scholarly journals New (p, q)-estimates for different types of integral inequalities via (α, m)-convex mappings

2020 ◽  
Vol 18 (1) ◽  
pp. 1830-1854
Author(s):  
Humaira Kalsoom ◽  
Muhammad Amer Latif ◽  
Saima Rashid ◽  
Dumitru Baleanu ◽  
Yu-Ming Chu
Keyword(s):  
Integral Identity ◽  
Integral Inequalities ◽  
First Order ◽  
Convex Mappings ◽  
Differentiable Functions ◽  
Different Types ◽  
Error Estimations ◽  
Quantum Error

Abstract In the article, we present a new ( p , q ) (p,q) -integral identity for the first-order ( p , q ) (p,q) -differentiable functions and establish several new ( p , q ) (p,q) -quantum error estimations for various integral inequalities via ( α , m ) (\alpha ,m) -convexity. We also compare our results with the previously known results and provide two examples to show the superiority of our obtained results.

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.

scholarly journals Fractional Integral Inequalities for Differentiable Convex Mappings and Applications to Special Means and a Midpoint Formula

2012 ◽  
Vol 8 (2) ◽  
pp. 21-28 ◽  
Author(s):  
Chun Zhu ◽  
Michal Fečkan ◽  
Jinrong Wang
Keyword(s):  
Error Estimates ◽  
Integral Identity ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Real Numbers ◽  
Liouville Type ◽  
Convex Mappings ◽  
Special Means

Abstract In this paper, Riemann-Liouville type fractional integral identity and inequality for differentiable convex mappings are studied. Some applications to special means of real numbers are given. Finally, error estimates for a midpoint formula are also obtained.

Post-Non-Classical World View in the On-Screen Reality of the Digital Epoch

2015 ◽  
pp. 4-12
Author(s):  
Elena V. Nikolaeva
Keyword(s):  
World View ◽  
Dynamic Chaos ◽  
Digital Culture ◽  
Fractal Nature ◽  
Late 20Th Century ◽  
First Order ◽  
Classical World ◽  
Different Types ◽  
Strange Loops ◽  
Cultural World

The article analyzes the correlation between the screen reality and the first-order reality in the digital culture. Specific concepts of the scientific paradigm of the late 20th century are considered as constituent principles of the on-screen reality of the digital epoch. The study proves that the post-non-classical cultural world view, emerging from the dynamic “chaos” of informational and semantic rows of TV programs and cinematographic narrations, is of a fractal nature. The article investigates different types of fractality of the TV content and film plots, their inner and outer “strange loops” and artistic interpretations of the “butterfly effect”.

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.

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

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.

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.

scholarly journals New Modifications of Integral Inequalities via ℘-Convexity Pertaining to Fractional Calculus and Their Applications

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1753
Author(s):  
Saima Rashid ◽  
Aasma Khalid ◽  
Omar Bazighifan ◽  
Georgia Irina Oros
Keyword(s):  
Integral Operator ◽  
Convex Functions ◽  
Hypergeometric Functions ◽  
Fractional Integral ◽  
Type Inequality ◽  
Fractional Integral Operator ◽  
Integral Inequalities ◽  
Convex Mappings ◽  
Special Cases ◽  
Harmonically Convex Functions

Integral inequalities for ℘-convex functions are established by using a generalised fractional integral operator based on Raina’s function. Hermite–Hadamard type inequality is presented for ℘-convex functions via generalised fractional integral operator. A novel parameterized auxiliary identity involving generalised fractional integral is proposed for differentiable mappings. By using auxiliary identity, we derive several Ostrowski type inequalities for functions whose absolute values are ℘-convex mappings. It is presented that the obtained outcomes exhibit classical convex and harmonically convex functions which have been verified using Riemann–Liouville fractional integral. Several generalisations and special cases are carried out to verify the robustness and efficiency of the suggested scheme in matrices and Fox–Wright generalised hypergeometric functions.

scholarly journals Quantum repeaters based on concatenated bosonic and discrete-variable quantum codes

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Filip Rozpędek ◽  
Kyungjoo Noh ◽  
Qian Xu ◽  
Saikat Guha ◽  
Liang Jiang
Keyword(s):  
Continuous Variable ◽  
Quantum Codes ◽  
Discrete Variable ◽  
Long Distance ◽  
Concatenated Code ◽  
Different Types ◽  
Optical Modes ◽  
Distance Communication ◽  
Quantum Repeaters ◽  
Quantum Error

AbstractWe propose an architecture of quantum-error-correction-based quantum repeaters that combines techniques used in discrete- and continuous-variable quantum information. Specifically, we propose to encode the transmitted qubits in a concatenated code consisting of two levels. On the first level we use a continuous-variable GKP code encoding the qubit in a single bosonic mode. On the second level we use a small discrete-variable code. Such an architecture has two important features. Firstly, errors on each of the two levels are corrected in repeaters of two different types. This enables for achieving performance needed in practical scenarios with a reduced cost with respect to an architecture for which all repeaters are the same. Secondly, the use of continuous-variable GKP code on the lower level generates additional analog information which enhances the error-correcting capabilities of the second-level code such that long-distance communication becomes possible with encodings consisting of only four or seven optical modes.

Quantitative Models of Motor Responses Subject to Longitudinal, Lateral, and Preview Constraints

1978 ◽  
Vol 20 (1) ◽  
pp. 35-39 ◽  
Author(s):  
Tarald O. Kvålseth
Keyword(s):  
Experimental Data ◽  
Motor Control ◽  
Linear Models ◽  
Movement Time ◽  
Arm Movements ◽  
Second Order ◽  
Motor Responses ◽  
First Order ◽  
Different Types ◽  
Index Of Difficulty

First- and second-order linear models of mean movement time for serial arm movements aimed at a target and subject to preview constraints and lateral constraints were formulated as extensions of the so-called Fitts's law of motor control. These models were validated on the basis of experimental data from five subjects and found to explain from 80% to 85% of the variation in movement time in the case of the first-order models and from 93% to 95% of such variation for the second-order models. Fitts's index of difficulty (ID) was generally found to contribute more to the movement time than did either the preview ID or the lateral ID defined. Of the different types of errors, target overshoots occurred far more frequently than undershoots.

scholarly journals Some new integral inequalities for Lipschitzian functions

2018 ◽  
Vol 8 (2) ◽  
pp. 259-265 ◽  
Author(s):  
İmdat İşcan ◽  
Mahir Kadakal ◽  
Alper Aydın
Keyword(s):  
Lipschitz Class ◽  
Integral Inequalities ◽  
Lipschitzian Functions ◽  
Special Means ◽  
Different Types ◽  
New Type

This paper is about obtaining some new type of integral inequalities for functions from the Lipschitz class. For this, some new integral inequalities related to the differences between the two different types of integral averages for Lipschitzian functions are obtained. Moreover, applications for some special means as arithmetic, geometric, logarithmic, -logarithmic, harmonic, identric are given.

Sign in / Sign up

Export Citation Format

Share Document