In this paper, we generalized the principle of Banach contractive to the relative formula and then used this formula to prove that the set valued mapping has a fixed point in a complete partial metric space. We also showed that the set-valued mapping can have a fixed point in a complete partial metric space without satisfying the contraction condition. Additionally, we justified an example for our proof.

In this paper, we introduce a new type of Drazin invertible operator on Hilbert spaces, which is called D-operator. Then, some properties of the class of D-operators are studied. We prove that the D-operator preserves the scalar product, the unitary equivalent property, the product and sum of two D-operators are not D-operator in general but the direct product and tenser product is also D-operator.

     In this paper, some conditions to guarantee the existence of bounded solution to the second order multi delayed arguments differential equation are given. The Krasnoselskii theorem used to the Lebesgue’s dominated convergence and fixed point to obtain some new sufficient conditions for existence of solutions. Some important lemmas are established that are useful to prove the main results for oscillatory property. We also submitted some sufficient conditions to ensure the oscillation criteria of bounded solutions to the same equation.

In this paper, an adaptive integral Sliding Mode Control (SMC) is employed to control the speed of Three-Phase Induction Motor. The strategy used is the field oriented control as ac drive system. The SMC is used to estimate the frequency that required to generates three phase voltage of Space Vector Pulse Width Modulation (SVPWM) invertor . When the SMC is used with current controller, the quadratic component of stator current is estimated by the controller. Instead of using current controller, this paper proposed estimating the frequency of stator voltage since that the slip speed is function of the quadratic current . The simulation results of using the SMC showed that a good dynamic response can be obtained under load

The aim of this research is to prove the idea of maximum m_X-N-open set, m-N-extremally disconnected with respect to t and provide some definitions by utilizing the idea of m_X-N-open sets. Some properties of these sets are studied.

Let  be an n-Banach space, M be a nonempty closed convex subset of , and S:M→M be a mapping that belongs to the class  mapping. The purpose of this paper is to study the stability and data dependence results of a Mann iteration scheme on n-Banach space

The aim of this paper is adopted to give an approximate solution for advection dispersion equation of time fractional order derivative by using the Chebyshev wavelets-Galerkin Method . The Chebyshev wavelet and Galerkin method properties are presented. This technique is used to convert the problem into the solution of linear algebraic equations. The fractional derivatives are described based on the Caputo sense. Illustrative examples are included to demonstrate the validity and applicability of the proposed technique.

 Computer theoretical study has been carried out on the design of five electrode immersion electrostatic lens used in electron gun application. The finite element method (FEM) is used in the solution of the Poisson's equation fro determine axial potential distribution, the electron trajectory under Zero magnification condition .      The optical  properties : focal length ,spherical and chromatic aberrations are calculated,From studying the properties of the designed electron gun. we have good futures for these  electron gun where are abeam current 4*10-4A    can be supplied by using cathode tip of radius 100 nm.

We develop the previously published results of Arab by using the function  under certain conditions and using G-α-general admissible and triangular α-general admissible to prove coincidence fixed point and common fixed point theorems for two weakly compatible self –mappings in complete b-metric spaces.

In this paper, certain types of regularity of topological spaces have been highlighted, which fall within the study of generalizations of separation axioms. One of the important axioms of separation is what is called regularity, and the spaces that have this property are not few, and the most important of these spaces are Euclidean spaces. Therefore, limiting this important concept to topology is within a narrow framework, which necessitates the use of generalized open sets to obtain more good characteristics and preserve the properties achieved in general topology. Perhaps the reader will realize through the research that our generalization preserved most of the characteristics, the most important of which is the hereditary property. Two t