In this paper, first a short history of the notion of equilibrium problem in Economics and Nash$acute{'}$ game theory is stated. Also the relationship between equilibrium problem among important mathematical problems like optimization problem, nonlinear programming, variational inequality problem, fixed point problem and complementarity problem is given. The concept of generalized pseudomonoton...

We set up precision holography for the non-conformal branes preserving 16 supersymmetries. The near-horizon limit of all such p-brane solutions with p ≤ 4, including the case of fundamental string solutions, is conformal to AdSp+2 × S8−p with a linear dilaton. We develop holographic renormalization for all these cases. In particular, we obtain the most general asymptotic solutions with appropri...

This paper first improves Chen and Hsieh’s definition of generalized fuzzy numbers, which makes it the generalization of definition of fuzzy numbers. Secondly, in terms of the generalized fuzzy numbers set, we introduce two different kinds of orders and arithmetic operations and metrics based on the λ-cutting sets or generalized λ-cutting sets, so that the generalized fuzzy numbers are integrat...

Generalized intuitionistic fuzzy soft set theory, proposed by Park et al. [Journal of Korean Institute of Intelligent Systems 21(3) (2011) 389-394], has been regarded as an effective mathematical tool to deal with uncertainties. In this paper, we prove that certain De Margan’s law hold in generalized intuitionistic fuzzy soft set theory with respect to union and intersection operations on gener...

Two new powerful mathematical languages, fuzzy set theory and possibility theory, have led to two optimization types that explicitly incorporate data whose values are not real-valued nor probabilistic: 1) flexible optimization and 2) optimization under generalized uncertainty. Our aim is to make clear what these two types are, make distinctions, and show how they can be applied. Flexible optimi...

In this paper, the basic constitutive equations and equations of motion are derived to describe the behavior of thermoelastic porous piezoelectric medium by using Biot’s theory and the theory of generalized thermoelasticity with on relaxation time (Lord-Shulman). The electrical enthalpy density function is derived in the general coordinates. Also, clear definitions for the poroelastic modulus, ...