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The primary goal of this research is to investigate the approximate numerical solution of variational inequalities using quasimonotone operators in infinite-dimensional real Hilbert spaces. In this study, the sequence obtained by the proposed iterative technique for solving quasimonotone variational inequalities converges strongly toward a solution due to the viscosity-type iterative scheme. Furthermore, a new technique is proposed that uses an inertial mechanism to obtain strong convergence iteratively without the requirement for a hybrid version. The fundamental benefit of the suggested iterative strategy is that it substitutes a monotone and non-monotone step size rule based on mapping (operator) information for its Lipschitz constant or another line search method. This article also provides a numerical example to demonstrate how each method works.

This study explores the unsteady hybrid nanofluid (NF) flow consisting of cobalt ferrite (CoFe2O4) and copper (Cu) nano particulates with natural convection flow due to an expanding surface implanted in a porous medium. The Cu and CoFe2O4 nanoparticles (NPs) are added to the base fluid water to synthesize the hybrid NF. The effects of second-order velocity slip condition, chemical reaction, heat absorption/generation, temperature-dependent viscosity, and Darcy Forchheimer are also assessed in the present analysis. An ordinary differential equation system is substituted for the modeled equations of the problem. Further computational processing of the differential equations is performed using the parametric continuation method. A validation and accuracy comparison are performed with the Matlab package BVP4C. Physical constraints are used for presenting and reviewing the outcomes. With the increase in second-order velocity slip condition and unsteady viscosity, the rates of heat and mass transition increase significantly with the variation in Cu and Fe2O4 NPs. The findings suggest that the uses of Cu and Fe2O4 in ordinary fluids might be useful in the aerodynamic extrusion of plastic sheets and extrusion of a polymer sheet from a dye.

This article analyses two schemes: Mann-type and viscosity-type proximal point algorithms. Using these schemes, we establish Δ-convergence and strong convergence theorems for finding a common solution of monotone vector field inclusion problems, a minimization problem, and a common fixed point of multivalued demicontractive mappings in Hadamard spaces. We apply our results to find mean and median values of probabilities, minimize energy of measurable mappings, and solve a kinematic problem in robotic motion control. We also include a numerical example to show the applicability of the schemes. Our findings corroborate some recent findings.

The study of nanofluid flow over a rotating disk has significant importance because of its enormous range of implementations, including cancer treatments, chemotherapy, nanomedicines, fermentation sciences, selective drug delivery, food sciences, biosensors, biomedicines, and electronics. Due to these applications of nanofluid, the present problem investigates the magnetohydrodynamic flow of nanofluid with nonlinear thermal radiation and viscous dissipation. In this analysis, the aluminum oxide nanoparticles are mixed with water. Furthermore, the mechanism for inter-particle spacing and radius of aluminum oxide nanoparticles on the dynamics of the two-dimensional flow of nanofluid are investigated. The present problem is modeled in the form of partial differential equations (PDEs), and these PDEs are converted into ordinary differential equations with the help of suitable similarity transformations. The analytical solution to the current modeled problem has been obtained by using the homotopy analysis technique. The main purpose of the present research work is to analyze the behavior of the velocity and temperature of the nanofluid for small and large radius of the aluminum oxide nanoparticles and inter-particle spacing. Also, the role of heat transport is computed for linear and nonlinear thermal radiation cases. The major findings and principal results of this investigation are concluded that the primary velocity of nanoliquid is augmented due to the intensification in suction parameter for both the small and larger radius of aluminum oxide nanoparticles. Furthermore, it is perceived that the heat rate transfer is larger when the Eckert number and nanoparticle volume fraction are higher for both nonlinear and linear thermal radiation cases.