]>
2019
12
4
ISSN 2008-1898
69
Some new inequalities of the Ostrowski-Grüss, Čebyšev, and Trapezoid types on time scales
Some new inequalities of the Ostrowski-Grüss, Čebyšev, and Trapezoid types on time scales
en
en
In this paper, we establish some novel Ostrowski-Grüss, Čebyšev, and
Trapezoid type inequalities involving functions whose second derivatives are
bounded on time scales. We also give some other interesting inequalities as
special cases of our results.
192
205
Eze R.
Nwaeze
Department of Mathematics
Tuskegee University
USA
enwaeze@tuskegee.edu
Nurhan
Kaplan
Art and Science Faculty, Mathematics Department
Niğde Ömer Halisdemir University
Turkey
nkaplan@ohu.edu.tr
Fatma Gozde
Tuna
Art and Science Faculty, Mathematics Department
Niğde Ömer Halisdemir University
Turkey
gtuna.com@gmail.com
Adnan
Tuna
Art and Science Faculty, Mathematics Department
Niğde Ömer Halisdemir University
Turkey
atuna@ohu.edu.tr
Ostrowski's inequality
Čebyšev inequality
Ostrowski-Grüss
Trapezoid inequality
time scales
Article.1.pdf
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M. Bohner, T. Matthews, Ostrowski inequalities on time scales , JIPAM. J. Inequal. Pure Appl. Math., 9 (2008), 1-8
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M. Bohner, E. R. Nwaeze, A. Tuna, Trapezoid-Type Inequalities on Time Scales, , (Submitted), -
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M. Bohner, A. Peterson, Advances in dynamic equations on time scales , Birkhäuser Boston, Boston (2003)
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M. Bohner, A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhäuser Boston, Boston (2001)
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P. L. Čebyšev , Sue les expressions approxmatives des intégrales définies par les autres prises entre les mêmes limites , Proc. Math. Soc. Charkov, 2 (1882), 93-98
##[8]
A. A. El-Deeb, H. A. Elsennary, E. R. Nwaeze, Generalized Weighted Ostrowski, Trapezoid and Grüss Type Inequalities on Time Scales, Fasc. Math., 60 (2018), 123-144
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W. J. Liu, A. Tuna, Diamond weighted Ostrowski type and Grüss type inequalities on time scales, Appl. Math. Comput., 270 (2015), 251-260
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W. J. Liu, A. Tuna, Weighted Ostrowski, Trapezoid and Grüss type inequalities on time scales, J. Math. Inequal., 6 (2012), 381-399
##[14]
W. J. Liu, A. Tuna, Y. Jiang, New weighted Ostrowski and Ostrowski-Grüss type inequalities on time scales , An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.), 60 (2014), 57-76
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W. J. Liu, A. Tuna, Y. Jiang, On weighted Ostrowski type, Trapezoid type, Grüss type and Ostrowski-Grüss like inequalities on time scales, Appl. Anal., 93 (2014), 551-571
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E. R. Nwaeze , Generalized weighted trapezoid and Grüss type inequalities on time scales, Aust. J. Math. Anal. Appl., 14 (2017), 1-13
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A. Ostrowski , Uber die Absolutabweichung einer differentiierbaren Funktion von ihrem Integralmittelwert, Comment. Math. Helv., 10 (1937), 226-227
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B. G. Pachpatte , On trapezoid and Grüss-like integral inequalities , Tamkang J. Math., 34 (2003), 365-369
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A. Tuna, Y. Jiang, W. J. Liu , Weighted Ostrowski, Ostrowski-Grüss and Ostrowski-Čebyšev Type Inequalities on Time Scales , Publ. Math. Debrecen, 81 (2012), 81-102
##[20]
A. Tuna, W. Liu, New weighted Čebyšev-Ostrowski type integral inequalities on time scales, J. Math. Inequal., 10 (2016), 327-356
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G. P. Xu, Z. B. Fang, A New Ostrowski type inequality on time scales, J. Math. Inequal., 10 (2016), 751-760
]
Approximation of general Pexider functional inequalities in fuzzy Banach spaces
Approximation of general Pexider functional inequalities in fuzzy Banach spaces
en
en
In this paper, we investigate a fuzzy version of a generalized Hyers-Ulam-Rassias type stability for the following
Pexider functional
inequalities
\[
f(x+y)+f(x-y)+g(z)+h(l) \leq
kp\left(\frac{2x+z+l}{k}\right) ,
\]
\[
f(x+y)+f(x-y) + g(z)+k h(l) \leq
kp\left(\frac{ x+ z }{k}+l\right) ,
\]
where $k$ are nonzero real scalars.
