend of PZ with AMPD deserves more comprehensive study as a solvent for commercial CO₂ capture. AMPD like other sterically hindered amines absorbs CO₂ in an equimolar ratio that is significantly higher than that of MEA. PZ serves as a promoter in the amine mixture and is required in a very small proportion.     

On some nonself mappings

Let X be a Banach space, let K be a non–empty closed subset of X and let T : K → X be a non–self mapping. The main result of this paper is that if T satisfies the contractive–type condition (1.1) below and maps ?K (?K the boundary of K) into K then T has a unique fixed point in K.