exists. The function f is continuously differentiable when it is differentiable and f ′ is continuous. A k-times continuously differentiable function is C, and a continuous function is C. A V -valued function f is weakly C when for every λ ∈ V ∗ the scalar-valued function λ◦ f is C. This sense of weak differentiability of a function f does not refer to distributional derivatives, but to differe...

After introducing the concept of functional dissipativity Dirichlet problem in a domain ??RN for systems partial differential operators form ?h(Ahk(x)?k) (Ahk(x) being m×m matrices with complex valued L? entries), we find necessary and sufficient conditions two-dimensional Lamé system. As an application our theory provide two regularity results displacement vector N-dimensional equilibrium prob...

in this paper, we improve some recent coupled fixed point resultsfor single-valued operators in the framework of ordered $b$-metricspaces established by bota et al. [m-f. bota, a. petrusel, g.petrusel and b. samet, coupled fixed point theorems forsingle-valued operators in b-metric spaces, fixed point theoryappl. (2015) 2015:231]. also, we prove that perov-type fixed pointtheorem in ordered gen...

In this article, we define the vector valued multiple of $chi^{2}$ over $p$-metric sequence spaces defined by Musielak and study some of their topological properties and some inclusion results.

In this paper, we establish some sufficient conditions for the existence of a solution equilibrium problem. The problem is understood in general form: find $ \overline{x}\in E such that$ \begin{equation*} \Phi(\overline{x},y) \vartriangleleft (-D\backslash\{0\})^c \text{ all }y \in E; \end{equation*} $and its variants, where Boolean-valued bifunction and \Phi multivalued mapping with values vec...