• 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.

• Nonlinear Functional Analysis and Applications
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• v.29 no.1
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• pp.275-293
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• 2024

In this paper, we obtain integral analogues of inequalities concerning polynomials proved by Soraisam et al. [33]. The results improve other known inequalities as well.

• The Pure and Applied Mathematics
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• v.19 no.3
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• pp.305-313
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• 2012

In this note we study Nesbitt's Inequality and modify it to make several inequalities. We prove some inequalities by using power series and Cauchy-Schwarz Inequality.

• The Pure and Applied Mathematics
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• v.26 no.3
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• pp.189-197
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• 2019

In this paper we obtain some new inequalities for the weighted chaotically geometric mean of two positive operators on a complex Hilbert space.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.239-251
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• 2019

In this paper we introduce a new formulation of symmetric homogeneous bivariate means that depends on the variation of a given continuous strictly increasing function on (0, ${\infty}$). It turns out that this class of means includes a lot of known bivariate means among them the arithmetic mean, the harmonic mean, the geometric mean, the logarithmic mean as well as the first and second Seiffert means. Using this new formulation we introduce a lot of new bivariate means and derive some mean-inequalities.

• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.325-338
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• 2023

In this paper, we derive a Reilly-type inequality for the Laplacian with density on weighted manifolds with boundary. As its applications, we obtain some new Poincaré-type inequalities not only on weighted manifolds, but more interestingly, also on their boundary. Furthermore, some mean-curvature type inequalities on the boundary are also given.

• Korean Journal of Mathematics
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• v.29 no.2
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• pp.227-237
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• 2021

Opial inequality and its consequences are useful in establishing existence and uniqueness of solutions of initial and boundary value problems for differential and difference equations. In this paper we analyze Opial-type inequalities for convex functions. We have studied different versions of these inequalities for a generalized integral operator. Further difference of Opial-type inequalities are utilized to obtain generalized mean value theorems, which further produce various interesting derivations for fractional and conformable integral operators.

• Korean Journal of Mathematics
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• v.32 no.2
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• pp.349-364
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• 2024

We propose a new method of investigation of an integral equality associated with tempered fractional integrals. In addition to this, several Newton-type inequalities are considered for differentiable convex functions by taking the modulus of the newly established identity. Moreover, we establish some Newton-type inequalities with the help of Hölder and power-mean inequality. Furthermore, several new results are presented by using special choices of obtained inequalities.

• Honam Mathematical Journal
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• v.42 no.2
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• pp.301-318
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• 2020

In this paper, we introduce and study the concept of hyperbolic type convexity functions and their some algebraic properties. We obtain Hermite-Hadamard type inequalities for this class of functions. In addition, we obtain some refinements of the Hermite-Hadamard inequality for functions whose first derivative in absolute value, raised to a certain power which is greater than one, respectively at least one, is hyperbolic convexity. Moreover, we compare the results obtained with both Hölder, Hölder-İşcan inequalities and power-mean, improved-power-mean integral inequalities.

• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1123-1132
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• 2020

In the present paper, we define new class of functions T_α,β(λ; z) which is an extension of the classical Wright function and the Mittag-Leffler function. We show some mean value inequalities for the this function, such as Turán-type inequalities, Lazarević-type inequalities and Wilker-type inequalities. Moreover, integrals formula and integral inequality for the function T_α,β(λ; z) are presented.