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In this paper, some properties of a BPFR were studied. Also, level sets of BPFRs were studied with their properties. Some results were given and, in some cases, examples and counter-examples were constructed. In particular, we have shown that if a BPFR Q is a subset of another BPFR ρ, (s, t)-level (or strong level) subsets of Q are classical subsets of the (s, t)-level (or strong level) subsets of ρ and that the strong level subsets of a BPFR is a subset of the ordinary level subset of the same among others. By these, we have improved on some of the results in the previous work and have laid the right foundation for further works on these concepts.

In this work, we suggest some variants of Broyden-like algorithm to solve systems of nonlinear equations using various combination of quadrature rules . The proposed methods are three-step in nature whereby the first step is the initial iterate of the Newton’s method and the remaining two steps are the predictor-corrector of Broyden method and quadrature rules. Numerical tests show that these methods give encouraging results with respect to some existing Broyden-like methods in view of Dolan and More performance profile and Bogle and Perkins comparison index. [ABSTRACT FROM AUTHOR]

Broyden-like methods (or hybrid Broyden methods) are one of the efficient modifications of the classical Broyden method proposed to solve nonlinear systems of equations and to overcome the deficiencies of the classical Newton method. In this work, a variant of the Broyden-like method is proposed using the weighted combination of the Trapezoidal, Simpson and Midpoint quadrature rules. Hence a new hybrid Broyden method known as TSMM has been created based on these rules. The numerical tests confirm that TSMM is promising when subjected to comparison with other Broyden-like methods. [ABSTRACT FROM AUTHOR]

Strategic entry of women into entrepreneurial activities and subsequent entrepreneurial development in informal economy within the social system has received little academic attention in spite of the fact that, entrepreneurship development is important to economic growth and decent work. It has also been found to promote quality of life. The focus of this paper is to examine the influence of social system in strategic entry of women into informal economic activities in Nigeria, using Yoruba women textile traders at Balogun market, Lagos State, South-West, Nigeria as a case study. The paper is anchored on Social action theory by Max Weber. The paper utilized only qualitative method of data collection. Eight focus group discussions, and forty In-depth - interviews were used to collect information from the women participants who were purposively chosen. The data reveal that parents, family members, and social friends had great influence in strategic entry of women into textile trading at Balogun market and subsequent development of women entrepreneurial activities. This information is essential towards policy formulation for women entrepreneurial development in informal economy. [ABSTRACT FROM AUTHOR]