In the present note, it is proved that if a random Mann iteration scheme defined by two operators is convergent under some contractive inequality the limit point is a common fixed point of each of two random operators in a Banach space.
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A layer of a couple-stress fluid heated from below and permeated with suspended particles is considered. For the case of stationary convection, the couple-stress has a stabilizing effect whereas suspended particles have a destabilizing effect on the couple-stress fluid permeated with suspended particles, heated from below. Graphs have been plotted by giving numerical values to the parameters, to depict the stability characteristics. The principle of exchange of stabilities is found to hold true for the couple-stress fluid in the presence of suspended particles, heated from below.
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