scholarly journals Some new quantum Trapezoid and quantum Midpoint type inequalities for preinvex functions

2020 ◽  
Author(s):  
Muhammad Aamir Ali ◽  
Hüseyin BUDAK
Keyword(s):  
Correct Version ◽  
Preinvex Functions

In this article, we derive Hermite-Hadamard inequalities for preinvex functions using the quantum integrals and show their validation with mathematical examples. We prove midpoint and trapezoidal inequalities for q^{ϰ₂}-differentiable preinvex functions via q^{ϰ₂}-quantum integrals. Moreover, we show with an example that the already proved inequality of Hermite-Hadamard type for preinvex functions via q_{ϰ₁}-quantum integrals is not valid for preinvex functions and we give its correct version. We prove the midpoint inequalities for q_{ϰ₁}-differentiable preinvex functions via q_{ϰ₁}-quantum integrals. It is also shown that the newly proved results transformed into some known results by considering the limit q→1⁻ and η(ϰ₂,ϰ₁)=-η(ϰ₁,ϰ₂)=ϰ₂-ϰ₁ in the newly derived results.

Big Heads title page

2019 ◽  
Author(s):  
vernon thornton
Keyword(s):  
Title Page ◽  
Language Of Thought ◽  
Correct Version ◽  
Evolutionary Context ◽  
The Mind ◽  
The Brain

A description of of the mind and its relationship to the brain, set in an evolutionary context. Introduction of a correct version of 'language-of-thought' called 'thinkish'.

Impact of sewage sludge applications on the biogeochemistry of soils

2008 ◽  
Vol 57 (6) ◽  
pp. 963-963
Author(s):  
D. Devaney ◽  
A. R. Godley ◽  
M. E. Hodson ◽  
K. Purdy ◽  
S. Yamulki
Keyword(s):  
Sewage Sludge ◽  
N2o Emissions ◽  
Correct Version ◽  
Main Text

Unfortunately an incorrect version of Figure 4 appears on p517 of this paper; the correct version is as printed below. A sentence (“Increased N2O emissions…. Conversely”) should then also be deleted from the corresponding paragraph of the main text as printed on pp516–517; the correct version of this paragraph is also given below. The authors and publisher regret any confusion or inconvenience this may have caused.

scholarly journals Erratum to: A new analysis of the MiniBooNE low-energy excess

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
C. Giunti ◽  
A. Ioannisian ◽  
G. Ranucci
Keyword(s):  
Low Energy ◽  
Correct Version ◽  
Energy Excess

After publication we discovered that some entries in table 2 and the corresponding contours in figures 3 and 4 have been misprinted. We provide here the correct version of table 2 and figures 3 and 4. The discussion and conclusions in the text of the paper remain unchanged.

scholarly journals A new q-integral identity and estimation of its bounds involving generalized exponentially μ-preinvex functions

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Muhammad Uzair Awan ◽  
Sadia Talib ◽  
Artion Kashuri ◽  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor ◽  
...  
Keyword(s):  
Differentiable Function ◽  
Integral Identity ◽  
Second Order ◽  
Integral Inequalities ◽  
Absolute Value ◽  
Type Integral ◽  
Preinvex Functions

Abstract In the article, we introduce the generalized exponentially μ-preinvex function, derive a new q-integral identity for second order q-differentiable function, and establish several new q-trapezoidal type integral inequalities for the function whose absolute value of second q-derivative is exponentially μ-preinvex.

An Afrocentric Re-storying of Africa’s Struggle for Emancipation in Ngugi’s Selected Novels

2021 ◽  
Vol 2 (1) ◽  
pp. 117-130
Author(s):  
M. Mogoboya
Keyword(s):  
Research Design ◽  
Textual Analysis ◽  
Primary Data ◽  
Exploratory Research ◽  
Correct Version ◽  
Purposive Sampling ◽  
African Identity ◽  
Dark Continent ◽  
Liberation Struggle

The story of African liberation struggle has, over many years, been related in a colonial and neo-colonial manner by the imperial powers, with Africa delineated as a dark continent and Europe as a civilised one. This article, therefore, strives to disrupt this oppressive narrative by painting the correct version through Ngugi's A Grain of Wheat (1967) (AGW) and Matigari (1987). Kenya is used as a microcosm of the entire Africa in these novels. Furthermore, the study is a qualitative recounting of the African liberation struggle which is underpinned by Afrocentricity as an emancipatory theoretical strand. Purposive sampling, guided by exploratory research design, was employed to select the two texts by Ngugi because of their appositeness to the study. Narrative textual analysis was used to interpret the two novels as primary data. Ngugi conscientises Africans about their African liberation history in order for them to cultivate a true African identity (Biko,1978).

