Normic Inequality of Two-dimensional Viscosity Operator

Max-Min averaging operator: fuzzy inequality systems and resolution

 Minimum and maximum operators are two well-known t-norm and s-norm used frequently in fuzzy systems. In this paper, two different types of fuzzy inequalities are simultaneously studied where the convex combination of minimum and maximum operators is applied as the fuzzy relational composition. Some basic properties and theoretical aspects of the problem are derived and four necessary and suffi...

An Operator Extension of Bohr's inequality

Numerical solution of two-dimensional fuzzy Fredholm integral equations using collocation fuzzy wavelet like ‎operator‎

In this paper‎, ‎first we propose a new method to approximate the solution of two-dimensional linear fuzzy Fredholm integral equations of the second kind based on the fuzzy wavelet like operator‎. ‎Then‎, ‎we discuss and investigate the convergence and error analysis of the proposed method‎. ‎Finally‎, ‎to show the accuracy of the proposed method‎, ‎we present two numerical ‎examples.‎

Inequalities of Ando's Type for $n$-convex Functions

By utilizing different scalar equalities obtained via Hermite's interpolating polynomial, we will obtain lower and upper bounds for the difference in Ando's inequality and in the Edmundson-Lah-Ribariv c inequality for solidarities that hold for a class of $n$-convex functions. As an application, main results are applied to some operator means and relative operator entropy.

Alexandroff-Bakelman-Pucci estimate and Harnack inequality for degenerate fully non-linear elliptic equations

In this paper, we study fully non-linear elliptic equations in nondivergence form which can be degenerate when “the gradient is small”. Typical examples are either equations involving the m-Laplace operator or BellmanIsaacs equations from stochastic control problems. We establish an AlexandroffBakelman-Pucci estimate and we prove a Harnack inequality for viscosity solutions of such degenerate e...