In this paper, we use the auxiliary principle technique to study the existence of a solution of the extended general variational inequalities, which were introduced and studied by the author. Several special cases are also discussed.

Since the fundamental theory of variational inequality was founded in the 1960s, the variational inequality theory with applications has made powerful progress and has become an important part of nonlinear analysis. It has been applied intensively to mechanics, differential equation, cybernetics, quantitative economics, optimization theory, nonlinear programming, and so forth (see [2]). In virt...

In this paper, we introduce and study a mixed variational inclusion problem involving infinite family of fuzzy mappings. An iterative algorithm is constructed for solving a mixed variational inclusion problem involving infinite family of fuzzy mappings and the convergence of iterative sequences generated by the proposed algorithm is proved. Some illustrative examples are also given.

‎in this paper‎, ‎we introduce and study a class of generalized vector quasi-equilibrium problem‎, ‎which includes many vector equilibrium problems‎, ‎equilibrium problems‎, ‎vector variational inequalities and variational inequalities as special cases‎. ‎using one person game theorems‎, ‎the concept of escaping sequences and without convexity assumptions‎, ‎we prove some existence results for ...

Perturbative Quantum Electrodynamics has been successfully tested to unparalleled precision for around half a century. In addition, and rather more recently, the theory’s behaviour in its strong coupling limit has attracted a growing amount of attention. The reason for this is not only that it serves as a simple prototype gauge theory for testing nonperturbative calculational techniques which o...

In this paper, we use the auxiliary principle technique to suggest and analyze an implicit iterative method for solving bifunction variational inequalities. We also study the convergence criteria of this new method under pseudomonotonicity condition.

Partially inspired by successful applications of variational recurrent neural networks, we propose a novel variational recurrent neural machine translation (VRNMT) model in this paper. Different from the variational NMT, VRNMT introduces a series of latent random variables to model the translation procedure of a sentence in a generative way, instead of a single latent variable. Specifically, th...