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It is the purpose of this paper to introduce an iterative process which converges strongly to a common point of the set of solutions of a finite family of generalized equilibrium problems, the set of fixed points of a finite family of continuous asymptotically quasi- $$\phi$$ -nonexpansive mappings in the intermediate sense, and the set of zeros of a finite family of $$\gamma$$ -inverse strongly monotone mappings in uniformly convex and uniformly smooth real Banach space. Our results improve and unify most of the results that have been proved for this important class of nonlinear mappings.

In this paper, we construct a Halpern-type subgradient extragradient iterative algorithm which converges strongly to a common point of the f-fixed point set of a continuous f-pseudocontractive mapp...

The purpose of this paper is to introduce an algorithm for approximating solutions of split equality variational inequality problems. A convergence theorem of the proposed algorithm is established in Hilbert spaces under the assumption that the associated mapping is uniformly continuous, pseudomonotone and sequentially weakly continuous. Finally, we provide several applications of our method and provide a numerical result to demonstrate the behavior of the convergence of the algorithm. Our results extend and generalize some related results in the literature.

The purpose of this paper is to study the method of approximation for zeros of the sum of a finite family of maximal monotone mappings in the setting of Banach spaces. Under some mild conditions, w...

Our purpose of this study is to construct an algorithm for finding a zero of the sum of two maximally monotone mappings in Hilbert spaces and discus its convergence. The assumption that one of the mappings is α-inverse strongly monotone is dispensed with. In addition, we give some applications to the minimization problem. Our method of proof is of independent interest. Finally, a numerical example which supports our main result is presented. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.

Let E be a real reflexive Banach space with its dual $$E^*$$ and f be a proper, convex and lower-semi-continuous function on E. The purpose of this paper is to introduce and study a new class of mappings from E into $$E^*$$ called f-pseudocontractive mappings with the notion of f-fixed points. In the case that E is a real reflexive Banach space and f is a strongly coercive, bounded and uniformly Frechet differentiable Legendre function which is strongly convex on bounded subsets of E, a sequence is constructed which converges strongly to a common f-fixed point of two f-pseudocontractive mappings. As a consequence, we obtain a scheme which converges strongly to a common zero of monotone mappings. Furthermore, this analog is applied to approximate solutions to convex optimization problems. Our results improve and generalize many of the results in the literature.

In this paper, we construct an iterative scheme for approximating common fixed points of a countable family of quasi-nonexpansive non-self mappings in a complete CAT(0) space. In addition, we prove $$\triangle $$ -convergence and strong convergence results of the scheme under appropriate conditions. Moreover, we construct an iterative scheme for approximating common fixed points of a countable family of demicontractive mappings and establish strong convergence result of the scheme under some mild conditions. Our results improve and generalize most of the results in the literature.

The purpose of this paper is to study the method of approximation for a zero of the sum of a finite family of maximally monotone mappings using viscosity type Douglas–Rachford splitting algorithm and prove some strong convergence theorems of the proposed algorithm under suitable conditions. In addition, we give some applications to the minimization problems. Finally, a numerical example which supports our main result is presented. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.

The purpose of this paper is to study the existence and approximation of a common fixed point of a pair of mappings satisfying a relaxed (?,?)-weakly N-contractive condition and existence and approximation of a fixed point of a relaxed (?,?)-weakly N-contraction mapping in the setting of modular spaces. Our theorems improve and generalize the results in Mongkolkeha and Kumam [23] and ?zt?rk et. al [26]. To validate our results numerical examples are provided.

Recently, Chang et al. (2015) constructed an algorithm that converges weakly to the solution of the split equality fixed point problem for quasi-pseudo-contractive mappings under some suitable cond...

The purpose of this paper is to study a forward–backward algorithm for approximating a zero of the sum of maximally monotone mappings in the setting of Banach spaces. Under some mild conditions, we prove a new strong convergence theorem for the algorithm produced by the method in real reflexive Banach spaces. In addition, we give some applications to the minimization problems. Finally, we provide a numerical example, which supports our main result. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.

