Search

The global outbreak of the coronavirus pandemic has been experienced differently by people depending on their socio-cultural contexts. These varied experiences are expressed in various forms of communication, including cartoons. This paper examines the pragmatic resources inherent in COVID-19-related cartoons depicting the impact of the virus on Nigerian society. Forty COVID-19-related cartoons, circulated on social media, were collected on Twitter and WhatsApp platforms between March and April 2020 as data. Multimodality and presupposition served as theoretical framework and descriptive research design was adopted. Findings reveal five socio-contextual domains, religion, health, economy, politics and governance nd family, characterizing the social experiences of Nigerians during the pandemic. Through the evocation of situational reality, pragmatic sarcasm, punning, and orientation to government insensitivity, the cartoonists evoke pragmatic functions of informing and warning about social behaviours in the religion, family and health domains; recreating situational realities on socioeconomic impacts in the domain of economy; and satirizing government policies and mocking politicians’ insincerity in the domain of politics and governance on sociopolitical experiences of Nigerians before and during the pandemic. The study concludes cartoons are a strong means of portraying societal realities and people’s experiences comically and graphically.

In this article, we study the split variational inclusion and fixed point problems using Bregman weak relatively nonexpansive mappings in the pp-uniformly convex smooth Banach spaces. We introduce an inertial shrinking projection self-adaptive iterative scheme for the problem and prove a strong convergence theorem for the sequences generated by our iterative scheme under some mild conditions in real pp-uniformly convex smooth Banach spaces. The algorithm is designed to select its step size self-adaptively and does not require the prior estimate of the norm of the bounded linear operator. Finally, we provide some numerical examples to illustrate the performance of our proposed scheme and compare it with other methods in the literature.

Abstract In this article, we propose a viscosity extragradient algorithm together with an inertial extrapolation method for approximating the solution of pseudomonotone equilibrium and fixed point problem of a nonexpansive mapping in the setting of a Hadamard manifold. We prove that the sequence generated by our iterative method converges to a solution of the above problems under some mild conditions. Finally, we outline some implications of our results and present several numerical examples showing the implementability of our algorithm. The results of this article extend and complement many related results in linear spaces.

Dakaliis a unique feature that plays a functional role in the Hausa Vernacular Architecture (HVA). However, events have revealed a gradual extinction from the streetscape due to contemporary changes in the cityscapes and the general physical development with the concomitant effect of reduction in the performance of the expected function in buildings. This paper focuses on the enumeration and documentation of buildings with or without this significant feature. It also appraises the attendant contemporary architectural design-shift. The paper adopts quantitative research approach; purposive sampling and Content analysis method in the selection of potential respondents and review of related literature respectively. This was complimented with the conduct of field survey, selective interviews and observation. Information extracted therefrom was descriptively presented. Findings revealed that out of the total of 235 selected samples, 50 buildings (about 21%) reflects the HVA features; only 14 buildings (about 5.95%), though with retained feature HVA like the Dakali, but have significantly lost the features and transiting towards the contemporary/modern trends; while, 171 (about 72.7%) of the buildings in the study area have completely been transformed. The paper concludes that there is the need for the identification and comprehensive documentation other HVA features for posterity, so as not to allow their total loss without any form of record of their historical existence, due to fast changes been experienced arising from the advent of innovative design, challenges of rapid rate of global urbanization and the trending break-through in technological advancement within our urban/city settings

This paper investigates the impact of modern and contemporary trends on an eighty-seven years’ old mosque in Jos built in the typical Hausa Vernacular Architectural style, as well as the extent to which its vernacular features have been lost and/or retained. The study focused on selected architectural features which do not essentially affects the performance of the primary mosque's functions. A qualitative survey was adopted using case study approach and complemented with content analysis of related literature reviewed to extract information on the challenges of restoration and preservation or conservation of the key features of traditional Hausa Architecture on the Mosque buildings in the study area of Jos, Plateau State, Nigeria from the randomly selected traditional/indigenous builders and practicing architects. The Yandoka Street Mosque was purposively selected as a case study, because of its historical antecedence, religious and communal attachment, as well as its socio-political and cultural relevance in the study area. Information was collected using the unobtrusive observation method and were descriptively presented in the form of layout plan, material deduction, construction techniques and technology adopted for the mosque’s construction. Findings shows that, the influence of the identified key factors have become a threatening phenomenon to the survival of the preservation and conservation historical values and heritages of Hausa mosque architectural style. The paper advocates preservation and conservation of the original mosque architectural style from the point of view of sustainability and made recommendations towards the preservation, development and execution of strategies for branding, national identity and protection of value systems for the public good

Abstract In this work, we study a self-adaptive extragradient algorithm for approximating a common solution of a pseudomonotone equilibrium problem and fixed-point problem for multivalued nonexpansive mapping in Hadamard spaces. Our proposed algorithm is designed in such a way that its step size does not require knowledge of the Lipschitz-like constants of the bifunction. Under some appropriate conditions, we establish the strong convergence of the algorithm without prior knowledge of the Lipschitz constants. Furthermore, we provide a numerical experiment to demonstrate the efficiency of our algorithm. This result extends and complements recent results in the literature.

