where f∗, u∗ (or f ∗, u∗) are lower (or upper) limit functions of f and u, respectively. Assume that u is the generalized solution of the FBVP constructed by Perron’s supersolutions or subsolutions method (see [1, 6]). It is well known that, in general, the generalized solution does not satisfy (1.3). We say that a point (x0, t0) ∈ ∂Ωδ is regular if, for any bounded function f : ∂Ω→R, the gener...

This paper presents a frequency weighted generalized total least squares linear prediction for estimating closely spaced sinusoids. In this method, the received data is first processed by a pole-zero prefilter and then a generalized total least squares linear prediction is applied to the prefiltered signal. A procedure of optimizing the generalized solution is introduced. By computer simulation...

Weyl’s theorem was proved independently by Nirenberg [15] and Pogorelov [16] using different approaches. Nirenberg used the continuity method that is more familiar to geometric analysts. The Pogorelov approach consists of two steps. First, Pogorelov exhibited a generalized solution as the limit of polyhedra and then Pogorelov proved the regularity of this generalized solution. Later, Pogorelov ...

A new class of generalized nonlinear set-valued quasivariational inclusions involving generalizedm-accretive mappings in Banach spaces are studied, which included many variational inclusions studied by others in recent years. By using the properties of the resolvent operator associated with generalized m-accretive mappings, we established the equivalence between the generalized nonlinear set-va...

In the paper, we advance a numerical technique for enclosing generalized AE-solution sets to interval linear systems. The main result of the paper is an extension of the well-known interval Gauss-Seidel method to the problems of outer estimation of these generalized solution sets. We give a theoretical study of the new method, prove an optimality property for the generalized interval Gauss-Seid...

in this paper, the picard method is proposed to solve the bernoulli equation with fuzzy initial condition under generalized h-differentiability. the existence and uniqueness of the solution and convergence of the proposed method are proved in details. finally an example shows the accuracy of this method.

in this paper, stochastic generalizations of some fixed point for operators satisfying random contractively generalized hybrid and some other contractive condition have been proved. we discuss also the existence of a solution to a nonlinear random integral equation in banah spaces.