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The Australian Journal of Mathematical Analysis and Applications
ISSN 1449-5910 |
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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:
On a subset of Bazilevic functions
Author(s):
Marjono and D. K. Thomas
Department of Mathematics,
Faculty of Mathematics and Natural Sciences,
Brawajaya University,
Malang, Jawa Timur 65145,
Indonesia.
E-mail: marjono@ub.ac.id
Department of Mathematics,
Swansea University, Singleton Park,
Swansea, SA2 8PP,
United Kingdom.
E-mail: d.k.thomas@swansea.ac.uk
Abstract:
Let S denote the class of analytic and
univalent functions in
of the form
For
α≥0, the subclass B1α of
S of Bazilevic functions has been extensively studied. In this paper we determine various properties of a subclass of B1α, for
α≥0 which extends early results of a class of starlike functions studied by Ram Singh.
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:
A Subordination Theorem for Analytic Functions
Author(s):
Marjono
Department of Mathematics, Faculty of
Mathematics and Natural Sciences,
University of Brawijaya,
Jl. Veteran Malang 65145,
INDONESIA.
E-mail: marjono@ub.ac.id
URL: http://matematika.ub.ac.id
Abstract:
It is shown that if f is analytic in D={z:|z|<1}, with
f(0)=f'(0)-1=0, then for
implies
where
and that
β(γ) is the largest number such that this implication holds.
Paper's Title:
Stability of an Almost Surjective epsilon-Isometry in The Dual of Real Banach Spaces
Author(s):
Minanur Rohman, Ratno Bagus Edy Wibowo, Marjono
Department of Mathematics, Faculty of
Mathematics and Natural Sciences,
Brawijaya University,
Jl. Veteran Malang 65145,
Indonesia.
E-mail:
miminanira@gmail.com
Department of Mathematics, Faculty of
Mathematics and Natural Sciences,
Brawijaya University,
Jl. Veteran Malang 65145,
Indonesia.
E-mail:
rbagus@ub.ac.id
Department of Mathematics, Faculty of
Mathematics and Natural Sciences,
Brawijaya University,
Jl. Veteran Malang 65145,
Indonesia.
E-mail:
marjono@ub.ac.id
Abstract:
In this paper, we study the stability of epsilon-isometry in the dual of real Banach spaces. We prove that the almost surjective epsilon-isometry mapping is stable in dual of each spaces. The proof uses Gâteaux differentiability space (GDS), weak-star exposed points, norm-attaining operator, and some studies about epsilon-isometry that have been done before.
Paper's Title:
Portfolio Optimization of Sharia and Non-Sharia Stocks Using Single Index Model (Case study: Jakarta Sharia Index and Kompas 100 Index)
Author(s):
Kwardiniya Andawaningtyas, Muhammad Luthfi, Marjono, Endang Wahyu Handamari, Umu S'adah, Evi Ardiyani
Department of Mathematics,
Brawijaya University, Malang,
Indonesia.
Department of Mathematics,
IPB University, Bogor,
Indonesia.
E-mail:
dina_math@ub.ac.id
muhammadluthfi@student.ub.ac.id
marjono@ub.ac.id
ewahyu-math@ub.ac.id
u.saadah@ub.ac.id
ardiyanievi@apps.ipb.ac.id
Abstract:
Stocks are instruments with high returns but also have increased risks. One way to overcome this risk is to form a stock portfolio. This study observed 30 sharia stocks listed on the Jakarta Islamic Index (JII) and 28 non-shariah stocks listed on the Kompas 100 Index from March 2020 to September 2022. The data used is the daily closing price of stocks, the number of stock dividends, and the daily closing price of the Jakarta Composite Index (JCI) from 3rd March 2020, to 31st August 2022. In addition, interest rate of Bank Indonesia Certificate (SBI) is used as risk-free rate. This study aims to optimize the sharia and non-sharia stocks portfolio using the Single Index Model (SIM), which will then be evaluated using the Sharpe, Treynor, and Jensen ratio. The result is that the optimal portfolio of sharia stocks have better performance than the optimal portfolio of non-sharia stocks based on the Treynor ratio. Meanwhile, the optimal portfolio of non-sharia stocks have better performance than the optimal portfolio of sharia stocks based on the Sharpe and Jensen ratio.
Paper's Title:
On Sufficient Conditions for Strong Starlikeness
Author(s):
V. Ravichandran, M. H. Khan, M. Darus, And
K. G. Subramanian School of Mathematical Sciences, Universiti Sains Malaysia,
11800 Usm Penang, Malaysia
vravi@cs.usm.my
Url: http://cs.usm.my/~vravi/index.html
Department of Mathematics, Islamiah College, Vaniambadi 635 751, India
khanhussaff@yahoo.co.in
School of Mathematical Sciences, Faculty of Science and Technology, UKM, Bangi
43600,
Malaysia
maslina@pkrisc.cc.ukm.my
Url:
http://www.webspawner.com/users/maslinadarus
Department of Mathematics, Madras Christian College, Tambaram, Chennai 600 059,
India
kgsmani@vsnl.net
Abstract:
In the present investigation, we obtain some sufficient
conditions for a normalized analytic function f(z) defined on the unit disk to
satisfy the condition
Paper's Title:
Local Boundedness of Weak Solutions for Singular Parabolic Systems of p-Laplacian Type
Author(s):
Corina Karim, Marjono
Department of Mathematics,
Universitas Brawijaya,
Indonesia.
E-mail: co_mathub@ub.ac.id,
marjono@ub.ac.id
Abstract:
We study the local boundedness of weak solutions for evolutional p-Laplacian systems in the singular case. The initial data is belonging to Lebesgue space L∞ (0,T;W(1,p) (Ω,Rn )). We use intrinsic scaling method to treat the boundedness of weak solutions. The main result is to make the local boundedness of weak solution for the systems well-worked in the intrinsic scaling.
Paper's Title:
The Conservativeness of Girsanov Transformed for Symmetric Jump-diffusion Process
Author(s):
Mila Kurniawaty and Marjono
Department of Mathematics,
Universitas Brawijaya,
Malang,
Indonesia.
E-mail: mila_n12@ub.ac.id,
marjono@ub.ac.id
Abstract:
We study about the Girsanov transformed for symmetric Markov processes with jumps associated with regular Dirichlet form. We prove the conservativeness of it by dividing the regular Dirichlet form into the "small jump" part and the "big jump" part.
Paper's Title:
Conservativeness Criteria of Girsanov Transformation for Non-Symmetric Jump-diffusion
Author(s):
Mila Kurniawaty
DDepartment of Mathematics,
Universitas Brawijaya, Malang,
Indonesia.
E-mail: mila_n12@ub.ac.id
Abstract:
We develop the condition in our previous paper [The Conservativeness of Girsanov transformed for symmetric jump-diffusion process (2018)] in the framework of nonsymmetric Markov process with jumps associated with regular Dirichlet form. We prove the conservativeness of it by relation in duality of Girsanov transformed process and recurrent criteria of Dirichlet form.
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