Applied Analysis Research Papers - Academia.edu (original) (raw)
New classes of generalized (F, ρ)-convexity are introduced for vector-valued functions. Examples are given to show their relations with (F, ρ)-pseudoconvex, (F, ρ)-quasiconvex, and strictly (F, ρ)-pseudoconvex vector-valued functions. The... more
New classes of generalized (F, ρ)-convexity are introduced for vector-valued functions. Examples are given to show their relations with (F, ρ)-pseudoconvex, (F, ρ)-quasiconvex, and strictly (F, ρ)-pseudoconvex vector-valued functions. The sufficient optimality conditions and duality results are obtained for multiobjective programming involving generalized (F, ρ)-convex vector-valued functions.
In this paper, we develop two-step collocation (2-SC) methods to solve two-dimensional nonlinear Volterra integral equations (2D-NVIEs) of the second kind. Here we convert a 2D-NVIE of the second kind to a one-dimensional case, and then... more
In this paper, we develop two-step collocation (2-SC) methods to solve two-dimensional nonlinear Volterra integral equations (2D-NVIEs) of the second kind. Here we convert a 2D-NVIE of the second kind to a one-dimensional case, and then we solve the resulting equation numerically by two-step collocation methods. We also study the convergence and stability analysis of the method. At the end, the accuracy and efficiency of the method is verified by solving two test equations which are stiff. In examples, we use the well-known differential transform method to obtain starting values.
- by Ana Peron and +1
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- Applied Mathematics, Pure Mathematics, Applied Analysis
Abstract. In the first part of this paper, we prove a minimax inequal-ity for maps satisfying a generalized coercivity type condition. As a consequence, we prove a result on the solvability of complementarity problems. In the second part,... more
Abstract. In the first part of this paper, we prove a minimax inequal-ity for maps satisfying a generalized coercivity type condition. As a consequence, we prove a result on the solvability of complementarity problems. In the second part, a result on the existence of maximal ele-ment in ...
We consider the numerical solution of quasilinear elliptic Neumann problems. The basic diculty is the non-injectivity of the operator, which can be overcome by suitable factorization. We extend the gradient-nite element method (GFEM),... more
We consider the numerical solution of quasilinear elliptic Neumann problems. The basic diculty is the non-injectivity of the operator, which can be overcome by suitable factorization. We extend the gradient-nite element method (GFEM), introduced earlier by the authors for Dirichlet problems, to the Neumann problem. The algorithm is constructed and its convergence is proved.
We deal with the wave equation with assigned moving boundary (
ABSTRACT: We consider an integro-differential equation, proposed in the literature as a model of neuronal activity. We establish conditions under which an initial activity function exhibiting localized pattern formation completely... more
ABSTRACT: We consider an integro-differential equation, proposed in the literature as a model of neuronal activity. We establish conditions under which an initial activity function exhibiting localized pattern formation completely characterizes the system. We also ...