In this paper, we propose a split nonconvex VARIATIONAL inequality PROBLEM which is a natural extension of split convex VARIATIONAL inequality PROBLEM in two different Hilbert spaces. Relying on the prox-regularity notion, we introduce and establish the convergence of an iterative method for the new split nonconvex VARIATIONAL inequality PROBLEM. Further, we also establish the convergence of an iterative method for the split convex VARIATIONAL inequality PROBLEM. The results presented in this paper are new and different form the previously known results for nonconvex (convex) VARIATIONAL inequality PROBLEMs. These results also generalize, unify, and improve the previously known results of this area.

The VARIATIONAL iteration method (VIM) has been applied to solve many functional equations, so far. In this paper the PROBLEM of conversion of three radioactive materials has been studied. By mathematical modeling of the PROBLEM a system of ordinary differential equations has been derived. The VARIATIONAL iteration method is applied to obtain exact solution of this system of ordinary differential equations.

In this paper, we introduce a new iterative algorithm of inertial form for approximating the solution of Split VARIATIONAL Inclusion PROBLEM (SVIP) involving accrective operators in Banach space. Mo-tivated by the inertial technique, we incorporate the inertial term to accelerate the convergence of the proposed method. Under standard and mild assumption of monotonicity of the SVIP associated mappings, we establish the weak convergence of the sequence generated by our algorithm. Some applications and numerical example are presented to illustrate the performance of our method as well as comparing it with the non-inertial version.

In this article, we examine a nonsmooth vector optimization PROBLEM with locally Lipschitz approximately convex mappings in terms of the convexificator and provide some ideas for approximate effective solutions. Additionally, we define the relationship between the convexificator-based solutions of Stampacchia type vector VARIATIONAL inequalities ($VVI$) and the approximate efficient approximation convex function of nonsmooth vector optimization PROBLEMs using the locally Lipschitz function. Furthermore, we provide a numerical example to demonstrate the veracity of our findings.

The goal of this article is to compute conservation law, Lagrangian and -conservation law of the generalized Rosenau-type equation using the homotopy operator, the -symmetry method and the VARIATIONAL PROBLEM method. The generalized Rosenau-type equation includes the generalized Rosenau equation, the generalized Rosenau-RLW equation and the generalized Rosenau-KdV equation, which admits the third-order Lagrangian. The article also compares the conservation law and the -conservation law of these three equation.

In this paper, a new version of Ekeland's VARIATIONAL principle by using the concept of $\tau$-distance for bounded from below functions which are not necessarily lower semicontinuous is provided. This new version of Ekeland's VARIATIONAL principle will be applied to establish an existence theorem for a solution to the equilibrium PROBLEM in the setting of complete metric spaces.

The PROBLEM of personal identity among others may stem from the following question—what does be the person that you are, from one day to the next, necessarily consist of? The diachronic PROBLEM of personal identity raises question on the necessary and sufficient conditions for the identity of the person over time. The synchronic PROBLEM is grounded in the question of what features or traits characterize a given person at one time. To answer these questions, John Locke discarded the soul and the body as necessary and sufficient substances for personal identity over time. He accepted consciousness as the only criterion for personal identity; the only thing capable of remaining the same and preserving personal identity through change. Though Locke’s argument is somewhat clear and coherent but what remains vague and incoherent is embedded in the question—what exactly is consciousness? How and why should it be the basis or criterion for the determination of personal identity? Using the method of critical analysis, I argue that Locke’s choice of consciousness as the determinant of personal identity, though quite novel, is incoherent and vague. Secondly, Locke had already presumed and anticipated clearly though fallaciously the very thing he wishes to substantiate. I therefore conclude that Locke’s argument is just another way of trying to escape but inadvertently prolonging the difficulty of apparently articulating a distinction between the psychological approach and physiological approach to the PROBLEM of personal identity. However, in my submission, I propose the concept of the “other” as alternative approach— a sort of an extrinsic-intrinsic approach to the PROBLEM of personal identity.