Differential Subordinations of Arithmetic and Geometric Means of Some Functionals Related to a Sector

نویسندگان

  • Adam Lecko
  • Millenia Lecko
چکیده

For r > 0 let r {z ∈ : |z| < r}. Let 1 . Let the functions f and F be analytic in the unit disc . A function f is called subordinate to F, written f ≺ F, if F is univalent in , f 0 F 0 and f ⊂ F . Let D be a domain in 2 and ψ : 2 ⊃ D → be an analytic function, and let p be a function analytic in with p z , zp′ z ∈ D, z ∈ and h be a function analytic and univalent in . The function p is said to satisfy the first-order differential subordination if

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A remark on the means of the number of divisors

‎We obtain the asymptotic expansion of the sequence with general term $frac{A_n}{G_n}$‎, ‎where $A_n$ and $G_n$ are the arithmetic and geometric means of the numbers $d(1),d(2),dots,d(n)$‎, ‎with $d(n)$ denoting the number of positive divisors of $n$‎. ‎Also‎, ‎we obtain some explicit bounds concerning $G_n$ and $frac{A_n}{G_n}$.

متن کامل

Some remarks on the arithmetic-geometric index

Using an identity for effective resistances, we find a relationship between the arithmetic-geometric index and the global ciclicity index. Also, with the help of majorization, we find tight upper and lower bounds for the arithmetic-geometric index.

متن کامل

Geometric-Arithmetic Index of Hamiltonian Fullerenes

A graph that contains a Hamiltonian cycle is called a Hamiltonian graph. In this paper we compute the first and the second geometric – arithmetic indices of Hamiltonian graphs. Then we apply our results to obtain some bounds for fullerene.

متن کامل

On the total version of geometric-arithmetic index

The total version of geometric–arithmetic index of graphs is introduced based on the endvertex degrees of edges of their total graphs. In this paper, beside of computing the total GA index for some graphs, its some properties especially lower and upper bounds are obtained.

متن کامل

A Note on the First Geometric-Arithmetic Index of Hexagonal Systems and Phenylenes

The first geometric-arithmetic index was introduced in the chemical theory as the summation of 2 du dv /(du  dv ) overall edges of the graph, where du stand for the degree of the vertex u. In this paper we give the expressions for computing the first geometric-arithmetic index of hexagonal systems and phenylenes and present new method for describing hexagonal system by corresponding a simple g...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Int. J. Math. Mathematical Sciences

دوره 2011  شماره 

صفحات  -

تاریخ انتشار 2011