In this paper, we propose a novel double inertial self-adaptive subgradient extragradient method with conjugate gradient direction for solving variational inequality problems involving quasi-monotone and Lipschitz continuous operators in real Hilbert spaces. The proposed algorithm incorporates the technique of double inertial steps combined with a conjugate gradient direction to accelerate the convergence speed. A remarkable feature of our method is the use of a self-adaptive step size strategy, which does not require prior knowledge of the Lipschitz constant of the cost operator. Under some suitable conditions, we establish the weak convergence theorem of the proposed algorithm. Finally, several numerical results are presented to illustrate the feasibility and superior efficiency of our method compared to other algorithms.
The paper presents a method for identifying pollutant compounds in the atmosphere that are brought to the ground in the form of ice and sleet, the later resulting into foaming waters. The method of investigation consists of FT-IR analysis to identify chemical compounds based on the vibration bands of functional groups in the spectra obtained. The validation of the chemical compounds was carried out by simulating the IR spectra using the Gaussian 6 software. Thus, urea and 1,3-dimethylurea were identified both in the blue ice and in the sleet water showing pollution in the atmosphere.
This paper aims to investigate a new composite algorithm for solving a split variational inequality problem and a split variational inclusion problem in real Hilbert spaces. Under very mild conditions, we prove a strong convergence theorem for the proposed algorithm. Furthermore, an application is given to illustrate the effectiveness of the algorithm. The results improve and extend the corresponding ones announced by some others in the earlier and recent literature.
We extend the Dirichlet character modulo 4 to integer partitions via an additive statistic on their parts, and introduce several associated partition functions under natural restrictions. Using generating function techniques and classical q-series identities, we establish formulas relating these functions, including representations involving generalized pentagonal numbers and squares. We also obtain an explicit evaluation supported on triangular numbers, together with three distinct infinite families of linear inequalities. These observations further motivate three conjectures concerning infinite families of linear inequalities.
We establish an Ekeland-type variational principle in a class of partial metric spaces whose diagonal map is strictly Lipschitz with respect to the associated symmetrized metric. This assumption gives a two-sided comparison between the induced quasi-metric and the symmetrized metric, and it permits the transfer of variational arguments from the complete metric framework to the partial metric setting. As consequences, we obtain a penalized strict minimization principle, Caristi-type fixed point theorems, a Takahashi-type minimization result, and common fixed point results for semigroups and commuting resolvent-type families. We also give a set-valued variational principle on closed graphs, an asymmetric equilibrium principle, and a discrete variational generation scheme for nonlinear evolution models. Explicit examples illustrate the abstract results.
