The duo module plays an important role in the module theory. Many researchers generalized this concept such as Ozcan AC, Hadi IMA and Ahmed MA. It is known that in a duo module, every submodule is fully invariant. This paper used the class of St-closed submodules to work out a module with the feature that all St-closed submodules are fully invariant. Such a module is called an Stc-duo module. This class of modules contains the duo module properly as well as the CL-duo module which was introduced by Ahmed MA. The behaviour of this new kind of module was considered and studied in detail,for instance, the hereditary property of the St-duo module was investigated, as the result; under certain conditions, every St-cl

  The aim of this paper is to prove a theorem on the Riesz means of expansions with respect to Riesz bases, which extends the previous results of [1] and [2] on the Schrödinger operator and the ordinary differential operator of 4-th order to the operator of order 2m by using the eigen functions of the ordinary differential operator. Some Symbols that used in the paper:     the uniform norm. <,>   the inner product in L2. G   the set of all boundary elements of G. ˆ u   the dual function of u.

     This article is devoted to presenting results on invariant approximations over a non-star-shsped weakly compact subset of a complete modular space by introduced a new notion called S-star-shaped with center f:  if   be a mapping and , . Then the existence of common invariant best approximation is proved for Banach operator pair of mappings by combined the hypotheses with Opial’s condition or demi-closeness condition

In this article, the partially ordered relation is constructed in geodesic spaces by betweeness property, A monotone sequence is generated in the domain of monotone inward mapping,  a monotone inward contraction mapping is a  monotone Caristi inward mapping is proved, the general fixed points for such mapping is discussed and A mutlivalued version of these results is also introduced.

In the present paper, the concepts of a quasi-metric space, quasi-Banach space
have been introduced. We prove some facts which are defined on these spaces and
define some polynomials on quasi-Banach spaces and studied their dynamics, such
as, quasi cyclic and quasi hypercyclic. We show the existence of quasi chaotic in the
sense of Devaney (quasi D-chaotic) polynomials on quasi Banach space of qsummable
sequences lq , 0<q<1 such polynomials P is defined by P((xi)i)=(p(xi+m))i
where p:CC, p(0) = 0. In general we also prove that P is quasi chaotic in the sense
of Auslander and Yorke (quasi AY-chaotic) if and only if 0 belong to the Julia set of
p, mN. And then we prove that if the above polynomial P o

In this paper, Nordhaus-Gaddum type relations on open support independence number of some derived graphs of path related graphs under addition and multiplication are studied.

The concern of this article is the calculation of an upper bound of second Hankel determinant for the subclasses of functions defined by Al-Oboudi differential operator in the unit disc. To study special cases of the results of this article, we give particular values to the parameters A, B and λ

     The linear non-polynomial spline is used here to solve the fractional partial differential equation (FPDE). The fractional derivatives are described in the Caputo sense. The tensor products are given for extending the one-dimensional linear non-polynomial spline to a two-dimensional spline  to solve the heat equation. In this paper, the convergence theorem of the method used to the exact solution is proved and the numerical examples show the validity of the method. All computations are implemented by Mathcad15.