A continuous operator $T$ between two Banach lattices $E$ and     $F$ is called Almost order-weakly compact, whenever for each Almost order bounded subset $A$ of $E$,  $T(A)$ is a relatively weakly compact subset of $F$. We show that the positive operator $T$ from  $E$ into a  Dedekind complete Banach lattice $F$  is Almost order-weakly compact iff  $T(x_n) \xrightarrow{\|.\|}0$ in $F$ for each disjoint Almost order bounded sequence $\{x_n\}$ in $E$. In this manuscript, we study some properties of this class of operators and its relationships with the others known classes of operators.

In this paper, we apply Newton's method to solve a class of integro-differential equations of the Volterra-Fredholm type with nonlocal characteristics, involving Almost sectorial operators and Hilfer fractional derivatives. Since these equations play a key role in mathematics, engineering, biology, physics, chemistry, control theory and  economy, finding an appropriate solution is important. By Newton's method, we linearize a nonlinear Volterra-Fredholm integro-differential equation which is equivalent to a category of Volterra-Fredholm integro-differential equations with nonlocal properties, incorporating Almost sectorial operators and Hilfer fractional derivatives and nearly sectorial operators. This technique has been shown to be an effective tool for the numerical solution of initial value problems in nonlinear integro-differential equations. The convergence analysis is also investigated.

Let $mathbb{C}^n$ be the space of $n$ complex variables. Let $Omega_{n, p_2, ldots, p_n}$ be a complete Reinhardt on $mathbb{C}^n$. The Minkowski functional on complete Reinhardt $Omega_{n, p_2, ldots, p_n}$ is denoted by $rho(z)$. The concept of spirallike mapping of type $beta$ and order $alpha$ is defined. So, the concept of the strong and Almost spirallike mappings of type $beta$ and order $alpha$ is discussed in this paper. From the Schwarz-Pick lemma, under certain conditions, we obtain that the generalized Roper-Suffridge operators preserve strong and Almost spirallikeness of type $beta$ and order $alpha$ on bounded and complete Reinhardt domains $Omega_{n, p_1, cdots, p_n}$. For specific values for $alpha$ and $beta$, we obtain the corresponding definitions of strong spirallike mappings of type $beta$, strong and Almost starlike mappings of order $alpha$, strong starlike mappings. Therefore we obtain the generalized Roper-Suffridge operators preserve strong spirallikeness of type $beta$, strong and Almost starlikeness of order $alpha$, strong starlikeness on the corresponding domains. In particular, our results reduce to many well-known results.

In this article, an analytical solution for buckling of annular sectorial porous plates, is presented. At first, based on first order shear deformation plate theory, the governing equilibrium equations and boundary conditions are obtained using minimum total potential energy principle. Then, the stability equations of the plate, are derived in terms of infinitesimal displacements using adjacent equilibrium criterion. Since these equations are highly coupled, it is so difficult to find an analytical solution for them. So, by introducing four auxiliary functions and doing some mathematical manipulations, the stability equations are decoupled and converted to two independent differential equation which can be solved analytically. For this purpose, it has been assumed the simply supported boundary conditions for the radial edges and desired boundary conditions for the circumferential edges of the plate. Finally, the critical buckling load has been calculated for different conditions of the plate. In section of numerical results, the effect of different geometrical parameters, such as sector angle, thickness and inner radius of the plate, also effect of porosity of the plate upon the critical buckling load has been studied for different arbitrary boundary conditions on circumferential edges. The result show that the effect of increase in porosity of the plate upon decrease of the critical buckling load is significantly fewer than the effect of geometrical parameters and the boundary conditions.

Let G = A B be the product of two groups A and B. In this paper we show that if the groups A and B are Almost central, then G is Almost soluble.We remind that N.S. Cernikov in 1981 gave a very condensed proof in short note, but here we present a completely different approach, which will be understandable for the interested readers.

The aim of the present work is to introduce the concept of $\lambda _{r}$-Almost convergence of sequences. We define the spaces $f\left( \lambda _{r}\right) $ and $f_{0}\left( \lambda _{r}\right) $ of $ \lambda _{r}$-Almost convergent and $\lambda _{r}$-Almost null sequences. We investigate some inclusion relations concerning those spaces with examples and we determine the $\beta $- and $\gamma $-duals of the space $f\left( \lambda _{r}\right) $. Finally, we give the characterization of some matrix classes.