In this paper, we introduce a Halpern iteration process for computing the common solution of split generalized equilibrium problem and fixed points of a countable family of Bregman W-mappings with multiple output sets in reflexive Banach spaces. We prove a strong convergence result for approximating the solutions of the aforementioned problems under some mild conditions. It is worth mentioning that the iterative algorithm employ in this article is designed in such a way that it does not require the prior knowledge of operator norm. We also provide some numerical examples to illustrate the performance of our proposed iterative method. The result discuss in this paper extends and complements many related results in literature.

In this paper, we introduce a new iterative algorithm for approximating a common solution of Split Hierarchical Monotone Variational Inclusion Problem (SHMVIP) and Fixed Point Problem (FPP) of k-strictly pseudocontractive mappings in real Hilbert spaces. Our proposed method converges strongly, does not require the estimation of operator norm and it is without imposing the strict condition of compactness; these make our method to be potentially more applicable than most existing methods in the literature. Under standard and mild assumption of monotonicity of the SHMVIP associated mappings, we establish the strong convergence of the iterative algorithm.We present some applications of our main result to approximate the solution of Split Hierarchical Convex Minimization Problem (SHCMP) and Split Hierarchical Variational Inequality Problem (SHVIP). Some numerical experiments are presented to illustrate the performance and behavior of our method. The result presented in this paper extends and complements some related results in literature.

Hausa Vernacular architecture is informed and shaped by cultural and religious values, wherein, Dakali and Zaure are unique features that plays a pivotal role. Cities are metaphorically described as historically solidified environment in time and in space. Thus, depicting physical, archival and artefacts of the past and present, from which it develops the future of human civilization and cultures set in a time series continuum. Hausa vernacular architecture is gradually getting evolved through modern trends by renewing, re-ordering and replacement of these features. Therefore, there is the need for studies to be carried out extensively on or before adaptation, adoption and implementation of evolving trends, in order to conserve and preserve the Hausa man’s cultural and religious values in their architecture. The paper seeks to draw attention towards the preservation and conservation of indigenous heritages through vernacular architecture, especially with the examples from the characters of Hausa architecture, without arguing for a complete reversal to the past life styles, value and techniques that would neither be out-of-place with emerging trends and acceptability of modern technology nor be balkanized. Information was essentially extracted from relevant literature on the subject matter; adopts purposive sampling and content analysis method in the selection of study area and sample size; as well as, in the extraction of features of Hausa vernacular architecture respectively. This was complimented with field survey in the form of interviews, observation and case study. Results therefrom were discussed and descriptively presented. Findings revealed that, the identified features have remained prominent and continued to perform their expected functions. The paper conclude by underscoring the need to stimulate awareness, rejuvenate and regenerate the Hausa/Fulani vernacular architecture and cultural-heritage perceptibility through creative and integrative use of architectural designs and planning concepts and skills that will be sensitive to the rebirth of cultural symbols, relics, configurations, ornamentations as symbolic expressions depicting history, branding and conveying one message or the other, about the inhabitants for better understanding and conservation of fun-memories of the cultural/traditional values and heritages.

Abstract In this paper, we study the existence of solution of the generalized equilibrium problem (GEP) in the framework of an Hadamard manifold. Using the KKM lemma, we prove the existence of solution of the GEP and give the properties of the resolvent function associated with the problem under consideration. Furthermore, we introduce an iterative algorithm for approximating a common solution of the GEP and a fixed point problem. Using the proposed method, we obtain and prove a strong convergence theorem for approximating a solution of the GEP, which is also a fixed point of a nonexpansive mapping under some mild conditions. We give an application of our convergence result to a solution of the convex minimization problem. To illustrate the convergence of the method, we report some numerical experiments. The result in this paper extends the study of the GEP from the linear settings to the Hadamard manifolds.

