New inertial projection methods for solving multivalued variational inequality problems beyond monotonicity

In this paper, we present two new inertial projection-type methods for solving multivalued variational inequality problems in finite-dimensional spaces. We establish the convergence of the sequence generated by these methods when the multivalued mapping associated with the problem is only required to be locally bounded without any monotonicity assumption. Furthermore, the inertial techniques that we employ in this paper are quite different from the ones used in most papers. Moreover, based on the weaker assumptions on the inertial factor in our methods, we derive several special cases of our methods. Finally, we present some experimental results to illustrate the profits that we gain by introducing the inertial extrapolation steps

A study of optimization and fixed point problems in certain geodesic metric spaces.

Doctoral Degree. University of KwaZulu-Natal, Durban.Abstract available in PDF

A new inertial condition on the subgradient extragradient method for solving pseudomonotone equilibrium problem

In this paper we study the pseudomonotone equilibrium problem. We consider a new inertial condition for the subgradient extragradient method with self-adaptive step size for approximating a solution of the equilibrium problem in a real Hilbert space. Our proposed method contains inertial factor with new conditions that only depend on the iteration coefficient. We obtain a weak convergence result of the proposed method under weaker conditions on the inertial factor than many existing conditions in the literature. Finally, we present some numerical experiments for our proposed method in comparison with existing methods in the literature. Our result improves, extends and generalizes several existing results in the literature

Iterative algorithms for approximating solutions of variational inequality problems and monotone inclusion problems.

Master of Science in Mathematics, Statistics and Computer Science. University of KwaZulu-Natal, Durban, 2017.In this work, we introduce and study an iterative algorithm independent of the operator norm for approximating a common solution of split equality variational inequality prob- lem and split equality xed point problem. Using our algorithm, we state and prove a strong convergence theorem for approximating an element in the intersection of the set of solutions of a split equality variational inequality problem and the set of solutions of a split equality xed point problem for demicontractive mappings in real Hilbert spaces. We then considered nite families of split equality variational inequality problems and proposed an iterative algorithm for approximating a common solution of this problem and the multiple-sets split equality xed point problem for countable families of multivalued type-one demicontractive-type mappings in real Hilbert spaces. A strong convergence re- sult of the sequence generated by our proposed algorithm to a solution of this problem was also established. We further extend our study from the frame work of real Hilbert spaces to more general p-uniformly convex Banach spaces which are also uniformly smooth. In this space, we introduce an iterative algorithm and prove a strong convergence theorem for approximating a common solution of split equality monotone inclusion problem and split equality xed point problem for right Bregman strongly nonexpansive mappings. Finally, we presented numerical examples of our theorems and applied our results to study the convex minimization problems and equilibrium problems

On Mixed Equilibrium Problems in Hadamard Spaces

The main purpose of this paper is to study mixed equilibrium problems in Hadamard spaces. First, we establish the existence of solution of the mixed equilibrium problem and the unique existence of the resolvent operator for the problem. We then prove a strong convergence of the resolvent and a ?-convergence of the proximal point algorithm to a solution of the mixed equilibrium problem under some suitable conditions. Furthermore, we study the asymptotic behavior of the sequence generated by a Halpern-type PPA. Finally, we give a numerical example in a nonlinear space setting to illustrate the applicability of our results. Our results extend and unify some related results in the literature. - 2019 Chinedu Izuchukwu et al.ledgments .e publication of this article was funded by the Qatar National Library. .e first and third authors acknowledge the bursary and financial support from Department of Science and Technology and National Research Foundation, Republic of South Africa Center of Excellence in Mathematical and Statistical Sciences (DST-NRF COE-MaSS) Doctoral Bursary. .e fourth author is supported in part by the National Research Foundation (NRF) of South Africa Incentive Funding for Rated Researchers (Grant NumberScopu

Prediction of the Phytochemical Properties of Luffa Cylindrica Seed Oil Using Artificial Neural Network

