Existence Theorems For a(u,v)-monotone of nonstandard Hemivariational Inequality

In this paper, we consider the existence result of a nonstandard hemivariational inequalities with a(u,v) -monotone mapping in reflexive and non reflexive Banachs space. Finally, we provide sufficient conditions for which that inequality has a solution in the case of unbounded sets, via the fixed point and KKM theorems

On a type of exponential functional equation and its superstability in the sense of Ger

In this paper, we deal with a type exponential functional equation as follows $$f(xy)=f(x)^{g(y)},$$ where $f$ and $g$ are two real valued functions on a commutative semigroup. Our aim of this paper is to proved that the above functional equation in the sense of Ger is superstable

Fixed Point in Minimal Spaces

This paper deals with fixed point theory and fixed point property in minimal spaces. We will prove that under some conditions f : (X,M) → (X,M) has a fixed point if and only if for each m-open cover {Bα} for X there is at least one x ∈ X such that both x and f(x) belong to a common Bα. Further, it is shown that if (X,M) has the fixed point property, then its minimal retract subset enjoys this property

Regularized fractional derivatives in Colombeau algebra

Abstract The present study aims at indicating the existence and uniqueness result of system in extended colombeau algebra. The Caputo fractional derivative is used for solving the system of ODEs. In addition, Riesz fractional derivative of Colombeau generalized algebra is considered. The purpose of introducing Riesz fractional derivative is regularizing it in Colombeau sense. We also give a solution to a nonlinear heat equation illustrating the application of the theory