Some Integral Inequalities for the Quadratic Functions of Bounded Variations and Application

Learning quadratic functions that had been performed by the majority of vocational school and high school mathematics teacher in Kuala Tungkal is still using conventional learning media. The use of conventional learning media is experiencing a lot of obstacles, such as: a fairly long time in describing the graph function, especially when analyzing some quadratic function graphs with various characteristics. APOS is one of the constructivist learning theory which states that students learn through several stages, namely: action – process – object – schema. And to integrate into media APOS writer adapting ADDIE development model. The effectiveness of the use of media-based learning theory APOS seen from the student activity sheet can be concluded more increased activity of students in the learning process. Study of the test results, students were able to meet the completeness criteria stipulated minimum is 75. With an average value of learning outcomes, namely 87.14. It can be seen from the students' responses on a test group of small and large groups where it is concluded that researchers develop learning media can be categorized as good / interesting in the teaching and learning of mathematics.

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Some new generalizations for GA-convex functions

Filomat ◽

10.2298/fil1704009a ◽

2017 ◽

Vol 31 (4) ◽

pp. 1009-1016 ◽

Cited By ~ 2

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.

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A new generalization of some quantum integral inequalities for quantum differentiable convex functions

Advances in Difference Equations ◽

10.1186/s13662-021-03382-0 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Yi-Xia Li ◽

Muhammad Aamir Ali ◽

Hüseyin Budak ◽

Mujahid Abbas ◽

Yu-Ming Chu

Keyword(s):

Integral Inequality ◽

Convex Functions ◽

Integral Identity ◽

Integral Inequalities ◽

Quantum Integral ◽

Special Cases

AbstractIn this paper, we offer a new quantum integral identity, the result is then used to obtain some new estimates of Hermite–Hadamard inequalities for quantum integrals. The results presented in this paper are generalizations of the comparable results in the literature on Hermite–Hadamard inequalities. Several inequalities, such as the midpoint-like integral inequality, the Simpson-like integral inequality, the averaged midpoint–trapezoid-like integral inequality, and the trapezoid-like integral inequality, are obtained as special cases of our main results.

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Eco-Driving for Different Electric Powertrain Topologies Considering Motor Efficiency

World Electric Vehicle Journal ◽

10.3390/wevj12010006 ◽

2021 ◽

Vol 12 (1) ◽

pp. 6

Author(s):

Alexander Koch ◽

Tim Bürchner ◽

Thomas Herrmann ◽

Markus Lienkamp

Keyword(s):

Dynamic Programming ◽

Electric Vehicles ◽

Quadratic Functions ◽

Simultaneous Optimization ◽

Speed Profile ◽

Power Demand ◽

Electric Motors ◽

Car Following ◽

Motor Efficiency ◽

Computationally Expensive

Electrification and automatization may change the environmental impact of vehicles. Current eco-driving approaches for electric vehicles fit the electric power of the motor by quadratic functions and are limited to powertrains with one motor and single-speed transmission or use computationally expensive algorithms. This paper proposes an online nonlinear algorithm, which handles the non-convex power demand of electric motors. Therefore, this algorithm allows the simultaneous optimization of speed profile and powertrain operation for electric vehicles with multiple motors and multiple gears. We compare different powertrain topologies in a free-flow scenario and a car-following scenario. Dynamic Programming validates the proposed algorithm. Optimal speed profiles alter for different powertrain topologies. Powertrains with multiple gears and motors require less energy during eco-driving. Furthermore, the powertrain-dependent correlations between jerk restriction and energy consumption are shown.

