scholarly journals On Aczel's inequality for real numbers

2001 ◽  
Vol 32 (2) ◽  
pp. 137-142
Author(s):  
S. S. Dragomir ◽  
Y. J. Cho
Keyword(s):  
Real Numbers ◽  
Aczél’S Inequality ◽  
New Inequalities

In this note, we point out some new inequalities of Aczel's type for real numbers.

scholarly journals On New Inequalities of Simpson’s Type for Functions Whose Second Derivatives Absolute Values are Convex

2013 ◽  
Vol 9 (1) ◽  
pp. 37-45 ◽  
Author(s):  
Mehmet Zeki Sarikaya ◽  
Erhan. Set ◽  
M. Emin Ozdemir
Keyword(s):  
Real Numbers ◽  
Special Means ◽  
Second Derivatives ◽  
New Inequalities

Abstract In this note, we obtain new some inequalities of Simpson’s type based on convexity. Some applications for special means of real numbers are also given.

scholarly journals Fractional Ostrowski type inequalities for differentiable harmonically convex functions

2021 ◽  
Vol 7 (3) ◽  
pp. 3939-3958
Author(s):  
Thanin Sitthiwirattham ◽  
◽  
Muhammad Aamir Ali ◽  
Hüseyin Budak ◽  
Sotiris K. Ntouyas ◽  
...  
Keyword(s):  
Convex Functions ◽  
Fractional Integrals ◽  
Real Numbers ◽  
Special Means ◽  
Special Cases ◽  
Harmonically Convex Functions ◽  
New Inequalities

<abstract><p>In this paper, we prove some new Ostrowski type inequalities for differentiable harmonically convex functions using generalized fractional integrals. Since we are using generalized fractional integrals to establish these inequalities, therefore we obtain some new inequalities of Ostrowski type for Riemann-Liouville fractional integrals and $ k $-Riemann-Liouville fractional integrals in special cases. Finally, we give some applications to special means of real numbers for newly established inequalities.</p></abstract>

scholarly journals More on Inequalities for Weaving Frames in Hilbert Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 141 ◽  
Author(s):  
Zhong-Qi Xiang
Keyword(s):  
Hilbert Spaces ◽  
Operator Theory ◽  
Triangle Inequality ◽  
Bounded Operator ◽  
Point Of View ◽  
Real Numbers ◽  
Linear Bounded Operator ◽  
Bessel Sequences ◽  
New Inequalities

In this paper, we present several new inequalities for weaving frames in Hilbert spaces from the point of view of operator theory, which are related to a linear bounded operator induced by three Bessel sequences and a scalar in the set of real numbers. It is indicated that our results are more general and cover the corresponding results recently obtained by Li and Leng. We also give a triangle inequality for weaving frames in Hilbert spaces, which is structurally different from previous ones.

Some refined Young type inequalities using different weights

2021 ◽  
Author(s):  
Leila Nasiri ◽  
Bahman Askari
Keyword(s):  
Type Inequality ◽  
Matrix Inequalities ◽  
Real Numbers ◽  
Positive Real ◽  
Unitarily Invariant Norms ◽  
New Inequalities

The Young type inequality asserts that if [Formula: see text] are two positive real numbers, then for each [Formula: see text], we have [Formula: see text] In this paper, we obtain some new inequalities using two different weights. For example, if [Formula: see text], then [Formula: see text] [Formula: see text] where [Formula: see text] In addition, we refine some matrix inequalities for Unitarily invariant norms by applying the deduced numerical inequalities.

scholarly journals On new inequalities of Simpson's type for quasi-convex functions with applications.

2012 ◽  
Vol 43 (3) ◽  
pp. 357-364 ◽  
Author(s):  
Erhan Set ◽  
M.Emin Özdemir ◽  
Mehmet Zeki Sarıkaya
Keyword(s):  
Convex Functions ◽  
Real Numbers ◽  
Special Means ◽  
New Inequalities

In this paper, we introduce some inequalities of Simpson's type based on quasi-convexity.Some applications for special means of real numbers are also given.

scholarly journals Some Improvements of the Cauchy-Schwarz Inequality Using the Tapia Semi-Inner-Product

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2112
Author(s):  
Nicuşor Minculete ◽  
Hamid Reza Moradi
Keyword(s):  
Hilbert Space ◽  
Normed Space ◽  
Triangle Inequality ◽  
Schwarz Inequality ◽  
Inner Product ◽  
Numerical Radius ◽  
Real Numbers ◽  
Norm Inequalities ◽  
Hilbert Space Operators ◽  
New Inequalities

The aim of this article is to establish several estimates of the triangle inequality in a normed space over the field of real numbers. We obtain some improvements of the Cauchy–Schwarz inequality, which is improved by using the Tapia semi-inner-product. Finally, we obtain some new inequalities for the numerical radius and norm inequalities for Hilbert space operators.

scholarly journals Some New Inequalities on Generalization of Hermite-Hadamard and Bullen Type Inequalities, Applications to Trapezoidal and Midpoint Formula

2021 ◽  
Vol 45 (4) ◽  
pp. 647-657
Author(s):  
İMDAT İŞCAN ◽  
◽  
TEKİN TOPLU ◽  
FATİH YETGİN ◽  
◽  
...  
Keyword(s):  
Error Estimates ◽  
Real Numbers ◽  
Absolute Value ◽  
General Identity ◽  
Differentiable Functions ◽  
Special Means ◽  
New Inequalities

In this paper, we give a new general identity for differentiable functions. A consequence of the identity is that we obtain some new general inequalities containing all of the Hermite-Hadamard and Bullen type for functions whose derivatives in absolute value at certain power are convex. Some applications to special means of real numbers are also given. Finally, some error estimates for the trapezoidal and midpoint formula are addressed.

scholarly journals NEW INEQUALITIES OF WIRTINGER TYPE FOR CONVEX AND MN-CONVEX FUNCTIONS

2019 ◽  
pp. 165
Author(s):  
Tatjana Z. Mirkovic
Keyword(s):  
Convex Functions ◽  
Real Numbers ◽  
Positive Real ◽  
Special Means ◽  
New Inequalities

In this paper, we obtain some inequalities of Wirtinger type by using some classical inequalities and means for convex functions and establish some applications to special means for positive real numbers.

scholarly journals New fractional inequalities of midpoint type via s-convexity and their application

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Ohud Almutairi ◽  
Adem Kılıçman
Keyword(s):  
Error Estimates ◽  
Integral Inequalities ◽  
Real Numbers ◽  
Special Means ◽  
Second Derivatives ◽  
The Absolute ◽  
New Inequalities

Abstract In this study, we introduced new integral inequalities of Hermite–Hadamard type via s-convexity and studied their properties. The absolute form of the first and second derivatives for the new inequalities is considered to be s-convex. As an application, the inequalities were applied to the special means of real numbers. We give the error estimates for the midpoint formula.

scholarly journals New Inequalities of Fejer´ and Hermite-Hadamard type Concerning Convex and QuasiConvex Functions With Applications

2021 ◽  
pp. 83-99
Author(s):  
Muhammad Amer Latif ◽  
Sever Silvestru Dragomir ◽  
Sofian Obeidat
Keyword(s):  
Convex Functions ◽  
Integral Inequalities ◽  
Quasiconvex Functions ◽  
Real Numbers ◽  
Positive Real ◽  
Special Means ◽  
New Inequalities

This research contains new integral inequalities of Fejer and ´ Hermite-Hadamard type involving convex and quasi-convex functions. Applications of the newly established results for special means of positive real numbers are given.

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