Contents IJPAM: Volume 116, No. 3 (2017)

The aim of this paper is to prove some results for equivalence of moduli of smoothnes in approximation theory , we used a"non uniform" modulus of smoothness and the weighted Ditzian –Totik moduli of smoothness in by spline functions ,several results are obtained .For example , it shown that ,for any the inequality , is satisfied ,finally, similar result for chebyshev partition and weighted Ditzian –Totik moduli of smoothness are also obtained.

Among a variety of approaches introduced in the literature to establish duality theory, Fenchel duality was of great importance in convex analysis and optimization. In this paper we establish some conditions to obtain classical strong Fenchel duality for evenly convex optimization problems defined in infinite dimensional spaces. The objective function of the primal problem is a family of (possible) infinite even convex functions. The strong duality conditions we present are based on the consideration of the epigraphs of the c-conjugate of the dual objective functions and the ε-c-subdifferential of the primal objective functions.

In this paper, the Azzallini’s method used to find a weighted distribution derived from the standard Pareto distribution of type I (SPDTI) by inserting the shape parameter (θ) resulting from the above method to cover the period (0, 1] which was neglected by the standard distribution. Thus, the proposed distribution is a modification to the Pareto distribution of the first type, where the probability of the random variable lies within the period  The properties of the modified weighted Pareto distribution of the type I (MWPDTI) as the probability density function ,cumulative distribution function, Reliability function , Moment and  the hazard function are found. The behaviour of probability density function for MWPDTI distrib

The principal factor in the proofs of many so-called intersection results and associated best approximation theorems—such as the famed Brouwer fixed-point theorem) is Knaster-Kuratowski-Mazurkiewicz theorem (KKM), which was extended from Rl to Hausdorff vector spaces by Ky Fan. This kind of theory necessitates introducing some form of abstract convex structure on a topological space. In both pure and applied mathematics, the theory of approximation plays a central role. The connection between best approximation and fixed-point theory provides a powerful tool for analyzing the nonlinear maps, the convergence of iterative processes, and the solving of variational problems. This paper is dedicated to presenting a new extension of the

Background: Characterization of the ovarian masses preoperatively is important to inform the surgeon about the possible management strategies. MRI may be of great help in identifying malignant lesion before surgery. Diffusion Weighted Imaging (DWI) is a sensitive method for changes in proton of water mobility caused by pathological alteration of tissue cellularity, cellular membrane integrity, extracellular space perfusion, and fluid viscosity.

Objective: to study the diagnostic accuracy of DWI in differentiation between benign and malignant ovarian masses.

Type of the study:Cross-sectional study.

Methods: this study included  53with complex