• Bulletin of the Korean Mathematical Society
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• v.49 no.1
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• pp.33-47
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• 2012

In this paper, the log-convexity of another class one-parameter mean is investigated. As applications, some new upper and lower bounds of logarithmic mean, new estimations for identric mean and new inequalities for power-exponential mean and exponential-geometric mean are first given.

• Bulletin of the Korean Mathematical Society
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• v.40 no.3
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• pp.411-423
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• 2003

Some B.-Y. Chen inequalities for different kind of submanifolds of generalized complex space forms are established.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.707-716
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• 2015

Some Hermite-Hadamard type inequalities for the fractional integrals are established and these results have some relationship with the obtained results of [11, 12].

• Journal of applied mathematics & informatics
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• v.32 no.3_4
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• pp.303-314
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• 2014

In this paper, a new lemma is established and several new inequalities for differentiable co-ordinated quasi-convex functions in two variables which are related to the left-hand side of Hermite-Hadamard type inequality for co-ordinated quasi-convex functions in two variables are obtained.

• Kyungpook Mathematical Journal
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• v.50 no.3
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• pp.371-378
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• 2010

In this paper, we establish new inequalities of Ostrowski's type for functions whose derivatives in absolute value are (${\alpha}$, m)-convex.

• Kyungpook Mathematical Journal
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• v.56 no.1
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• pp.161-172
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• 2016

In this paper, we use the Riemann-Liouville fractional integrals to establish several new inequalities for some differantiable mappings that are connected with the celebrated Ostrowski type integral inequality.

• Honam Mathematical Journal
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• v.45 no.4
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• pp.689-700
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• 2023

In this note, we establish a new subfamily of spirallike functions by making use of a generalized q-integral operator. We examine characterization rule for functions which are member of this subclass. We further obtain coefficient estimate, subordination results and integral mean inequalities for functions in this class. The Fekete-Szegö inequalities are also derived.

• The Pure and Applied Mathematics
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• v.31 no.1
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• pp.33-48
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• 2024

In this study, we would like to state two refined results related to Hermite Hadamard type inequality for convex functions with two distinct techniques. Hence our obtained results would be better than the results already established for the class of convex functions. Applications to trapezoidal rule and special means are also discussed.

• Communications of Mathematical Education
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• v.19 no.4 s.24
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• pp.699-713
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• 2005

In this paper, we attempted to find out the meaning of several means and inequalities, their relationships and proposed the effective ways to teach them in college mathematics classes. That is, we introduced 8 proofs of arithmetic-geometric mean equality to explain the fact that there exist diverse ways of proof. The students learned the diverseproof-methods and applied them to other theorems and projects. From this, we found out that the attempt to develop the students' logical thinking ability by encouraging them to find out diverse solutions of a problem could be a very effective education method in college mathematics classes.

• International Journal of Reliability and Applications
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• v.4 no.3
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• pp.141-156
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• 2003

Nonparametric families of aging distributions have been the subject of investigation from long period of time and still. Both probabilistic and statistical properties of these distributions were studied for such families as new better than used renewal failure rate (NBURFR) and new better average renewal failure rate (NBARFR) classes. They have been studied by Abouammoh and Ahmed (1992). In the present work, moment inequalities are derived for the above mentioned families that demonstrate that if the mean life is finite for any of them then all higher order moments exist. Next, based on these inequalities, new test procedures for exponentiality against these families are studied showing that it is simple and hold high relative efficiency for some commonly used alternatives. Dealing with censored data case also studied.