scholarly journals Some perturbed inequalities of Ostrowski type for twice differentiable functions

Mathematica ◽  
2021 ◽  
Vol 63 (86) (2) ◽  
pp. 232-242
Author(s):  
Samet Erden ◽  
◽  
Hüseyin Budak ◽  
Mehmet Zeki Sarikaya ◽  
◽  
...  
Keyword(s):  
Bounded Variation ◽  
Integral Inequalities ◽  
Absolutely Continuous ◽  
Differentiable Functions ◽  
Continuous Mappings ◽  
Second Derivatives

We establish new perturbed Ostrowski type inequalities for functions whose second derivatives are of bounded variation. In addition, we obtain some integral inequalities for absolutely continuous mappings. Finally, some inequalities related to Lipschitzian derivatives are given.

Some new generalizations for GA-convex functions

Filomat ◽  
2017 ◽  
Vol 31 (4) ◽  
pp. 1009-1016 ◽  
Author(s):  
Ahmet Akdemir ◽  
Özdemir Emin ◽  
Ardıç Avcı ◽  
Abdullatif Yalçın
Keyword(s):  
Convex Functions ◽  
Integral Identity ◽  
Integral Inequalities ◽  
General Integral ◽  
Second Derivatives ◽  
Derivatives Of

In this paper, firstly we prove an integral identity that one can derive several new equalities for special selections of n from this identity: Secondly, we established more general integral inequalities for functions whose second derivatives of absolute values are GA-convex functions based on this equality.

The Factorisation of the rectangular distribution

1967 ◽  
Vol 4 (3) ◽  
pp. 529-542 ◽  
Author(s):  
T. Lewis
Keyword(s):  
Bounded Variation ◽  
Distribution Functions ◽  
Absolutely Continuous ◽  
Rectangular Distribution ◽  
Factor Type

Questions of the decomposability of distribution functions into real-valued components of bounded variation were discussed by P. Lévy (1964) in relation to the nature of the components, whether non-decreasing (distribution functions in particular) or absolutely continuous (a.c.) or both. Hanson (1965), in a review of Lévy's paper, raised the question of whether or not a rectangular distribution could be decomposed into two a.c. distributions. In fact, D. G. Kendall had conjectured earlier (Kendall (1960)) that no such decomposition is possible. The object of this paper is to state and prove the truth of Kendall's conjecture. “Decomposition” or “factorisation” will be understood throughout the paper to mean decomposition into distributions. Decompositions of the rectangular distribution into one a.c. and one discrete factor are well known (see, e.g., Lukacs (1960) pp. 128–9), and decompositions in which both factors are singular continuous (s.c.) have been discovered by Kendall and by P. M. Lee; it is shown here that no other combinations of factor-type can exist. References to other work on related decomposability properties are given in the papers by Lévy and Kendall cited above.

scholarly journals Sharp integral inequalities based on general Euler two-point formulae

2005 ◽  
Vol 46 (4) ◽  
pp. 555-574 ◽  
Author(s):  
J. Pečarić ◽  
I. Perić ◽  
A. Vukelić
Keyword(s):  
Bounded Variation ◽  
Integral Inequalities ◽  
Functions Of Bounded Variation ◽  
Quadrature Formulae ◽  
Lipschitzian Functions ◽  
Integrable Functions

AbstractWe consider a family of two-point quadrature formulae, using some Euler-type identities. A number of inequalities, for functions whose derivatives are either functions of bounded variation, Lipschitzian functions or R-integrable functions, are proved.

scholarly journals Equilibrium states for piecewise monotonic transformations

1982 ◽  
Vol 2 (1) ◽  
pp. 23-43 ◽  
Author(s):  
Franz Hofbauer ◽  
Gerhard Keller
Keyword(s):  
Periodic Orbits ◽  
Bounded Variation ◽  
Critical Points ◽  
Equilibrium States ◽  
Absolutely Continuous ◽  
Specification Property ◽  
Ergodic Properties ◽  
Piecewise Monotonic

