scholarly journals Norm inequalities for the difference between weighted and integral means of operator differentiable functions

2020 ◽  
pp. 183-197
Author(s):  
Silvestru Sever Dragomir
Keyword(s):  
Integral Means ◽  
Norm Inequalities ◽  
Differentiable Functions ◽  
The Difference

scholarly journals General Norm Inequalities of Trapezoid Type for Fréchet Differentiable Functions in Banach Spaces

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1288
Author(s):  
Silvestru Sever Dragomir
Keyword(s):  
Banach Spaces ◽  
Error Bounds ◽  
Norm Inequalities ◽  
Differentiable Functions ◽  
Fréchet Differentiable ◽  
General Norm

In this paper we establish some error bounds in approximating the integral by general trapezoid type rules for Fréchet differentiable functions with values in Banach spaces.

scholarly journals A Hopf-type Boundary Point Lemma for Pairs of Solutions to Quasilinear Equations

2019 ◽  
Vol 62 (3) ◽  
pp. 607-621 ◽  
Author(s):  
Leobardo Rosales
Keyword(s):  
Weak Solutions ◽  
Boundary Point ◽  
Quasilinear Equation ◽  
Divergence Form ◽  
Quasilinear Equations ◽  
Differentiable Functions ◽  
The Difference ◽  
Type Boundary

AbstractWe present a Hopf boundary point lemma for the difference between two Hölder continuously differentiable functions, each weak solutions to a divergence-form quasilinear equation, under mild boundedness assumptions on the coefficients of this equation.

ON AN INEQUALITY FOR DIVIDED DIFFERENCES

2008 ◽  
Vol 01 (01) ◽  
pp. 113-120 ◽  
Author(s):  
J. Pečarić ◽  
M. Rodić Lipanović
Keyword(s):  
Divided Differences ◽  
Integral Means ◽  
The Difference

The main purpose of this paper is to give the generalization and improvement of the result given in [2] on the inequality of the difference of two integral means which can also be represented as the difference of two divided differences.

SOME RESULTS ON COMPARING TWO INTEGRAL MEANS FOR ABSOLUTELY CONTINUOUS FUNCTIONS AND APPLICATIONS

2014 ◽  
Vol 90 (2) ◽  
pp. 264-274
Author(s):  
DAH-YAN HWANG ◽  
SILVESTRU SEVER DRAGOMIR
Keyword(s):  
Probability Density ◽  
Continuous Functions ◽  
Probability Density Functions ◽  
Density Functions ◽  
Absolutely Continuous Functions ◽  
Integral Means ◽  
Absolutely Continuous ◽  
Special Means ◽  
The Difference

AbstractSome better estimates for the difference between the integral mean of a function and its mean over a subinterval are established. Various applications for special means and probability density functions are also given.

scholarly journals On some Ostrowski type inequalities via Montgomery identity and Taylor's formula

2005 ◽  
Vol 36 (3) ◽  
pp. 199-218 ◽  
Author(s):  
A. Aglic Aljinovic ◽  
J. Pecaric
Keyword(s):  
Integral Means ◽  
Montgomery Identity ◽  
Taylor’S Formula ◽  
The Difference ◽  
Taylor's Formula

A new extension of the weighted Montgomery identity is given, by using Taylor's formula, and used to obtain some Ostrowski type inequalities and the estimations of the difference of two integral means.

Some Applications of Fractional Velocities

2016 ◽  
Vol 19 (1) ◽  
Author(s):  
Dimiter Prodanov
Keyword(s):  
Fractional Power ◽  
Leibniz Rule ◽  
Difference Quotient ◽  
Singular Behavior ◽  
Hölder Functions ◽  
Integer Order ◽  
Differentiable Functions ◽  
The Difference ◽  
Product Rules ◽  
Derivatives Of

AbstractFractional velocity is defined as the limit of the difference quotient of the increments of a function and its argument raised to a fractional power. The fractional velocity can be suitable for characterizing singular behavior of derivatives of Hölderian functions and non differentiable functions. Relations to integer-order derivatives and other integral-based definitions are discussed.It is demonstrated that for Hölder functions under certain conditions the product rules deviates from the Leibniz rule. This deviation is expressed by another quantity, fractional co-variation.

scholarly journals On some Ostrowski type inequalities via Montgomery identity and Taylor's formula II

2005 ◽  
Vol 36 (4) ◽  
pp. 279-301 ◽  
Author(s):  
A. Aglic Aljinovic ◽  
J. Pecaric ◽  
A. Vukelic
Keyword(s):  
Integral Means ◽  
Montgomery Identity ◽  
Taylor’S Formula ◽  
The Difference ◽  
Taylor's Formula

A new extension of the weighted Montgomery identity is given, by using Taylor's formula and used to obtain some Ostrowski type inequalities and estimations of the difference of two integral means.

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