In Part I of this work we derived a duality theorem for partially finite convex programs, problems for which the standard Slater condition fails almost invariably. Our result depended on a constraint qualification involving the notion of quasi relative interior. The derivation of the primal solution from a dual solution depended on the differentiability of the dual objective function: the diffe...

In this paper, we use an intuitionistic fuzzy Laplace transforms for solving hyperbolic equations precisely the transport equation with data under strongly generalized H-differentiability concept. For purpose, is converted to boundary value problem (IFBVP) based on laplace transform. The related theorems and properties are proved in detail. Finally, solve example illustrate method.

This paper concerns with the initial value problem for random set-valued functional differential equations with the second type Hukuhara derivative (RSFDEs). By using the techniques of successive approximations, the existence and uniqueness of solutions are established. Two kinds of boundedness of the solution are also established. In addition, the problem at least one solution under some condi...

We study analyticity, differentiability, and semismoothness of Löwner’s operator and spectral functions under the framework of Euclidean Jordan algebras. In particular, we show that many optimization-related classical results in the symmetric matrix space can be generalized within this framework. For example, the metric projection operator over any symmetric cone defined in a Euclidean Jordan a...

Studying a critical value function φ in parametric nonlinear programming, we recall conditions guaranteeing that φ is a C function and derive second order Taylor expansion formulas including second-order terms in the form of certain generalized derivatives of Dφ. Several specializations and applications are discussed. These results are understood as supplements to the well–developed theory of f...

We firstly present a generalized concept of higher-order differentiability for fuzzy functions. Then we interpret Nth-order fuzzy differential equations using this concept. We introduce new definitions of solution to fuzzy differential equations. Some examples are provided for which both the new solutions and the former ones to the fuzzy initial value problems are presented and compared. We pre...

In this paper we propose Runge-Kutta Fehlberg method for solving fully fuzzy differential equations (FFDEs) of the form y ′ (t) = a⊗ y(t), y(0) = y0, t ∈ [0,T ] under strongly generalized H-differentiability. The algorithm used here is based on cross product of two fuzzy numbers. Using cross product we investigate the problem of finding a numerical approximation of solutions. The convergence of...

In this paper we develop with considerable details a theory of multivector functions of a p-vector variable. The concepts of limit, continuity and differentiability are rigorously studied. Several important types of derivatives for these multivector functions are introduced, as e.g., the A-directional derivative (where A is a p-vector) and the generalized concepts of curl, divergence and gradie...