Mutual bounds for Jensen-type operator inequalities related to higher order convexity

2019 ◽  
Vol 93 (6) ◽  
pp. 1159-1176
Author(s):  
Mario Krnić ◽  
Rozarija Mikić ◽  
Josip Pečarić
Keyword(s):  
Higher Order ◽  
Type Operator ◽  
Operator Inequalities ◽  
Higher Order Convexity

scholarly journals Pointwise estimates for higher order convexity preserving polynomial approximation

1994 ◽  
Vol 36 (2) ◽  
pp. 213-233 ◽  
Author(s):  
Jia-Ding Cao ◽  
Heinz H. Gonska
Keyword(s):  
Polynomial Approximation ◽  
Convex Functions ◽  
Higher Order ◽  
Second Order ◽  
Convolution Type ◽  
Shape Preservation ◽  
Moduli Of Continuity ◽  
Pointwise Estimates ◽  
Higher Order Convexity ◽  
Boolean Sum

AbstractDeVore-Gopengauz-type operators have attracted some interest over the recent years. Here we investigate their relationship to shape preservation. We construct certain positive convolution-type operators Hn, s, j which leave the cones of j-convex functions invariant and give Timan-type inequalities for these. We also consider Boolean sum modifications of the operators Hn, s, j show that they basically have the same shape preservation behavior while interpolating at the endpoints of [−1, 1], and also satisfy Telyakovskiῐ- and DeVore-Gopengauz-type inequalities involving the first and second order moduli of continuity, respectively. Our results thus generalize related results by Lorentz and Zeller, Shvedov, Beatson, DeVore, Yu and Leviatan.

scholarly journals The higher order commutators of the fractional integrals on Hardy spaces

2005 ◽  
Vol 79 (1) ◽  
pp. 11-24
Author(s):  
Shunchao Long ◽  
Jian Wang
Keyword(s):  
Hardy Spaces ◽  
Fractional Integral ◽  
Higher Order ◽  
Type Operator ◽  
Fractional Integrals ◽  
Integral Type ◽  
Bmo Function

AbstractIn this paper we investigate the boundedness on Hardy spaces for the higher order commutator Tb, m generated by the BMO function b and fractional integral type operator Tτ, and establish the boundness theorems for Tτb, m from Hp1.q1.sb, m to Lp2 and to Hp2 (0 < p1 ≤ 1), and from H Ka. p1.sq1, b, m to Ka.p2q2 and to H Ka. p2q2, respectively, for certain ranges of α, p1, q1, p2, q2 and s.

scholarly journals On duality theory for multiobjective semi-infinite fractional optimization model using higher order convexity.

2021 ◽  
Author(s):  
Tamanna Yadav ◽  
S. K. Gupta
Keyword(s):  
Optimization Model ◽  
Higher Order ◽  
Support Functions ◽  
Duality Results ◽  
Fractional Optimization ◽  
Different Types ◽  
Convexity Assumptions ◽  
Higher Order Equation ◽  
Higher Order Convexity ◽  
Dual Models

In the article, a semi-infinite fractional optimization model having multiple objectives is first formulated. Due to the presence of support functions in each numerator and denominator with constraints, the model so constructed is also non-smooth. Further, three different types of dual models viz Mond -Weir, Wolfe  and  Schaible  are presented and then usual duality results are proved using higher-order [[EQUATION]]   convexity assumptions. To show the existence of such generalized convex  functions, a nontrivial example has also been exemplified. Moreover, numerical examples have been  illustrated at suitable places to justify various results presented in the paper. The formulation and duality results discussed also generalize the well known results appeared in the literature.

scholarly journals Kantorovich type operator inequalities via the Specht ratio

2004 ◽  
Vol 377 ◽  
pp. 69-81 ◽  
Author(s):  
Jun Ichi Fujii ◽  
Yuki Seo ◽  
Masaru Tominaga
Keyword(s):  
Type Operator ◽  
Operator Inequalities

Reverse Jensen-Mercer Type Operator Inequalities

2016 ◽  
Vol 31 ◽  
pp. 87-99 ◽  
Author(s):  
Ehsan Anjidani ◽  
Mohammad Reza Changalvaiy
Keyword(s):  
Hilbert Space ◽  
Selfadjoint Operator ◽  
Type Operator ◽  
Operator Inequalities ◽  
Linear Map ◽  
Positive Linear Map

Let $A$ be a selfadjoint operator on a Hilbert space $\mathcal{H}$ with spectrum in an interval $[a,b]$ and $\phi:B(\mathcal{H})\rightarrow B(\mathcal{K})$ be a unital positive linear map, where $\mathcal{K}$ is also a Hilbert space. Let $m,M\in J$ with $m

Characterization of chaotic order and its applications to furuta's type operator inequalities

1998 ◽  
Vol 43 (4) ◽  
pp. 339-349 ◽  
Author(s):  
Masatoshi Fujii ◽  
Jian Fei Jiang ◽  
Eizaburo Kamei
Keyword(s):  
Type Operator ◽  
Operator Inequalities
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