In the fuzzy normed linear space setting is presented. In this condition, we give an alternative proof of this result in fuzzy Banach space.
206
216
Gang
Lu
Department of Mathematics, School of Science
ShenYang University of Technology
P. R. China
lvgang1234@hanmail.net
Jincheng
Xin
Department of Mathematics, School of Science
ShenYang University of Technology
P. R. China
1146196932@qq.com
Yuanfeng
Jin
Department of Mathematics
Yanbian University
People's Republic of China
yfkim@ybu.edu.cn
Choonkil
Park
Department of Mathematics, Research Institute for Natural Sciences
Hanyang University
Republic of Korea
baak@hanyang.ac.kr
Fuzzy approximation
Pexider functional inequality
fuzzy Banach space
Article.2.pdf
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]
The transmuted transmuted-G family: properties and applications
The transmuted transmuted-G family: properties and applications
en
en
This paper introduces a new family of continuous distributions called the
transmuted transmuted-G family which extends the quadratic rank
transmutation map pioneered by Shaw and Buckley [W. T. Shaw, I. R. Buckley, arXiv preprint, \(\textbf{2007}\) (2007), 28 pages]. We provide two
special models of the new family which can be used effectively to model
survival data since they accommodate increasing, decreasing, unimodal,
bathtub-shaped and increasing-decreasing-increasing hazard functions. We
also provide two new characterization theorems of the proposed family. The
estimation of the model parameters is performed by the maximum likelihood
method. The flexibility of the proposed family is illustrated by means of
two applications to real data.
217
229
M. M.
Mansour
Department of MIS, Yanbu
Department of Statistics, Mathematics and Insurance
Taibah University
Benha University
Saudi Arabia
Egypt
mmmansour@taibahu.edu.sa
Enayat M.
Abd Elrazik
Department of MIS, Yanbu
Department of Statistics, Mathematics and Insurance
Taibah University
Benha University
Saudi Arabia
Egypt
enayat15@yahoo.com
Ahmed Z.
Afify
Department of Statistics, Mathematics and Insurance
Benha University
Egypt
ahmed.afify@fcom.bu.edu.eg
Mohammad
Ahsanullah
Department of Management Sciences
Rider University NJ
USA
ahsan@rider.edu
Emrah
Altun
Department of Statistics
Bartin University
Turkey
emrahaltun@bartin.edu.tr
Characterization
maximum likelihood
moments
transmuted family
Article.3.pdf
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[1]
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##[2]
A. Z. Afify, G. G. Hamedani, I. Ghosh, M. E. Mead, The transmuted Marshall-Olkin Fréchet distribution: properties and applications, International Journal of Statistics and Probability, 4 (2015), 132-184
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A. Z. Afify, Z. M. Nofal, N. S. Butt , Transmuted complementary Weibull geometric distribution , Pak. J. Stat. Oper. Res., 10 (2014), 435-454
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A. Z. Afify, H. M. Yousof, N. S. Butt, G. G. Hamedani, The transmuted Weibull-Pareto distribution, Pakistan J. Statist., 32 (2016), 183-206
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]
Statistical analysis of Rayleigh competing risks model based on partially step stress Type-II censoring samples
Statistical analysis of Rayleigh competing risks model based on partially step stress Type-II censoring samples
en
en
This paper, discusses the problem of partially step-stress ALTs
(accelerated life tests) form Rayleigh competing risks model.
Type-II censored scheme is used in obtaining the observed censoring
data. The method of MLE (maximum likelihood estimation) of the model
parameters for point and approximate confidence intervals are
considered. Also, bootstrap confidence intervals of model parameters
are discussed. Simulation study is adopted to assess and compare our
proposed method. Finally, some comment to illustrate the behavior of
numerical results.
