نوقشت رسالة ماجستير في قسم الرياضيات – كلية التربية للعلوم الصرفة بعنوان Approximation of unbounded Functions in Weighted Spaces) ) للطالب عبد السلام محمد صبري

his thesis introduces the best approximation of unbounded functions that have one variable properties by algebraic polynomials and trigonometric polynomials in weighted space . The modulus of smoothness of fractional order is on the consideration to obtain direct (Jackson) and converse approximation theorems with constructive properties of weighted spaces. In this study also the inverse approximation by algebraic polynomials of unbounded functions in weighted space is inserted.

Next, in terms of modulus of smoothness, the approximation of -derivative of functions are investigated. What is also discussed is that the derivative of the function of degree with is less than or equal to the degree of the best approximation polynomial of the same function. Furthermore, the study proves that the modulus of smoothness of a function in a weight spaceis less than or equal to the sum of the degree the best approximation for a function in the same space. Later, the equivalent relationship between the modulus of continuity and k- functional is studied.

Finally, the fundamental approximation problems such as Jacksons (direct) and converse theorems of unbounded functions by trigonometric polynomials in weighted space is proved. Besides, this study presents constructive characteristic of the best approximation degree of unbounded functions in the same space.

عبد السلام 1

عبد السلام 11 

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