The research used an artificial neural network (ANN) to examine optimum extraction conditions and phytochemical contents of Luffa cylindrica seed oil. The oil yield was predicted using an artificial neural network. The performance of the ANN and response surface methodology models was compared. The optimum extraction yielded 7.567% oil yield, 185.676 mg/l phenol, and 45.087 mg/l terpineol at 75.57 °C extraction temperature, 5.77 h extraction time, and 10.68 g/mol n-hexane concentration, respectively. These data show that the oil output is poor but has a significant phenol and terpenoid content that may be employed in pharmaceutical sectors. The FT-IR analysis of Luffa cylindrica seed oil revealed a high level of unsaturated hydrocarbons and esters, making the oil appropriate for using in the paint industry and creating cosmetics

Intellectual Capital and Financial Performance of Quoted Manufacturing Firms

Purpose: This study examined the effect of intellectual capital on the financial performance of quoted manufacturing firms on the Nigerian Stock Exchange (NSE). The study specifically evaluated the effect of the value-added intellectual coefficient (VAIC) on Asset Turnover (ATR), Gross Profit Margin (GPM) and Return on Assets (ROA) from 2011 to 2019. Research Methodology: The research design used in the study is ex post facto. Non-probability sampling was the method of sampling that was employed in the investigation. Twenty (20) consumer products manufacturing companies that had been listed on the NSE for nine years made up the final sample. In earlier investigations, this was deemed sufficient for regression analysis. The analysis makes use of secondary data taken from the companies’ annual reports. The information spanned a nine-year span, from 2011 to 2019. Result: There is a non-significant negative effect of value added intellectual coefficient on the Asset Turnover Rate (ATR) of quoted manufacturing firms; however, there is a non-significant positive effect of VAIC on Gross Profit Margin (GPM) and Return on Assets (ROA) of quoted manufacturing firms. Limitation: The main limitation is the duration of time the study was conducted and the delisting of some firms during the period. Contribution: The research adds to the body of knowledge about developing nations, on the nexus of VAIC and financial performance. It reiterates the point that firms should emphasize intellectual capital accounting and disclosure to boost and maintain a motivated workforce and its potentially beneficial effect on firm valuation in this knowledge era

Accounting Information and Stock Price: Empirical Evidence from Quoted Manufacturing Firms in Nigeria

The objective of the study is to examine the nexus between accounting information and stock price of quoted consumer goods manufacturing firms in Nigeria. The study adopts an ex post facto research design; and, the sample drawn from quoted consumer goods manufacturing firms on the Nigerian Stock Exchange (NSE). The study employs a combination of descriptive and inferential statistical technique to analyse the data. The panel data from 2011 to 2019 was retrieved from annual financial reports and empirically analysed using the pooled OLS procedure. The results showed a non-significant negative effect of earnings per share and sales growth ratio on the stock price indicator; while, the operating cashflow ratio had a significant positive effect. The profitability ratio, i.e., return on assets had a non-significant positive effect on stock price indicator. Based on this, the study recommended that investors pay closer attention to information from the statement of cashflows as they tend to portray the true state of affairs in most companies.  The futility of using only the profitability indicators as a yardstick for stock purchase decision. In addition, the use of supporting documents such as the corporate governance report to reveal otherwise information not obtained from the quantitative counterpart and vital for investment decisions

Self-adaptive forward–backward contraction-type methods for generalized split feasibility problems

Based on the recent important results of Takahashi–Xu–Yao [Set-Valued and Variational Analysis 23(2015), 205–221] and other related results on split feasibility problems, we study a certain class of generalized split feasibility problems which includes many other split-type problems. We propose some new self-adaptive forward–backward contraction-type methods and prove that they converge strongly to a minimum-norm solution of the generalized split feasibility problems in real Hilbert spaces. As a by-product, we obtain self-adaptive methods for solving other classes of generalized split feasibility problems in real Hilbert spaces. Finally, we apply our results to solve an optimal control problem and an image restoration problem through numerical implementations, and compare our methods with related strongly convergent methods in the literature.</p