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

Forward-backward splitting algorithm with self-adaptive method for finite family of split minimization and fixed point problems in Hilbert spaces

In this paper, we introduce an inertial forward-backward splitting method together with a Halpern iterative algorithm for approximating a common solution of a finite family of split minimization problem involving two proper, lower semicontinuous and convex functions and fixed point problem of a nonexpansive mapping in real Hilbert spaces. Under suitable conditions, we proved that the sequence generated by our algorithm converges strongly to a solution of the aforementioned problems. The stepsizes studied in this paper are designed in such a way that they do not require the Lipschitz continuity condition on the gradient and prior knowledge of operator norm. Finally, we illustrate a numerical experiment to show the performance of the proposed method. The result discussed in this paper extends and complements many related results in literature

IMPACT OF DIESEL FUEL GENERATORS ON SOIL HEAVY METALS

Heavy metals are ubiquitous and are released into the atmosphere/ environment by a variety of natural processes, but their quantities have been greatly augmented by anthropogenic activities. This study investigated the concentration of heavy metals Iron (Fe), Arsenic (As), Cadmium (Cd), Chromium (Cr), Zinc (Zn), Manganese (Mn) and Lead (Pb) in the soil around the power plant obtained at the old power plant, new power plant and a far-away point from the plants which served as the control. In each location, two samples were obtained top layer and bottom layer of soil. Standard laboratory methods were employed for all the analyses. High concentration was obtained for the selected heavy metals in the soil at both the old and the new power plants with Arsenic having an average of 0.67 mg/kg and 0.40 mg/kg, Lead having an average of 2.63 mg/kg and 1.67 mg/kg, Iron having 1.25 mg/kg and 0.95 mg/kg, Chromium having 1.08 mg/kg and 0.67 mg/kg, Cadmium having 1.46 mg/kg and 0.54 mg/kg, Manganese having 1.97 mg/kg and 1.86 mg/kg and Zinc having 2.43 mg/kg and 0.86 mg/kg at the old and new site respectively. All the obtained concentration levels are above the permissible limit of the United States, United Kingdom, Europe and WHO. It is expedient that necessary measures be put in place to control the emissions from the plants to reduce the contaminating impact of the soil around the power plant as well as moving some human intakes far from the locations

IMPACT OF DIESEL FUEL GENERATORS ON SOIL HEAVY METALS

Heavy metals are ubiquitous and are released into the atmosphere/ environment by a variety of natural processes, but their quantities have been greatly augmented by anthropogenic activities. This study investigated the concentration of heavy metals Iron (Fe), Arsenic (As), Cadmium (Cd), Chromium (Cr), Zinc (Zn), Manganese (Mn) and Lead (Pb) in the soil around the power plant obtained at the old power plant, new power plant and a far-away point from the plants which served as the control. In each location, two samples were obtained top layer and bottom layer of soil. Standard laboratory methods were employed for all the analyses. High concentration was obtained for the selected heavy metals in the soil at both the old and the new power plants with Arsenic having an average of 0.67 mg/kg and 0.40 mg/kg, Lead having an average of 2.63 mg/kg and 1.67 mg/kg, Iron having 1.25 mg/kg and 0.95 mg/kg, Chromium having 1.08 mg/kg and 0.67 mg/kg, Cadmium having 1.46 mg/kg and 0.54 mg/kg, Manganese having 1.97 mg/kg and 1.86 mg/kg and Zinc having 2.43 mg/kg and 0.86 mg/kg at the old and new site respectively. All the obtained concentration levels are above the permissible limit of the United States, United Kingdom, Europe and WHO. It is expedient that necessary measures be put in place to control the emissions from the plants to reduce the contaminating impact of the soil around the power plant as well as moving some human intakes far from the locations

A Strong Convergence Theorem for Split Null Point Problem and Generalized Mixed Equilibrium Problem in Real Hilbert Spaces

In this paper, we study a schematic approximation of solutions of a split null point problem for a finite family of maximal monotone operators in real Hilbert spaces. We propose an iterative algorithm that does not depend on the operator norm which solves the split null point problem and also solves a generalized mixed equilibrium problem. We prove a strong convergence of the proposed algorithm to a common solution of the two problems. We display some numerical examples to illustrate our method. Our result improves some existing results in the literature

A Strong Convergence Theorem for Split Null Point Problem and Generalized Mixed Equilibrium Problem in Real Hilbert Spaces

In this paper, we study a schematic approximation of solutions of a split null point problem for a finite family of maximal monotone operators in real Hilbert spaces. We propose an iterative algorithm that does not depend on the operator norm which solves the split null point problem and also solves a generalized mixed equilibrium problem. We prove a strong convergence of the proposed algorithm to a common solution of the two problems. We display some numerical examples to illustrate our method. Our result improves some existing results in the literature

Common Fixed Point Results for a Pair of Multivalued Mappings in Complex-Valued b-Metric Spaces

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

Strong convergence of a Bregman projection method for the solution of pseudomonotone equilibrium problems in Banach spaces

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.</p

A self-adaptive inertial subgradient extragradient algorithm for solving bilevel equilibrium problems

In this paper, we introduce an inertial subgradient extragradient method with a self-adaptive technique for solving bilevel equilibrium problem in real Hilbert spaces. The algorithm is designed such that its stepsize is chosen without the need for prior estimates of the Lipschitz-like constants of the upper level bifunction nor a line searching procedure. This provides computational advantages to the algorithm compared with other similar methods in the literature. We prove a strong convergence result for the sequences generated by our algorithm under suitable conditions. We also provide some numerical experiments to illustrate the performance and efficiency of the proposed method.</p

A self-adaptive extragradient method for fixed-point and pseudomonotone equilibrium problems in hadamard spaces

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.</p