Let T : K → H be a nonlinear mapping from a nonempty closed invex subset K of an infinite-dimensional Hilbert space H into H . Let f : K → R be proper, invex, and lower semicontinuous on K and let h : K → R be continuously Fréchet-differentiable on K with h′, the gradient of h, (η,α)-strongly monotone, and (η,β)-Lipschitz continuous on K . Suppose that there exist an x∗ ∈ K , and numbers a > 0,...

This paper surveys a number of well-known expert systems in the domain of finance. The idea is to illustrate the span of typical expert systems in finance and to provide an insight into the approaches and techniques they employ. The systems considered in the paper are all working systems, and come from different fields of finance. Specifically, the systems considered are FINEVA (from the field ...

The Human Variation Model views disability as simply "an extension of the natural physical, social, and cultural variability of mankind." Given this human variation, it can be difficult to distinguish between a prosthetic device such as a pair of glasses (which extends limited visual abilities into the "normal" range) and a visual enhancement device such as a pair of binoculars (which extends v...

In this work, several extended approximately invex vector-valued functions of higher order involving a generalized Jacobian are introduced, and some examples are presented to illustrate their existences. The notions of higher-order (weak) quasi-efficiency with respect to a function are proposed for a multi-objective programming. Under the introduced generalization of higher-order approximate in...

Abstract In this study, we use the fuzzy order relation to show some novel variants of Hermite–Hadamard inequalities for pre-invex fuzzy-interval-valued mappings ( F-I∙V-Ms ), which term fuzzy-interval and Hermite–Hadamard–Fejér inequalities. This is defined as level space by Kulisch–Miranker relation. There are also new exceptional instances mentioned. The theory proposed in research shown wit...

In this paper we present optimization problems with biconvex objective function and linear constraints such that the set of global minima of the optimization problems is the same as the set of Nash eqilibria of a n-player general-sum normal form game. We further show that the objective function is an invex function and consider a projected gradient descent algorithm. We prove that the projected...

In this paper, we extend the class of strongly $ E $-preinvex and $-invex functions to quasi $-preinvex, pseudo functions. Some non-trivial suitable examples have been constructed in support our definitions. Several interesting properties relationships these are discussed. Furthermore, show application results, consider a non-linear programming problem that local minimum point is also strictly ...