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Fractional Integral Inequalities for Exponentially Nonconvex Functions and Their Applications

Fractal and Fractional ◽

10.3390/fractalfract5030080 ◽

2021 ◽

Vol 5 (3) ◽

pp. 80

Author(s):

Hari Mohan Srivastava ◽

Artion Kashuri ◽

Pshtiwan Othman Mohammed ◽

Dumitru Baleanu ◽

Y. S. Hamed

Keyword(s):

Integral Inequalities ◽

Fractional Integrals ◽

Auxiliary Result ◽

Wright Function ◽

Nonconvex Functions ◽

Special Cases ◽

Type Integral ◽

Generic Class ◽

Two Parameters ◽

Class Of Functions

In this paper, the authors define a new generic class of functions involving a certain modified Fox–Wright function. A useful identity using fractional integrals and this modified Fox–Wright function with two parameters is also found. Applying this as an auxiliary result, we establish some Hermite–Hadamard-type integral inequalities by using the above-mentioned class of functions. Some special cases are derived with relevant details. Moreover, in order to show the efficiency of our main results, an application for error estimation is obtained as well.

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On the Locally Polynomial Complexity of the Projection-Gradient Method for Solving Piecewise Quadratic Optimisation Problems

Entropy ◽

10.3390/e23040465 ◽

2021 ◽

Vol 23 (4) ◽

pp. 465

Author(s):

Agnieszka Prusińska ◽

Krzysztof Szkatuła ◽

Alexey Tret’yakov

Keyword(s):

Computational Complexity ◽

Polynomial Complexity ◽

Initial Point ◽

Quadratic Functions ◽

Problem Dimension ◽

Piecewise Quadratic Functions ◽

Large Systems ◽

Systems Of Linear Inequalities ◽

Number Of Iterations ◽

Finite Number Of Iterations

This paper proposes a method for solving optimisation problems involving piecewise quadratic functions. The method provides a solution in a finite number of iterations, and the computational complexity of the proposed method is locally polynomial of the problem dimension, i.e., if the initial point belongs to the sufficiently small neighbourhood of the solution set. Proposed method could be applied for solving large systems of linear inequalities.

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Some Hermite–Hadamard type integral inequalities for convex functions defined on convex bodies in ℝn\mathbb{R}^{n}

Journal of Applied Analysis ◽

10.1515/jaa-2020-2005 ◽

2020 ◽

Vol 26 (1) ◽

pp. 67-77 ◽

Cited By ~ 1

Author(s):

Silvestru Sever Dragomir

Keyword(s):

Euclidean Space ◽

Convex Functions ◽

Convex Bodies ◽

Integral Inequalities ◽

Divergence Theorem ◽

Several Variables ◽

Type Integral ◽

Bounded Convex

AbstractIn this paper, by the use of the divergence theorem, we establish some integral inequalities of Hermite–Hadamard type for convex functions of several variables defined on closed and bounded convex bodies in the Euclidean space {\mathbb{R}^{n}} for any {n\geq 2}.

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New parameterized quantum integral inequalities via η-quasiconvexity

Advances in Difference Equations ◽

10.1186/s13662-019-2358-z ◽

2019 ◽

Vol 2019 (1) ◽

Cited By ~ 5

Author(s):

Eze R. Nwaeze ◽

Ana M. Tameru

Keyword(s):

Integral Inequalities ◽

Quantum Integral ◽

Alpha Beta ◽

Appl Math

Abstract We establish new quantum Hermite–Hadamard and midpoint types inequalities via a parameter $\mu \in [0,1]$ μ ∈ [ 0 , 1 ] for a function F whose $|{}_{\alpha }D_{q}F|^{u}$ | α D q F | u is η-quasiconvex on $[\alpha ,\beta ]$ [ α , β ] with $u\geq 1$ u ≥ 1 . Results obtained in this paper generalize, sharpen, and extend some results in the literature. For example, see (Noor et al. in Appl. Math. Comput. 251:675–679, 2015; Alp et al. in J. King Saud Univ., Sci. 30:193–203, 2018) and (Kunt et al. in Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. 112:969–992, 2018). By choosing different values of μ, loads of novel estimates can be deduced. We also present some illustrative examples to show how some consequences of our results may be applied to derive more quantum inequalities.

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