• 호남수학학술지
• /
• 제44권2호
• /
• pp.244-258
• /
• 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
• /
• 제29권1호
• /
• pp.275-293
• /
• 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.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제19권3호
• /
• pp.305-313
• /
• 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.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제26권3호
• /
• pp.189-197
• /
• 2019

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

• 대한수학회논문집
• /
• 제34권1호
• /
• pp.239-251
• /
• 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.

• 대한수학회보
• /
• 제60권2호
• /
• pp.325-338
• /
• 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
• /
• 제29권2호
• /
• pp.227-237
• /
• 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.

• 호남수학학술지
• /
• 제42권2호
• /
• pp.301-318
• /
• 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.

• 대한수학회논문집
• /
• 제35권4호
• /
• pp.1123-1132
• /
• 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.

• 대한수학회보
• /
• 제45권4호
• /
• pp.763-780
• /
• 2008

An Ostrowski type inequality is developed for estimating the deviation of the integral mean of an absolutely continuous function, and the linear combination of its values at k + 1 partition points, on a segment of (real) linear spaces. Several particular cases are provided which recapture some earlier results, along with the results for trapezoidal type inequalities and the classical Ostrowski inequality. Some inequalities are obtained by applying these results for semi-inner products; and some of these inequalities are proven to be sharp.