| dc.description.abstract | The notion of rotundity of norms is a very interesting area of research in analysis. The question whether if a norm is Highly Rotund implies it is Midpoint Locally Uniformly Rotund or whether a Uniformly Ro¬tund norm in Weakly Compact sets of direction implies Weakly Uniformly Rotund is not clear. It remains an open question whether or not Mid¬point Locally Uniformly Rotund implies Highly Rotund. In this study, we considered the Rotundity properties in a Frechet space. The Rotundity properties of major concern were Locally Uniformly Rotund, Midpoint Locally Uniformly Rotund and Highly Rotund. The objectives of this study therefore were to: Characterize Midpoint Locally Uniformly Ro¬tund norms; Determine the relationship between a Rotund norm and Locally Uniformly Rotund norms; Establish the relationship between a Rotund norm and a Highly Rotund norm. The methodology involved the use of triangle inequality, method of modulus of convexity in estimating the suprema and infima within the space and the method of renorrning Frechet spaces to satisfy the rotundity conditions. The results show that uniform and most rotundity exist in Frechet spaces. It is also confirmed that any equivalent norm on a Frechet space which is Very Rotund is also Rotund in Frechet space. Moreover, it is shown that if a norm is Locally Uniformly Rotund in a Frechet space then it implies that it is Rotund in a Frechet space. The result obtained will be helpful in comprehensive study on electromagnetic spectrum by quantum physicists and also in determination of the periodic points of the orbit of chaotic operators on Banach spaces. | en_US |