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Register a new userThe properties and approximation of functions class
دراسة تقريب صف الدوال و خواصه
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يهدف هذا البحث إلى دراسة صفين جديدين من الدوال العقدية. و هما يرتبطان بصف دوال ليبيغ الشهير ، و صف دوال أورليتش . ثم تمت دراسة العلاقة بين الصفين الجديدين، و كل من الصفين، حيث تم إثبات بعض الخواص الجديدة التي يتمتع بها كل من الصفين. و في نهاية هذا البحث قمنا باستخدام هذه الدراسة لتقريب الصف على مجموعة واسعة من المنحنيات.
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 between 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.
References used
Mohammad Ali, The effect of some conformal mapping on Riesz curves and on modulus of continuity, Tishreen university journal for studies and scientific research-Basic science series ,Vol(24) No(12) 2002
Ali Guven , Daniyal M. Polynomial Approximation in Smirnov-Orlicz classes, Computational Methods and Function Theory,Volume2(2002),No.2,509-517.urves
RAMAZAN AKGUN, DANIYAL m. Israfilov, Approximation and Moduli of fractional order in smirnov- orlicz classes, GLASNIK. Mathematic, Vo1,43(63), 2008, 121-136
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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.
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 fi
nally applied this study to approximate the class of complex functions on closed curves , which belong to a wide class of 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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