A New Iteration Process for Approximation of Common Fixed Points for Finite Families of Total Asymptotically Nonexpansive Mappings

LetEbe a real Banach space, andKa closed convex nonempty subset ofE. LetT1,T2,…,Tm:K→Kbemtotal asymptotically nonexpansive mappings. A simple iterative sequence{xn}n≥1is constructed inEand necessary and sufficient conditions for this sequence to converge to a common fixed point of{Ti}i=1mare given. Furthermore, in the case thatEis a uniformly convex real Banach space, strong convergence of the sequence{xn}n=1∞to a common fixed point of the family{Ti}i=1mis proved. Our recursion formula is much simpler and much more applicable than those recently announced by several authors for the same problem

Convergence of Path and Approximation of Common Element of Null Spaces of Countably Infinite Family of m

We prove path convergence theorems and introduce a new iterative sequence for a countably infinite family of m-accretive mappings and prove strong convergence of the sequence to a common zero of these operators in uniformly convex real Banach space. Consequently, we obtain strong convergence theorems for a countably infinite family of pseudocontractive mappings. Our theorems extend and improve some important results which are announced recently by various authors

Chemical composition, antibacterial efficacy, and antioxidant capacity of essential oil and oleoresin from Monodora myristica and Tetrapleura tetraptera in Southeast Nigeria

Specific to the West African sub-region, previous studies involving fruit, stem, and bark of Tetrapleura tetraptera as well as seeds of Monodora myristica have largely focused on phytochemical properties of aqueous and methanolic and ethanolic extracts. To supplement existing information, the chemical composition, antibacterial efficacy (tested against Escherichia coli and Staphylococcus aureus), and antioxidant capacity (1,1-diphenyl-2-picrylhydrazyl (DPPH∙) radical scavenging, ferric reducing power, and total antioxidant capacity) of essential oil and oleoresin extracted from T. tetraptera fruit and M. myristica seeds cultivated in Southeast Nigeria, were studied. Essential oil and oleoresin were respectively extracted by steam distillation and aqueous maceration. By way of gas chromatograph mass spectrometry (GC–MS) analysis, the chemical compounds from essential oil and oleoresin from M. myristica and T. Tetraptera samples totaled 6 and 5, as well as 27 and 16, respectively. Besides the oleoresin of M. myristica and the essential oil of T. tetraptera showing some resistance against S. aureus, the oleoresins seemed highly susceptible to E. coli—all of which demonstrated concentration-dependence to the antibacterial inhibition zone. Scavenging DPPH radical, reduction power activity, and total antioxidant capacity increased with essential oil and oleoresin extracts' concentrations, which positions M. myristica and T. tetraptera spices as very promising for food preservation, especially against autoxidation and microbial spoilage. © 2022, The Author(s).Wrocław University of Environmental and Life Sciences, PolandMinistry of Education and Science of the Russian Federation, MinobrnaukaAuthor Q.N.O. gratefully acknowledges the research funding from the Ministry of Science and Higher Education of the Russian Federation (Ural Federal University Program of Development within the Priority-2030 Program). Author S.J. and C.O.R.O. appreciate the financial support from Wrocław University of Environmental and Life Sciences, Poland

Iterative Approximation of a Common Zero of a Countably Infinite Family of m-Accretive Operators in Banach Spaces

Let E be a real reflexive and strictly convex Banach space which has a uniformly Gâteaux differentiable norm and C be a closed convex nonempty subset of E. Strong convergence theorems for approximation of a common zero of a countably infinite family of m-accretive mappings from C to E are proved. Consequently, we obtained strong convergence theorems for a countably infinite family of pseudocontractive mappings

Convergence of Path and Approximation of Common Element of Null Spaces of Countably Infinite Family of m-Accretive Mappings in Uniformly Convex Banach Spaces

We prove path convergence theorems and introduce a new iterative sequence for a countably infinite family of m-accretive mappings and prove strong convergence of the sequence to a common zero of these operators in uniformly convex real Banach space. Consequently, we obtain strong convergence theorems for a countably infinite family of pseudocontractive mappings. Our theorems extend and improve some important results which are announced recently by various authors

Family biosocial variables influencing the use of insecticide treated nets for children in Eastern Nigeria

Background: Effective reduction of malaria morbidity and mortality in Nigerian children under the age of five depends to a large extent on family biosocial factors. Although, the awareness of insecticide treated bed nets (ITNs) is reportedly high and increasing in Nigeria there remain large gaps between awareness, possession and use by families with children under the age of five in Nigeria. Aim: To determine the family biosocial variables that influence the use of insecticide treated nets for children in Eastern Nigeria. Materials and Methods: A descriptive hospital-based study was carried out from June 2008-June 2011 on a cross-section of 415 mothers with children under the age of five, who were treated for confirmed malaria, and met the selection criteria were interviewed using a pretested, structured researcher-administered questionnaire. The questionnaire tool elicited information on family socio-demographic variables, inter-spousal discussion, communication, concurrence and participation in the use of insecticide treated bed nets; and reasons for non-utilization. The period of usage in the previous 6 months was assessed and graded using a scoring system of 0-4. Scores of 1-4 indicated usage while score of 0 meant non use. Results: The rate of ITNs use was 53.0%. The family variables that significantly influenced utilization were secondary education and above of parents (mother: P0 = 0.009; father: P = 0.001), monogamy (P value = 0.024), family size of 1-4 (P value = 0.016) and parents living together ( P = 0.001); others included parents′ occupation (mother: P = 0.003; father: P = 0.04) and inter-spousal discussion (P value = 0.001), communication (P value = 0.001), concurrence ( P = 0.000) and participation ( P = 0.000). The commonest reason for non- use was inconvenience during sleep ( P = 0.04). Conclusion: This study shows that the rate of ITN use was marginally good. Specifically, this rate was significantly influenced by some family variables. The families of children under the age of five should, therefore, be the focus of intensive health promotion campaign to influence the use of ITNs to produce ITN family friendly communities