Proximal Point Algorithms for Finding a Zero of a Finite Sum of Monotone Mappings in Banach Spaces

We introduce an iterative process which converges strongly to a zero of a finite sum of monotone mappings under certain conditions. Applications to a convex minimization problem are included. Our theorems improve and unify most of the results that have been proved in this direction for this important class of nonlinear mappings

Convergence theorems for fixed points of demicontinuous pseudocontractive mappings

Let be an open subset of a real uniformly smooth Banach space . Suppose is a demicontinuous pseudocontractive mapping satisfying an appropriate condition, where denotes the closure of . Then, it is proved that (i) for every ; (ii) for a given , there exists a unique path , , satisfying . Moreover, if or there exists such that the set is bounded, then it is proved that, as , the path converges strongly to a fixed point of . Furthermore, explicit iteration procedures with bounded error terms are proved to converge strongly to a fixed point of

Convergence of Mann’s type iteration method for generalized asymptotically nonexpansive mappings

AbstractLet C be a nonempty, closed and convex subset of a real Hilbert space H. Let Ti:C→H,i=1,2,…,N, be a finite family of generalized asymptotically nonexpansive mappings. It is our purpose, in this paper to prove strong convergence of Mann’s type method to a common fixed point of {Ti:i=1,2,…,N} provided that the interior of common fixed points is nonempty. No compactness assumption is imposed either on T or on C. As a consequence, it is proved that Mann’s method converges for a fixed point of nonexpansive mapping provided that interior of F(T)≠0̸. The results obtained in this paper improve most of the results that have been proved for this class of nonlinear mappings

Strong Convergence Theorems for a Common Fixed Point of a Family of Asymptotically k

We provide an iterative process which converges strongly to a common fixed point of finite family of asymptotically k-strict pseudocontractive mappings in Banach spaces. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators

Women empowerment and uptake of antenatal care services : A meta-analysis of Demographic and Health Surveys from 33 Sub-Saharan African countries

Background: Women empowerment has been linked to increased skilled antenatal care (ANC) service use. However, there is no evidence on the net effect of women empowerment on ANC in the Sub-saharan African (SSA) region. We aim to address the knowledge gap on whether or not women empowerment positively influences the uptake of ANC at the SSA regional level. Methods: We analyzed the Demographic Health Survey (DHS) datasets from 33 SSA countries. Following the DHS data analysis guideline, we measured women empowerment using two indicators. The first indicator is an index, which comprises decision-making on women’s own health, household purchase and visit to family or relatives whilst disagreeing statements that husband is justified in beating his wife constitutes the second indictor. We performed confounder-adjusted logistic regression analysis for the two indicators with ANC attendance in each of the 33 countries. Then, we pooled the adjusted Odds Ratios (OR) using the random effect model through the two-stage Individual Participant Data meta-analysis technique. Summary findings are reported in OR and corresponding 95 %CI and are presented in a forest plot. Results: Moderately empowered women had marginally higher odd of skilled ANC service across the SSA region (aOR = 1.19; 95 %CI: 1.03, 1.38, with a prediction interval of 0.58, 2.45). Conversely, being involved in the three decisions (aOR = 1.15; 95 %CI: 0.99, 1.33, with prediction interval 0.57, 2.31), and attitude towards wife-beating (aOR = 0.97; 95 %CI: 0.88, 1.06, with prediction interval of 0.63, 1.48) had no statistically significant relationship with ANC. Conclusions: Women empowerment did not predict the use of skilled ANC in the context of the SSA region. We recommend that further studies be conducted in order to understand how women empowerment affects skilled ANC service utilization in the region