• East Asian mathematical journal
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• v.23 no.2
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• pp.229-246
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• 2007

Some inequalities related to the $H{\ddot{o}}lder$ integral inequality and applications for bounding the ${\check{C}}eby{\check{s}}ev$ functional are given.

• Journal of the Chungcheong Mathematical Society
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• v.8 no.1
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• pp.79-87
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• 1995

We complete the proofs of integral and integro-differential inequalities presented in Lakshmikantham, Leela and Raos' results.

• Honam Mathematical Journal
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• v.44 no.2
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• pp.244-258
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• 2022

In this work, by using an integral identity together with both the Hölder and the power-mean integral inequalities we establish several new inequalities for n-times differentiable arithmetic-harmonically-convex function. Then, using this inequalities, we obtain some new inequalities connected with means. In special cases, the results obtained coincide with the well-known results in the literature.

• Communications of the Korean Mathematical Society
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• v.20 no.3
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• pp.487-503
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• 2005

Some companions of Gruss inequality in 2-inner product spaces and applications for determinantal integral inequalities are given.

• Korean Journal of Mathematics
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• v.28 no.1
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• pp.9-15
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• 2020

In 2012, Sulaiman [7] proved integral inequalities concerning reverse of Holder's. In this paper two results are given. First one is further improvement of the reverse Hölder inequality. We note that many existing inequalities related to the Hölder inequality can be proved via obtained this inequality in here. The second is further generalization of Sulaiman's integral inequalities concerning reverses of Holder's [7].

• Honam Mathematical Journal
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• v.39 no.1
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• pp.49-59
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• 2017

In this paper, a generalization of the exponential integral is given. As a consequence, several inequalities involving the generalized function are derived. Among other analytical techniques, the procedure utilizes the $H{\ddot{o}}lder^{\prime}s$ and Minkowskis inequalities for integrals.

• East Asian mathematical journal
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• v.19 no.1
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• pp.27-39
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• 2003

Integral inequalities of Gruss type obtained via $P\acute{o}lya-Szeg\ddot{o}$ and Shisha-Mond results are given. Some applications for Taylor's generalized expansion are also provided.

• Korean Journal of Mathematics
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• v.27 no.2
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• pp.357-374
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• 2019

In this paper, first we obtain some inequalities of Hadamard type for (h - m)-convex functions via Caputo k-fractional derivatives. Secondly, two integral identities including the (n + 1) and (n+ 2) order derivatives of a given function via Caputo k-fractional derivatives have been established. Using these identities estimations of Hadamard type integral inequalities for the Caputo k-fractional derivatives have been proved.

• Communications of the Korean Mathematical Society
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• v.34 no.4
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• pp.1163-1173
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• 2019

In this article, we deduced some new inequalities related to hyper-Bessel function. By using these inequalities we will find some sufficient conditions under which certain families of integral operators are convex in the open unit disc. Some applications related to these results are also the part of our investigation.

• Nonlinear Functional Analysis and Applications
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• v.26 no.2
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• pp.393-409
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• 2021

Three common fixed point theorems for weakly compatible mappings satisfying three classes of contractive inequalities of integral type are proved. Three examples are included. The results obtained in this paper extend and improve a few results existing in literature.