The purpose of this paper is to study the method of approximation for a zero of the sum of two maximal monotone mappings in Banach spaces and prove strong convergence of the proposed method under suitable conditions. The method of proof is of independent interest. In addition, we give some applications to the minimization problems. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.

Let X be a real Banach space and X* be its dual. Let F : X → X* and K : X → X* be Lipschitz monotone mappings. In this paper an explicit iterative scheme is constructed for approximating solutions of the Hammerstein type equation, 0 = u + KFu; when they exist. Strong convergence of the scheme is obtained under appropriate conditions. Our results improve and unify many of the results in the literature.Mathematics Subject Classification (2010): 47H30, 47H05, 34A34.Keywords: Hammerstein type equation, monotone mapping, nonlinear equations

Our purpose in this paper is to construct Ishikawa iterative scheme formulti-valued non-self mappings in CAT(0) spaces. Then we obtain strong convergence of the scheme to a fixed point of multi-valued hemicontractive non-self mapping in a complete CAT(0) space. In addition, we define pseudocontractive mapping in CAT(0) spaces and show that a pseudocontractive mapping T with $$F(T)\not =\emptyset $$ and $$Tp=\{p\}, \forall p\in F(T)$$ is hemicontractive mapping. Furthermore, we give an example of hemicontractive mapping which is not pseudocontarctive to show that the converse is not necessarily true. Our theorems improve and unify most of the results in the literature.

We define Mann iterative scheme in CAT(0) spaces and obtain 4-convergence and strong convergence of the iterative scheme to a fixed point of multi-valued nonexpansive non-self mappings. We also obtain strong convergence of the scheme to a fixed point of multi-valued quasi-nonexpansive non-self mappings under appropriate conditions. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators.

In this paper, we prove strong convergence of Mann iterative schemes to fixed points of multi-valued demicontractive non-self mappings in complete CAT(0) spaces under appropriate conditions. In addition, △− convergence or strong convergence of Mann iterative scheme to a fixed point of single-valued k-strictly pseudocontractive non-self mapping is obtained. Our theorems improve and unify most of the results in the literature.

A Mann-type iterative scheme which converges strongly to a fixed point of a multi-valued nonexpansive non-self mapping T is constructed in a real Hilbert space H. We also constructed a Mann-type sequence which converges to a fixed point of a multi-valued quasi-nonexpansive non-self mapping under appropriate conditions. In addition, an Ishikawa-type iterative scheme which approximates the fixed points of multi-valued Lipschitz pseudocontractive non-self mappings is constructed in Banach spaces. The results obtained in this paper improve and extend the known results in the literature.

BackgroundTuberculosis is a global public health problem. One of the overarching dilemmas and challenges facing most tuberculosis program is non-adherence to treatment. However, in Ethiopia there are few studies with variable and inconsistent findings regarding non-adherence to treatment for tuberculosis.MethodsThis systematic review and meta-analysis was conducted to determine the prevalence of non-adherence to tuberculosis treatment and its determinants in Ethiopia. Biomedical databases including PubMed, Google Scholar, Science Direct, HINARI, EMBASE and Cochrane Library were systematically and comprehensively searched. To estimate the pooled prevalence, studies reporting the prevalence of adherence or non-adherence to tuberculosis treatment and its determinants were included. Data were extracted using a standardized data extraction tool prepared in Microsoft Excel and transferred to STATA/se version-14 statistical software for further analyses. To assess heterogeneity, the Cochrane Q test statistics and I2 test were performed. Since the included studies exhibited high heterogeneity, a random effects model meta- analysis was used to estimate the pooled prevalence of non-adherence to tuberculosis treatment. Finally, the association between determinant factors and non-adherence to tuberculosis treatment was assessed.ResultsThe result of 13 studies revealed that the pooled prevalence of non-adherence to tuberculosis treatment in Ethiopia was found to be 21.29% (95% CI: 15.75, 26.68). In the subgroup analysis, the highest prevalence was observed in Southern Nations and Nationalities of Ethiopia, 23.61% (95% CI: 21.05, 26.17) whereas the lowest prevalence was observed in Amhara region, 10.0% (95% CI: 6.48, 13.17.0;). Forgetfulness (OR = 3.22, 95% CI = 2.28, 4.53), fear side effect of the drugs (OR = 1.93, 95% CI = 1.37, 2.74), waiting time ≥ 1 hour during service (OR = 4.88, 95% CI = 3.44, 6.91) and feeling distance to health institution is long (OR = 5.35, 95% CI = 4.00, 7.16) were found to be determinants of non-adherence to tuberculosis treatment.ConclusionIn this meta-analysis, the pooled prevalence of non-adherence to tuberculosis treatment in Ethiopia was high. Forgetfulness, fear of side effect of the drugs, long waiting time (≥1 hour) during service and feeling distance to health institution is long were the main risk factors for non-adherence to tuberculosis treatment in Ethiopia. Early monitoring of the side effects and other reasons which account for missing medication may increase medication adherence in patients with tuberculosis in Ethiopia.