scholarly journals Some Hermite-Hadamard type integral inequalities for operator AG-preinvex functions

2016 ◽  
Vol 8 (2) ◽  
pp. 312-323
Author(s):  
Ali Taghavi ◽  
Haji Mohammad Nazari ◽  
Vahid Darvish
Keyword(s):  
Integral Inequalities ◽  
Unitarily Invariant Norm ◽  
Norm Inequalities ◽  
Invariant Norm ◽  
Type Integral ◽  
Preinvex Functions ◽  
Inequalities For Operators

Abstract In this paper, we introduce the concept of operator AG-preinvex functions and prove some Hermite-Hadamard type inequalities for these functions. As application, we obtain some unitarily invariant norm inequalities for operators.

scholarly journals Constructing a pseudo-free family of finite computational groups under the general integer factoring intractability assumption

2019 ◽  
Vol 11 (2) ◽  
pp. 133-134
Author(s):  
Mikhail Anokhin
Keyword(s):  
Correct Version

Abstract We provide a correct version of Remark 3.5 of the paper mentioned in the title. Also, we fix a typo in Remark 4.4 of that paper.

scholarly journals New Integral Inequalities via Generalized Preinvex Functions

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 296
Author(s):  
Muhammad Tariq ◽  
Asif Ali Shaikh ◽  
Soubhagya Kumar Sahoo ◽  
Hijaz Ahmad ◽  
Thanin Sitthiwirattham ◽  
...  
Keyword(s):  
Integral Inequality ◽  
Type Inequality ◽  
Integral Inequalities ◽  
Power Mean ◽  
Science And Engineering ◽  
Special Means ◽  
Algebraic Properties ◽  
Convexity Theory ◽  
Hölder’S Integral Inequality ◽  
Preinvex Functions

The theory of convexity plays an important role in various branches of science and engineering. The objective of this paper is to introduce a new notion of preinvex functions by unifying the n-polynomial preinvex function with the s-type m–preinvex function and to present inequalities of the Hermite–Hadamard type in the setting of the generalized s-type m–preinvex function. First, we give the definition and then investigate some of its algebraic properties and examples. We also present some refinements of the Hermite–Hadamard-type inequality using Hölder’s integral inequality, the improved power-mean integral inequality, and the Hölder-İşcan integral inequality. Finally, some results for special means are deduced. The results established in this paper can be considered as the generalization of many published results of inequalities and convexity theory.

scholarly journals Fractional trapezium type inequalities for twice differentiable preinvex functions and their applications

2020 ◽  
Vol 10 (2) ◽  
pp. 226-236
Author(s):  
Artion Kashuri ◽  
Rozana Liko
Keyword(s):  
Integral Operator ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Recent Past ◽  
Trapezium Type ◽  
Special Means ◽  
Special Cases ◽  
Type Integral ◽  
Preinvex Functions ◽  
Almost All

Trapezoidal inequalities for functions of divers natures are useful in numerical computations. The authors have proved an identity for a generalized integral operator via twice differentiable preinvex function. By applying the established identity, the generalized trapezoidal type integral inequalities have been discovered. It is pointed out that the results of this research provide integral inequalities for almost all fractional integrals discovered in recent past decades. Various special cases have been identified. Some applications of presented results to special means have been analyzed. The ideas and techniques of this paper may stimulate further research.

scholarly journals SOME PROPERTIES OF EXPONENTIALLY PREINVEX FUNCTIONS

2019 ◽  
pp. 941
Author(s):  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor
Keyword(s):  
Optimality Conditions ◽  
Convex Functions ◽  
New Concepts ◽  
Preinvex Functions

In this paper, we introduce some new concepts of the exponentially preinvex functions. We investigate several properties of the exponentially preinvex functions and discuss their relations with convex functions. Optimality conditions are characterized by a class of variational-like inequalities. Several interesting results characterizing the exponentially preinvex functions are obtained. Results obtained in this paper can be viewed as significant improvement of previously known results.

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