Paper's Title:

Fekete Szegö problem on the Class of Bazilevič functions B₁(α) related to the Lemniscate Bernoulli

Author(s):

N. M. Asih, Marjono, Sa'adatul Fitri, Ratno Bagus Edy Wibowo

Department of Mathematics,
University of Brawijaya,
Malang 65145,
Indonesia.
Department of Mathematics,
University of Udayana,
Bali,
Indonesia.
E-mail: madeasih@unud.ac.id

Department of Mathematics,
University of Brawijaya,
Malang 65145,
Indonesia.
E-mail: marjono@ub.ac.id

Department of Mathematics,
University of Brawijaya,
Malang 65145,
Indonesia.
E-mail: saadatulfitri@ub.ac.id

Department of Mathematics,
University of Brawijaya,
Malang 65145,
Indonesia.
E-mail: rbagus@ub.ac.id

Abstract:

We provide a sharp boundaries inequalities for Fekete Szegö problem |a₃-μ a₂²|, the coefficients of logarithmic function log~ f(z)/z, and the coefficients of the inverse function f(f'(w)) on the Bazilevič functions B₁(α) related to the Lemniscate Bernoulli on the unit disk D={z: |z| < 1}. We obtained the result by using some properties of function with positive real part relates to coefficients problems.

Paper's Title:

The Higher Coefficients for Bazilevic Functions B₁(α)

Author(s):

Marjono, Sa'adatul Fitri, and Krisna Adilia Daniswara

Department of Mathematics,
Faculty of Mathematics and Natural Sciences,,
Brawijaya University, Malang Jawa Timur 65145
Indonesia.
E-mail: marjono@ub.ac.id
saadatulfitri@ub.ac.id
krisnaadiliadaniswara@gmail.com
 

Abstract:

Let f be analytic in D{z: |z|< 1} with , and normalized by the conditions f(0)=f'(0)-1=0. We give sharp estimates for the seventh and eighth coefficients for the class of Bazilevic functions with logarithmic growth, B₁α, defined by for α≥0.

Paper's Title:

Walrasian Equilibrium for Set-valued Mapping

Author(s):

M. Muslikh, R.B.E Wibowo, S. Fitri

Department of Mathematics,
University of Brawijaya,
Malang,
Indonesia.
E-mail: mslk@ub.ac.id
rbagus@ub.ac.id
saadatul@ub.ac.id

Abstract:

In this article, we obtain the existence of Walras equilibrium for set-valued demand mappings in a pure exchange economy. In this case, the set-valued mappings are defined by the loss function. Therefore, we shall summarize the features describing the exchange economy system which contain the loss function.

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