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Register a new userOn properties and approximation of class of functions
دراسة خواص و تقريب صف التوابع العقدية
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Authors
محمد علي( باحث )
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يهدف البحث إلى إدخال صف جديد من التوابع العقدية رمزنا له بالرمز يعتمد في تعريفه على تعريف صف هولدر الشهير ,حيث قمنا بدراسة العلاقة بين الصف الجديد و صف هولدر و من ثم اثبتنا بعض الخواص التي يتمتع بها الصف. و في النهاية قمنا بتطبيق هذه الدراسة لتقريب صف التوابع على منحنيات مغلفة تنتمي الى اسرة واسعة من المنحنيات.
This research aimed to define a new class of complex functions , which depends in its definition on the definition of famous Holder class. We studied the relation between the new and Holder classes, then we proved some properties of the class. We finally applied this study to approximate the class of complex functions on closed curves , which belong to a wide class of curves.
References used
Ali Guven ; Daniyal Israfilov On approximation in weidhted Orlicz space .math slovaca J,62,NO1,2012,PP.77-86
Israfilov .D.M Approximation in Morry – Smirnov classes.Azerbijan journal of mathematics,V1,NO1,2011,pp.99-113
Mamedkhanov ,J.I.Approximation in complex plane and singular operetors with Cauchy’s kernel .Dr.dis, USSR-BAKU,1982
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We study in this paper one of functional analysis problems, involved with
construction a new class of functions, denoted by . The definition of the new
class depends on definition of Lebesgueclass of functions and on the Holder clas .
We study the
relation between the new class and approximation of the new class
to rational functions.
The aim of this research is to present the two new classes of complex functions . The first class is denoted , and the second one is denoted. The definition of both of them depends on the famous Lebesgue class ,and orlicz class .The relationship bet
ween the two new classes the two classes is studied. This study gives some properties .
Finally, this study is used for approximation of the class on group of wide curves.
We study in this research some properties of wide class of curves, called k-curves, which is defined by a relation existing between arches and chords connecting any two arbitrary points on it
Especially we study the effect of some mappes on the curves of this class.
Then we study the approximation of weighted Holder class of function on k-curves.
We study in this research approximation of complex functions from Orlicz space on a subclass of Carlson curves, which called Dini smooth curves to rational functions by using polynomials related with Dzjadyk sums which obtained from Faber polynomials. We depend on some concepts of complex analysis such as formulas of Sokhotski to reach the desired goal
In this research, we have studied the issue of approximation of complex functions from weighted Lebesgue space ; and (Mukenhoupt weight) to rational functions by using p- Faber polynomials on large group of curves, which called Carlson curves. This
is also considered as a follow-up to the work done by researchers: Israfilov and Testici in 2014 , where they studied approximation of functions from weighted Smirnov space on domains with a Carlson curve boundary.
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