In the last few decades, concept of Birkhoff–James orthogonality has been used in several applications. this survey article, results known on necessary and sufficient conditions for certain Banach spaces are mentioned. Their applications studying geometry normed given. The connections between orthogonality, Gateaux derivative subdifferential set norm function provided. Several interesting dista...

We establish the generalized Evans–Krylov and Schauder type estimates for nonlocal fully nonlinear elliptic equations with rough kernels of variable orders. In contrast to fractional Laplacian operators having a fixed order differentiability ??(0,2), under consideration have orders differentiability. Since is not characterized by single number, we consider function ? describing differentiabilit...

In this paper, solution of fuzzy differential equation under general differentiability is obtained by simulink. The simulink solution is equivalent or very close to the exact solution of the problem. Accuracy of the simulink solution to this problem is qualitatively better. An illustrative numerical example is presented for the proposed method. Keywords—Fuzzy differential equation, Generalized ...

In this paper, we consider Simultaneous Perturbation Stochastic Approximation (SPSA) for function minimization. The standard assumption for convergence is that the function be three times differentiable, although weaker assumptions have been used for special cases. However, all work that we are aware of at least requires differentiability. In this paper, we relax the differentiability requireme...

This article studies differentiability properties for a reformulation of a player convex generalized Nash equilibrium problem as a constrained and possibly nonsmooth minimization problem. By using several results from parametric optimization we show that, apart from exceptional cases, all locally minimal points of the reformulation are differentiability points of the objective function. This ju...

It is known that directional differentiability of metric projection onto a closed convex set in a finite dimensional space is not guaranteed. In this paper we discuss sufficient conditions ensuring directional differentiability of such metric projections. The approach is based on a general theory of sensitivity analysis of parameterized optimization problems.