The purpose of this paper is to find the best multiplier approximation of unbounded functions in    –space by using some discrete linear positive operators. Also we will estimate the degree of the best multiplier approximation in term of modulus of continuity and the averaged modulus.

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

The following dilutions -710X46, -610X46, -510X46 of Bacillus thuringiensis were used for bioassay against the different larval instar of the potato tuber moth Phthorimaea operculella by the spraying method, the results showed that there was no significant influence in the percentage of egg hatching in comparison with the control. The sensitivity of larval stages was reduced with the increasing the age and exposure period. The study also showed that the larvae infected with B.t. stopped feeding, movement and a general paralysis causing the death of larva after (24-48) hours , and the larva color was changed from the natural waxy colour to brown finally to the black after death.

In this paper, we illustrate how to use the generalized homogeneous -shift operator  in generalizing various well-known q-identities, such as Hiene's transformation, the q-Gauss sum, and Jackson's transfor- mation. For the polynomials , we provide another formula for the generating function, the Rogers formula, and the bilinear generating function of the Srivastava-Agarwal type. In addition, we also generalize the extension of both the Askey-Wilson integral and the Andrews-Askey integral.

This paper presents results about the existence of best approximations via nonexpansive type maps defined on modular spaces. 

I n  this  paper ,we 'viii  consider  the density  questions  associC;lted with  the single  hidden layer feed forward  model. We proved  that a FFNN   with   one   hidden   layer  can   uniformly   approximate   any continuous  function  in C(k)(where k is a compact set in R11 ) to any required accuracy.

However, if the set of basis function is dense then the ANN's can has al most one hidden layer. But if the set of basis function  non-dense, then we  need more  hidden layers. Also, we have shown  that there exist  localized functions and that there is no t

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 present paper, we obtain some differential subordination and superordination results, by using generalized operators for certain subclass of analytic functions in the open unit disk. Also, we derive some sandwich results.