In the present paper, a new generalization of Browder fixed point theorem is obtained. As its applications, we obtain some generalized versions of Browder’s theorems for quasi-variational inequality and Ky Fan’s minimax inequality and minimax principle.

In the present work, we introduce and study completely generalized quasi-variational inequality problem for fuzzy mappings. By using the definitions of strongly accretive and retraction mappings, we propose an iterative algorithm for computing the approximate solutions of this class of variational inequalities. We prove that approximate solutions obtained by the proposed algorithm converge to t...

A generalized skew correlation and a generalized skew information are defined and then a kind of the generalization of uncertainty relation is established by the help of the trace inequality which was recently proven by J.I.Fujii. In addition, we prove the trace inequality which is an extension of the conjecture addressed in [1]. This manuscript is based on our recent paper [2]. Mathematics Sub...

We present in this work a new and shorter proof of the generalized λ-Newton inequalities for elementary symmetric functions defined on a self-conjugate set which lies essentially in the open right half-plane. We also point out some interesting consequences of the generalized λ-Newton inequalities. In particular, we establish an improved complex version of the arithmetic mean-geometric mean ineq...

We study the antieigenvectors of the generalized eigenvalue problem Af = λBf by using the concept of stationary vectors and then obtain an operator inequality complementary to Schwarz’s inequality in Hilbert space. AMS Mathematics Subject Classification (2000): 47A63,47A75

A relation between Shannon entropy and Kerridge inaccuracy, which is known as Shannon inequality, is well known in information theory. In this communication, first we generalized Shannon inequality and then given its application in coding theory.

The analysis of the connections among generalized systems, Vector Optimization Problems and Variational Inequalities allows to deepen the study of the properties of the Minty Vector Variational Inequality. In particular, under suitable regularity assumptions,the equivalence between Minty Vector Variational Inequality and Stampacchia Vector Variational Inequality is shown.

We introduce and study a new class of generalized nonlinear mixed variational-like inequalities in reflexive Banach spaces. By applying Ding’s technique we prove several existence and uniqueness theorems of solutions for the generalized nonlinear mixed variational-like inequality, extend the auxiliary problem technique to suggest and analyze an iterative method to compute the approximate soluti...

Generalized predictive control with flexible constraints is investigated. To apply fuzzy technique, the flexible parts in the inequality constraints are fuzzified as fuzzy constraints. The optimization problem of the generalized predictive control with flexible inequality constraints is converted into two sub-problems to get the lower and upper bound of the objective values, and then the object...

Some properties of conditionally independent random variables are studied. Conditional versions of generalized Borel-Cantelli lemma, generalized Kolmogorov’s inequality and generalized Hájek-Rényi inequality are proved. As applications, a conditional version of the strong law of large numbers for conditionally independent random variables and a conditional version of the Kolmogorov’s strong law...