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All Journal Indonesian Journal of Social and Environmental Issues (IJSEI) Indonesian Journal of Research and Educational Review (IJRER) Journal of Fundamental Mathematics and Applications (JFMA) Indonesian Journal Of Educational Research and Review Journal of Environment and Sustainability Education Indonesian Journal of Mathematics and Applications
Wanjara, Amos Otieno
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Religion Agriculture, Biological Sciences & Forestry Arts Humanities Chemistry Computer Science & IT Decision Sciences, Operations Research & Management Education Environmental Science Languange, Linguistic, Communication & Media Law, Crime, Criminology & Criminal Justice Mathematics Physics Social Sciences Other

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A Classical Survey On Rotundity of Norms in Banach Spaces Wanjara, Amos Otieno
Indonesian Journal of Mathematics and Applications Vol. 2 No. 1 (2024): Indonesian Journal of Mathematics and Applications
Publisher : Universitas Brawijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21776/ub.ijma.2024.002.01.5

Abstract

The study on rotundity of norms in Banach spaces is of interest to many mathematicians. This is because rotundity properties are strongly applicable in many branches of Mathematics including but not restricted to functional analysis and topology. Some of the properties include: Rotund, Locally Uniformly Rotund, Uniformly Rotund in every direction, Uniformly Rotund in Weakly Compact sets of direction among others. In this paper, we give a survey of the standard results that will really revolutionize the study and research on rotundity of norms in the fields of functional analysis and topology among others.
ON A HIGHLY ROTUND NORM AND UNIFORMLY ROTUND NORM IN EVERY DIRECTION ON A FRECHE’T SPACE Wanjara, Amos Otieno
Journal of Fundamental Mathematics and Applications (JFMA) Vol 8, No 1 (2025)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v8i1.24207

Abstract

The word rotund comes from Latin word "rotundus" implying wheel-shaped or round (from rota wheel). Rotundity is the roundness of a 3-dimensional object. Some of the properties of rotundity include: UR-Uniformly Rotund, LUR-Locally Uniformly Rotund, MLUR-Midpoint Locally Uniformly Rotund, WUR-Weakly Uniformly Rotund, URED-Uniformly Rotund in Every Direction, HR- Highly Rotund, WLUR-Weakly Locally Uniformly Rotund and URWC-Uniformly Rotund in Weakly Compact sets of directions. Problems on Rotundity properties are still open. Smith gave a summary chart on rotundity of norms in Banach spaces. The chart left an open question whether or not a Highly Rotund norm(HR) implies Uniformly Rotund norm on Every Direction(URED). It is not clear whether if a Banach space has a Highly Rotund(HR) norm it follows that it has and equivalently URED. In this paper, we investigated the relationship between a Highly Rotund norm(HR) and a Uniformly Rotund norm in Every Direction(URED) on a Freche’t Space. The result shows that both Highly Rotund norm and Uniformly Rotund norm on Every Direction(URED) exist in Freche’t spaces. The implication of this result is that rotundity properties can be extended within spaces. This research work is very important since rotundity properties are strongly applicable in many branches of mathematics.
Impact of climate change on food production in Kenya Wanjara, Amos Otieno; Ogembo, Paul Okeyo
Journal of Environment and Sustainability Education Vol. 4 No. 2 (2026)
Publisher : Education and Development Research

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62672/joease.v4i2.207

Abstract

Climate Change Phenomena has posed a serious threat toward food production with ramifications on; food security, human and livestock lives.  This has led to dozens of Global Climate Summits to address the subject. The objectives of the study were to establish effects of climate change on grain crop production and livestock production in Kenya. Methodology was anchored on the work of Ferrer (1998), through which a meta-analysis of 39 empirical studies were done. The findings indicated that Climate Change occasioned by extreme weather events like La Nino (prolonged droughts) and El Nino (Rains Above normal annual average) have negative impacts on food and livestock production in Kenya.  High incidence of human and livestock diseases also occurs. Weather extremes, with serious repercussions on crop and livestock production have been reported in Kenya during the 2021/2022, 2023/2024 calendar years. Climate change make the naturally drier areas suffer flash floods and other associated challenges. It negatively impacts livestock rearing and food crop production especially in the Argo-Ecological zones of medium to low rainfall amounts of Arid and Semi-Arid lands. The findings have implications for essential mitigation/adaptation strategies including; crop diversification, planting of drought resistant food crops, improved seeds and diversified socio-economic livelihoods, towards improving food and livestock production in Kenya and possible remedies and resilience towards coping with the phenomenon.
Co-Authors Ogembo, Paul O Ogembo, Paul Okeyo