The Study Higher-order Wolfe-type Non-differentiable Multiple Objective Symmetric Duality Involving Generalized Convex Functions

2021 ◽  
Vol 2 (4) ◽  
Author(s):  
Arun Kumar Tripathy
Keyword(s):  
Convex Functions ◽  
Higher Order ◽  
Multiple Objective ◽  
Symmetric Duality ◽  
Generalized Convex Functions

Characterizations of Higher Order Strongly Generalized Convex Functions

2021 ◽  
pp. 341-364
Author(s):  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor ◽  
Michael Th. Rassias
Keyword(s):  
Convex Functions ◽  
Higher Order ◽  
Generalized Convex Functions

scholarly journals A note on generalized convex functions

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Syed Zaheer Ullah ◽  
Muhammad Adil Khan ◽  
Yu-Ming Chu
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Type Inequality ◽  
Generalized Convex Functions

Abstract In the article, we provide an example for a η-convex function defined on rectangle is not convex, prove that every η-convex function defined on rectangle is coordinate η-convex and its converse is not true in general, define the coordinate $(\eta _{1}, \eta _{2})$(η1,η2)-convex function and establish its Hermite–Hadamard type inequality.

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 Simpson type inequalities and applications

2021 ◽  
Author(s):  
Muhammad Uzair Awan ◽  
Muhammad Zakria Javed ◽  
Michael Th. Rassias ◽  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor
Keyword(s):  
Quadrature Formula ◽  
Convex Functions ◽  
Integral Identity ◽  
Higher Order ◽  
Auxiliary Result ◽  
First Order ◽  
New Class ◽  
Differentiable Functions

AbstractA new generalized integral identity involving first order differentiable functions is obtained. Using this identity as an auxiliary result, we then obtain some new refinements of Simpson type inequalities using a new class called as strongly (s, m)-convex functions of higher order of $$\sigma >0$$ σ > 0 . We also discuss some interesting applications of the obtained results in the theory of means. In last we present applications of the obtained results in obtaining Simpson-like quadrature formula.

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