The purpose of this article is to study and analyse a new extragradient-type algorithm with an inertial extrapolation step for solving split fixed-point problems for demicontractive mapping, equilibrium problem, and pseudomonotone variational inequality problem in real Hilbert spaces. One of the advantages of the proposed algorithm is that a strong convergence result is achieved without a prior estimate of the Lipschitz constant of the cost operator, which is very difficult to find. In addition, the stepsize is generated at each iteration by some simple computations, which allows it to be easily implemented without the prior knowledge of the Lipschitz constant of the cost operator. Some numerical experiments are reported to show the performance and behaviour of the sequence generated by our algorithm. The obtained results in this article extend and improve many related recent results in this direction in the literature.

In this research paper, we present a new inertial method with a self-adaptive technique for solving the split variational inclusion and fixed point problems in real Hilbert spaces. The algorithm is designed to choose the optimal choice of the inertial term at every iteration, and the stepsize is defined self-adaptively without a prior estimate of the Lipschitz constant. A convergence theorem is demonstrated to be strong even under lenient conditions and to showcase the suggested method’s efficiency and precision. Some numerical tests are given. Moreover, the significance of the proposed method is demonstrated through its application to an image reconstruction issue.

In this paper, we introduce a self-adaptive projection method for finding a common element in the solution set of variational inequalities (VIs) and fixed point set for relatively nonexpansive mappings in 2-uniformly convex and uniformly smooth real Banach spaces. We prove a strong convergence result for the sequence generated by our algorithm without imposing a Lipschitz condition on the cost operator of the VIs. We also provide some numerical examples to illustrate the performance of the proposed algorithm by comparing with related methods in the literature. This result extends and improves some recent results in the literature in this direction.

The main purpose of this paper is to introduce a parallel iterative algorithm for approximating the solution of a split feasibility problem on the zero of monotone operators, generalized mixed equilibrium problem and fixed point problem. Using our algorithm, we state and prove a strong convergence theorem for approximating a common element in the set of solutions of a problem of finding zeroes of sum of two monotone operators, generalized mixed equilibrium problem and fixed point problem for a finite family of $\eta$-demimetric mappings in the frame work of a reflexive, strictly convex and smooth Banach spaces. We also give a numerical experiment applying our main result. Our result improves, extends and unifies other results in this direction in the literature.

Abstract In this paper, using a Bregman distance technique, we introduce a new single projection process for approximating a common element in the set of solutions of variational inequalities involving a pseudo-monotone operator and the set of common fixed points of a finite family of Bregman quasi-nonexpansive mappings in a real reflexive Banach space. The stepsize of our algorithm is determined by a self-adaptive method, and we prove a strong convergence result under certain mild conditions. We further give some applications of our result to a generalized Nash equilibrium problem and bandwidth allocation problems. We also provide some numerical experiments to illustrate the performance of our proposed algorithm using various convex functions and compare this algorithm with other algorithms in the literature.

Informal trading activities such as street hawking and sedentary trade have assumed a prominent role in public space use in Lagos Island. They have contributed significantly to the Island’s built environment morphology as an urban commercial centre having a vernacular nature and outlook. This paper seeks to examine the spatial impact of informal trading activities on the public space by understanding the background issues in order to evolve a spatial based framework for urban sustainability. To this end, the paper adopts field survey methodology with Isale Eko, Lagos Island as the case study area. The theoretical framework, based on Henri Lefebvre’s spatial triad is the underpinning guide for the field survey. This is supported with Socio-cultural and Linguistic methods in Anthropology to obtain Primary data, which are descriptively presented. Respondents are nominated using stratified random selection, target groups and participants’ observations. Findings reveal that informal trading activities evolve the public space as social space through vernacular and thus, connote socio-cultural expressions in order to ensure livelihood and wellbeing. It further suggests a spatial adaptation strategy to mitigate the challenge of high land use and population density of the island which, from a conventional urban land use perspective, indicates spatial conflict and contestation, hence, a problem. The paper therefore concludes by recommending an inclusive, postmodernism approach which adopts vernacular as a dynamic, sustainable panacea to address urban spatial challenges.

In this article, a derivative-free method of Hestenes-Stiefel type is proposed for solving system of monotone operator equations with convex constraints. The method proposed is matrix-free, and its sequence of search directions are bounded and satisfies the sufficient descent condition. The global convergence of the proposed approach is established under the assumptions that the underlying operator is monotone and Lipschitz continuous. Numerical experiment results are reported to show the efficiency of the proposed method. Furthermore, to illustrate the applicability of the proposed method, it is used in restoring blurred images.

Abstract In this paper, we introduce a new inertial self-adaptive projection method for finding a common element in the set of solution of pseudomonotone variational inequality problem and set of fixed point of a pseudocontractive mapping in real Hilbert spaces. The self-adaptive technique ensures the convergence of the algorithm without any prior estimate of the Lipschitz constant. With the aid of Moudafi’s viscosity approximation method, we prove a strong convergence result for the sequence generated by our algorithm under some mild conditions. We also provide some numerical examples to illustrate the accuracy and efficiency of the algorithm by comparing with other recent methods in the literature.