AbstractWe show that equilibrium states μ of a function φ on ([0,1], T), where T is piecewise monotonic, have strong ergodic properties in the following three cases:(i) sup φ — inf φ <htop(T) and φ is of bounded variation.(ii) φ satisfies a variation condition and T has a local specification property.(iii) φ = —log |T′|, which gives an absolutely continuous μ, T is C2, the orbits of the critical points of T are finite, and all periodic orbits of T are uniformly repelling.

scholarly journals The Nemitskij operator on Lipk-type and BVk-type spaces

2013 ◽  
Vol 46 (3) ◽  
Author(s):  
José Giménez ◽  
Lorena López ◽  
N. Merentes
Keyword(s):  
Bounded Variation ◽  
Continuous Functions ◽  
Function Spaces ◽  
Compact Interval ◽  
Absolutely Continuous Functions ◽  
Absolutely Continuous ◽  
Type Spaces

AbstractIn this paper, we discuss and present various results about acting and boundedness conditions of the autonomous Nemitskij operator on certain function spaces related to the space of all real valued Lipschitz (of bounded variation, absolutely continuous) functions defined on a compact interval of ℝ. We obtain a result concerning the integrability of products of the form

Differentiable functions on algebras and the equation grad (w) = M grad (v)

1992 ◽  
Vol 122 (3-4) ◽  
pp. 353-361 ◽  
Author(s):  
William C. Waterhouse
Keyword(s):  
Second Order ◽  
Frobenius Algebra ◽  
Constant Matrix ◽  
Second Order Differential Equations ◽  
Differentiable Functions ◽  
Open Set ◽  
Finite Dimensional ◽  
Taylor Expansions ◽  
Second Derivatives ◽  
Real Algebra

SynopsisLet U be a convex open set in a finite-dimensional commutative real algebra A. Consider A-differentiable functions f: U → A. When they are C2 as functions of their real variables, their A-derivatives are again A-differentiable, and they have second-order Taylor expansions. The real components of such functions then have second derivatives for which the A-multiplications are self-adjoint. When A is a Frobenius algebra, that condition (a system of second-order differential equations) actually forces a real function on U to be a component of some such f. If v is a function of n real variables, and M is a constant matrix, then the requirement that M∇(u) should equal ∇(w) for some w usually falls into this setting for a suitable A, and the quite special properties of such v, w can be deduced from known properties of A-differentiable functions.

DEFINITION AND CLASSIFICATION OF ONE-DIMENSIONAL CONTINUOUS FUNCTIONS WITH UNBOUNDED VARIATION

Fractals ◽  
2017 ◽  
Vol 25 (05) ◽  
pp. 1750048 ◽  
Author(s):  
Y. S. LIANG
Keyword(s):  
Fractal Dimension ◽  
Bounded Variation ◽  
Continuous Functions ◽  
Functions Of Bounded Variation ◽  
One Dimensional ◽  
Nondifferentiable Functions ◽  
Differentiable Functions ◽  
Closed Intervals ◽  
Bounded Variation Functions

The present paper mainly investigates the definition and classification of one-dimensional continuous functions on closed intervals. Continuous functions can be classified as differentiable functions and nondifferentiable functions. All differentiable functions are of bounded variation. Nondifferentiable functions are composed of bounded variation functions and unbounded variation functions. Fractal dimension of all bounded variation continuous functions is 1. One-dimensional unbounded variation continuous functions may have finite unbounded variation points or infinite unbounded variation points. Number of unbounded variation points of one-dimensional unbounded variation continuous functions maybe infinite and countable or uncountable. Certain examples of different one-dimensional continuous functions have been given in this paper. Thus, one-dimensional continuous functions are composed of differentiable functions, nondifferentiable continuous functions of bounded variation, continuous functions with finite unbounded variation points, continuous functions with infinite but countable unbounded variation points and continuous functions with uncountable unbounded variation points. In the end of the paper, we give an example of one-dimensional continuous function which is of unbounded variation everywhere.

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