Background Tuberculosis and HIV/AIDS are the major public health problems in many parts of the world particularly in resource limited countries like Ethiopia. Although studies have been conducted on the prevalence and associated factors of TB / HIV co-infection in Ethiopia, there is no comprehensive data on the magnitude and risk factors at a national and regional levels. Therefore, this review is aimed to summarize the prevalence of TB /HIV co-infection in Ethiopia using meta-analysis based on a systematic review of published articles & grey literatures. Methods To conduct this systematic review and meta-analysis, major databases such as Pub Med, Google scholar, CINAHL, Africa Journals Online and Google were systematically searched using search terms. PRISMA guideline was followed in the study. Two authors extracted all necessary data using a standardized data extraction format, and analysis was done using STATA version 11. A Statistical heterogeneity across the studies was evaluated by using Cochran's Q test and I2 statistic. The pooled effect size was conducted in the form of prevalence and associations were measured using odds ratio. Moreover, the univariate meta regression was performed by considering the sample size to determine potential sources of heterogeneity. The Egger's weighted regression and Begg's rank correlation tests were used to assess potential publication biases. Results This meta-analysis included 21 studies with a total of 12,980 participants. The pooled prevalence of TB / HIV Co-infection was 25.59% (95% CI (20.89%-30.29%). A significant association was found between low CD4 counts (OR: 3.53; 95% CI: 1.55, 8.06), advanced WHO stage (OR: 6.81; 95% CI: 3.91, 11.88) and TB/ HIV/AIDS Co-infection. Conclusion This finding revealed that the magnitude of TB /HIV co-infection in Ethiopia is increasing and deserves special attention. Low CD4 count and advanced WHO stage are contributing factors for dual infection. Establishing mechanisms such as Conducting surveillance to determine HIV burden among TB patients and TB burden among HIV patients, and intensifying the three I's (Intensive case finding, INH Preventive Therapy and Infection control) should be routine work of clinicians. Moreover, early screening & treatment should be provided to those patients with low CD4 count and advanced WHO stage.

In this paper, we define a Halpern–Ishikawa type iterative method for approximating a fixed point of a Lipschitz pseudocontractive non-self mapping T in a real Hilbert space settings and prove strong convergence result of the iterative method to a fixed point of T under some mild conditions. We give a numerical example to support our results. Our results improve and generalize most of the results that have been proved for this important class of nonlinear mappings.

The purpose of this paper is to prove convergence of a one-step iterative algorithm to approximate a common fixed point of finite family of asymptotically quasi-nonexpansive mappings in a uniformly convex Banach space by assuming some control conditions on the parameters. Our results extend and improve the corresponding results in the literature.

In this article, we introduce an algorithm which has strong convergence for solving the variational inequality problem for η-inverse strongly accretive mappings in the set of common fixed points of finite family of λ-strictly 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.

The purpose of this paper is to propose and study an algorithm for solving the general split equality problem governed by Bregman quasi-nonexpansive mappings in Banach spaces. Under some mild conditions, we established the norm convergence of the proposed algorithm. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.