In this paper, we introduce a Mann-Krasnoselskii algorithm of inertial form for approximating a common solution of Spit Variational Inclusion Problem (SVIP) and Equilibrium Problem (EP) with paramonotone bifunction in real Hilbert spaces. Motivated by the self-adaptive technique, we incorporate the inertial technique to accelerate the convergence of the proposed method. Under standard and mild assumptions such as monotonicity and lower semicontinuity of the SVIP and EP associated mappings, we establish the strong convergence of the iterative algorithm. Some applications and numerical experiments are presented to illustrate the performance and behaviour of our method as well as comparing it with some related methods in the literature. Our results improve and generalize many existing results in this direction.

In this work, we introduce two new inertial-type algorithms for solving variational inequality problems (VIPs) with monotone and Lipschitz continuous mappings in real Hilbert spaces. The first algorithm requires the computation of only one projection onto the feasible set per iteration while the second algorithm needs the computation of only one projection onto a half-space, and prior knowledge of the Lipschitz constant of the monotone mapping is not required in proving the strong convergence theorems for the two algorithms. Under some mild assumptions, we prove strong convergence results for the proposed algorithms to a solution of a VIP. Finally, we provide some numerical experiments to illustrate the efficiency and advantages of the proposed algorithms.

Abstract In this paper, we introduce a self-adaptive inertial subgradient extragradient method for solving pseudomonotone equilibrium problem and common fixed point problem in real Hilbert spaces. The algorithm consists of an inertial extrapolation process for speeding the rate of its convergence, a monotone nonincreasing stepsize rule, and a viscosity approximation method which guaranteed its strong convergence. More so, a strong convergence theorem is proved for the sequence generated by the algorithm under some mild conditions and without prior knowledge of the Lipschitz-like constants of the equilibrium bifunction. We further provide some numerical examples to illustrate the performance and accuracy of our method.

Abstract In this paper, we introduce Bregman subgradient extragradient methods for solving variational inequalities with a pseudo-monotone operator which are not necessarily Lipschitz continuous. Our algorithms are constructed such that the stepsizes are determined by an Armijo line search technique, which improves the convergence of the algorithms without prior knowledge of any Lipschitz constant. We prove weak and strong convergence results for approximating solutions of the variational inequalities in real reflexive Banach spaces. Finally, we provide some numerical examples to illustrate the performance of our algorithms to related algorithms in the literature.

In this paper, we introduce a proximal point algorithm for approximating a common solution of finite family of convex minimization problems and fixed point problems for k-demicontractive mappings in complete CAT(0) spaces. We prove a strong convergence result and obtain other consequence results which generalize and extend some recent results in the literature. We further provide a numerical example to illustrate the convergence behaviour of the sequence generated by our algorithm.

In this paper, we proposed two mixed algorithms of Newton’s and Abbasbandy’s methods using a known iteration scheme from fixed point theory in polynomiography. We numerically investigated some properties of the proposed algorithms using periodic sequence parameters instead of the constant parameters that are mostly used by many authors. Two pseudo-Newton algorithms were introduced based on the mixed iterations for the purpose of generating polynomiographs. The properties of the obtained polynomiographs were studied with respect to their graphics, turning effects and computation time. Moreover, some of these polynomiographs exhibited symmetrical properties when the degree of the polynomial was even.

In this paper, we aimed to introduce a new viscosity-type approximation method for finding the common fixed point of a class of quasi-pseudocontractive mapping and a system of monotone inclusion problems in CAT(0) spaces. We proved some fixed-point properties concerning the class of quasi-pseudocontractive mapping in CAT(0) spaces, which is more general than many other mappings such as nonexpansive, quasi-nonexpansive, pseudocontractive and demicontractive mappings which have been studied by other authors. A strong convergence result is proved under some mild conditions on the control sequences and some numerical examples were presented to illustrate the performance and efficiency of the proposed method.

In this paper, we propose some modifications of the basic family of iterations with a new four-step iteration called RK iteration and its s-convexity. We present some graphical examples showing the dynamics of the new iteration in the colouring and shapes of the obtained polynomiographs compared to the ones from the basic family only. Moreover, the computational results reveal that the value of s in the s-convex combination of the RK iteration has a significant impact on the time taken by the iteration process for approximating the roots of the polynomials. The obtained results are interesting from an artistic and computational point of view.