230
238
Abdullah M.
Almarashi
Statistic Department, Faculty of Science
King Abdulaziz University
Saudi Arabia
aalmarashi@kau.edu.sa
Ali
Algarni
Statistic Department, Faculty of Science
King Abdulaziz University
Saudi Arabia
G. A.
Abd-Elmougod
Mathematics department, Faculty of Science
Taif University
Saudi Arabia
Sayed
Abdel-Khalek
Mathematics department, Faculty of Science
Sohag University
Egypt
sayedquantum@yahoo.co.uk
Competing risk model
accelerate life test
Rayleigh distribution
maximum likelihood estimations
bootstrap confidence intervals
Article.4.pdf
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[1]
B. N. Al-Matrafi, G. A. Abd-Elmougod, Statistical Inferences with Jointly Type-II Censored Samples From Two Rayleigh Distributions, Global J. Pure Appl. Math., 13 (2017), 8361-8372
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D. Kundu, A. M. Sarhan, Analysis of incomplete data in the presence of competing risks among several groups, IEEE Tran. Reliab., 55 (2006), 262-271
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A. M. Sarhan, Analysis of incomplete, censored data in competing risks models with generalized Exponential distribution, IEEE Transactions on Reliability, 56 (2007), 132-138
##[19]
A. A. Soliman, G. A. Abd-Elmougod, M. M. Al-Sobhi, Estimation in step-stress partially accelerated life tests for the Chen distribution using progressive Type-II censoring, Appl. Math. Infor. Sci., 11 (2017), 325-332
]
Alpha power transformed extended exponential distribution: properties and applications
Alpha power transformed extended exponential distribution: properties and applications
en
en
In this paper, a three-parameter lifetime model motivated by alpha power transformation is considered. We call the proposed distribution as; the \textit{alpha power transformed extended exponential} (APTEE). The APTEE model contains new recent models as; alpha power transformed exponential and alpha power transformed Lindley distributions. At the same time, it contains classical models as exponential, gamma, and Lindley distributions. The properties of the APTEE distribution are derived. Parameter estimation is accomplished using maximum likelihood, percentiles, and Cramer-von Mises methods. Simulation issues and applications to real data are emphasized.
239
251
Amal S.
Hassan
Institute of Statistical Studies and Research
Cairo University
Egypt
dr.amalelmoslamy@gmail.com
Rokaya E.
Mohamd
Institute of Statistical Studies and Research
Cairo University
Egypt
rokayaelmorsy@gmail.com
M.
Elgarhy
Vice Presidency for Graduate Studies and Scientific Research
University of Jeddah
KSA
m_elgarhy85@yahoo.com
Aisha
Fayomi
Statistics Department, Faculty of Science
King AbdulAziz University
KSA
afayomi@kau.edu.sa
Extended exponential
moments
maximum likelihood
percentiles and Cramer-von Mises
Article.5.pdf
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Lag synchronization of uncertain complex dynamical networks with derivative coupling
Lag synchronization of uncertain complex dynamical networks with derivative coupling
en
en
In this study, uncertain complex dynamical network model with time varying coupling delay and derivative coupling delay is considered. The lag synchronization between two such uncertain networks with different nodes is investigated.
An adaptive control method is designed by using Lyapunov stability theory for achieving the lag synchronization and some corollaries are also given.
In addition, on the basis of the adaptive update law, unknown parameters of the networks are estimated.
The analytical results show that the states of the dynamical network with derivative delay coupling can be asymptotically synchronized under the designed control. The numerical simulation results also demonstrate the validity of the designed method.
252
261
Ghada
Al-mahbashi
School of mathematical Sciences, Faculty of Science and Technology
Universiti Kebangsaan Malaysia
Malaysia
mahbashighada@yahoo.com
M. S. M.
Noorani
School of mathematical Sciences, Faculty of Science and Technology
Universiti Kebangsaan Malaysia
Malaysia
msn@ukm.edu.my
Lag synchronization
derivative coupling
complex dynamical networks
adaptive control
Article.6.pdf
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