In this paper, we introduce an inertial self-adaptive projection method using Bregman distance techniques for solving pseudomonotone equilibrium problems in reflexive Banach spaces. The algorithm requires only one projection onto the feasible set without any Lipschitz-like condition on the bifunction. Using this method, a strong convergence theorem is proved under some mild conditions. Furthermore, we include numerical experiments to illustrate the behaviour of the new algorithm with respect to the Bregman function and other algorithms in the literature. [ABSTRACT FROM AUTHOR]

We consider a new subgradient extragradient iterative algorithm with inertial extrapolation for approximating a common solution of variational inequality problems and fixed point problems of a multivalued demicontractive mapping in a real Hilbert space. We established a strong convergence theorem for our proposed algorithm under some suitable conditions and without prior knowledge of the Lipschitz constant of the underlying operator. We present numerical examples to show that our proposed algorithm performs better than some recent existing algorithms in the literature.

This paper proposes a modified scaled spectral-conjugate-based algorithm for finding solutions to monotone operator equations. The algorithm is a modification of the work of Li and Zheng in the sense that the uniformly monotone assumption on the operator is relaxed to just monotone. Furthermore, unlike the work of Li and Zheng, the search directions of the proposed algorithm are shown to be descent and bounded independent of the monotonicity assumption. Moreover, the global convergence is established under some appropriate assumptions. Finally, numerical examples on some test problems are provided to show the efficiency of the proposed algorithm compared to that of Li and Zheng.

The performance and impact of Senna alata on experimental heavy metal contaminated soil were investigated in this study. Soils in different pots were contaminated with different levels of lead, nickel, chromium and cadmium based on WHO limits for heavy metals. Seeds of S. alata were planted in the contaminated soils. The plant growth was studied for 60 days. Some soil parameters and heavy metal contents of the soil were evaluated at the beginning and at the end of the study. The leaf area, the plant height and the number of actively growing stems decreased with increase in the amount of each metal added to the soil. At 60 days, there was significant reduction (p

Several fixed point results for the existence of common fixed points of multivalued contractive mappings have been established in complex-valued metric space. In this paper, we study the existence of common fixed points for a pair of multivalued contractive mappings satisfying some rational inequalities in the framework of complex-valued b-metric spaces. The contractive condition used in this paper generalizes many contractive conditions used by other authors in the literature. Employing our results, we check the existence solution to the Riemann-Liouville equation.

In this paper, we propose a generalized explicit algorithm for approximating the common solution of generalized split feasibility problem and the fixed point of demigeneralized mapping in uniformly smooth and 2-uniformly convex real Banach spaces. The generalized split feasibility problem is a general mathematical problem in the sense that it unifies several mathematical models arising in (symmetry and non-symmetry) optimization theory and also finds many applications in applied science. We designed the algorithm in such a way that the convergence analysis does not need a prior estimate of the operator norm. More so, we establish the strong convergence of our algorithm and present some computational examples to illustrate the performance of the proposed method. In addition, we give an application of our result for solving the image restoration problem and compare with other algorithms in the literature. This result improves and generalizes many important related results in the contemporary literature.

The purpose of this paper is to study a split generalized mixed equilibrium problem and a fixed point problem for nonspreading mappings in real Hilbert spaces.We introduce a new iterative algorithm and prove its strong convergence for approximating a common solution of a split generalized mixed equilibrium problem and a fixed point problem for nonspreading mappings in real Hilbert spaces. Our algorithm is developed by combining a modified accelerated Mann algorithm and a viscosity approximation method to obtain a new faster iterative algorithm for finding a common solution of these problems in real Hilbert spaces. Also, our algorithm does not require any prior knowledge of the bounded linear operator norm. We further give a numerical example to show the efficiency and consistency of our algorithm. Our result improves and compliments many recent results previously obtained in this direction in the literature.

In Nigeria heavy dependence of cattle on natural pasture for grazing has resulted in the emergence of a range of grazing systems and ecosystem challenges. Consequently this study appraised the grazing systems in use and their eco-relational outcomes for sustainable cattle management in Yewa Division of Ogun State. A total of 143 pastoralists agreed to take part in the survey and provided data on the commonly practiced grazing systems and ecological effects through the use of an interview format, interactive discussions plus field observations. The study outcome showed continuous, unpatterned rotational and transverse grazing systems were commonly practiced. The study also revealed that the employed grazing systems were independent of size of the cattle herds. While cattle were healthy under the grazing systems employed, soil degradation occurred in some instances. While the grazing systems employed by the pastoralists were satisfactory from the animal perspective, studies are needed to minimize the extent of soil degradation in the area.