Probabilistic contractor couple and solutions for a system of nonlinear equations in non-archimedean menger probabilistic normed spaces

1991 ◽  
Vol 12 (11) ◽  
pp. 1031-1038 ◽  
Author(s):  
Zhang Shi-sheng ◽  
Peng Yong-cheng
Keyword(s):  
Nonlinear Equations ◽  
System Of Nonlinear Equations ◽  
Normed Spaces ◽  
Probabilistic Normed Spaces

Nonlinear equations for fuzzy mappings in probabilistic normed spaces

2000 ◽  
Vol 110 (1) ◽  
pp. 115-122 ◽  
Author(s):  
Y.J. Cho ◽  
N.J. Huang ◽  
S.M. Kang
Keyword(s):  
Nonlinear Equations ◽  
Normed Spaces ◽  
Probabilistic Normed Spaces

Solutions and Stability of Generalized Mixed Type QCA-Functional Equations in Random Normed Spaces

2013 ◽  
Vol 59 (2) ◽  
pp. 299-320
Author(s):  
M. Eshaghi Gordji ◽  
Y.J. Cho ◽  
H. Khodaei ◽  
M. Ghanifard
Keyword(s):  
Functional Equation ◽  
General Solution ◽  
Functional Equations ◽  
Mixed Type ◽  
Additive Functional ◽  
Normed Spaces ◽  
Additive Functional Equation ◽  
Probabilistic Normed Spaces ◽  
Random Normed Spaces ◽  
Generalized Stability

Abstract In this paper, we investigate the general solution and the generalized stability for the quartic, cubic and additive functional equation (briefly, QCA-functional equation) for any k∈ℤ-{0,±1} in Menger probabilistic normed spaces.

Solving System of Nonlinear Equations using Genetic Algorithm

2019 ◽  
Vol 10 (4) ◽  
pp. 877-886 ◽  
Author(s):  
Chhavi Mangla ◽  
Musheer Ahmad ◽  
Moin Uddin
Keyword(s):  
Genetic Algorithm ◽  
Nonlinear Equations ◽  
System Of Nonlinear Equations

scholarly journals Statistical convergence of double sequences on probabilistic normed spaces defined by $[ V, \lambda, \mu ]$-summability

2014 ◽  
Vol 33 (2) ◽  
pp. 59-67
Author(s):  
Pankaj Kumar ◽  
S. S. Bhatia ◽  
Vijay Kumar
Keyword(s):  
Statistical Convergence ◽  
Convergence Criteria ◽  
Double Sequences ◽  
Normed Spaces ◽  
Real Numbers ◽  
Positive Real ◽  
Probabilistic Normed Spaces

In this paper, we aim to generalize the notion of statistical convergence for double sequences on probabilistic normed spaces with the help of two nondecreasing sequences of positive real numbers $\lambda=(\lambda_{n})$ and $\mu = (\mu_{n})$  such that each tending to zero, also $\lambda_{n+1}\leq \lambda_{n}+1, \lambda_{1}=1,$ and $\mu_{n+1}\leq \mu_{n}+1, \mu_{1}=1.$ We also define generalized statistically Cauchy double sequences on PN space and establish the Cauchy convergence criteria in these spaces.

scholarly journals Typical curve with G1 constraints for curve completion

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Chuan He ◽  
Gang Zhao ◽  
Aizeng Wang ◽  
Fei Hou ◽  
Zhanchuan Cai ◽  
...  
Keyword(s):  
Nonlinear Equations ◽  
Interpolation Problem ◽  
Sufficient Conditions ◽  
System Of Nonlinear Equations ◽  
Simple Construction ◽  
Completion Task ◽  
Curve Completion ◽  
Novel Algorithm

AbstractThis paper presents a novel algorithm for planar G1 interpolation using typical curves with monotonic curvature. The G1 interpolation problem is converted into a system of nonlinear equations and sufficient conditions are provided to check whether there is a solution. The proposed algorithm was applied to a curve completion task. The main advantages of the proposed method are its simple construction, compatibility with NURBS, and monotonic curvature.

scholarly journals Compact Operators Defined on2-Normed and2-Probabilistic Normed Spaces

2009 ◽  
Vol 2009 ◽  
pp. 1-17
Author(s):  
Fatemeh Lael ◽  
Kourosh Nourouzi
Keyword(s):  
Compact Operators ◽  
Normed Spaces ◽  
Probabilistic Normed Spaces ◽  
Main Ideas

The compact operators defined on2-normed spaces are investigated, and then the main ideas are generalized to operators defined on2-probabilistic normed spaces.

Quantum Newton’s Method for Solving the System of Nonlinear Equations

SPIN ◽  
2021 ◽  
pp. 2140004
Author(s):  
Cheng Xue ◽  
Yuchun Wu ◽  
Guoping Guo
Keyword(s):  
Quantum Computing ◽  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Linear Equations ◽  
Data Conversion ◽  
System Of Nonlinear Equations ◽  
Dimensional System ◽  
System Of Linear Equations ◽  
Whole Process

While quantum computing provides an exponential advantage in solving the system of linear equations, there is little work to solve the system of nonlinear equations with quantum computing. We propose quantum Newton’s method (QNM) for solving [Formula: see text]-dimensional system of nonlinear equations based on Newton’s method. In QNM, we solve the system of linear equations in each iteration of Newton’s method with quantum linear system solver. We use a specific quantum data structure and [Formula: see text] tomography with sample error [Formula: see text] to implement the classical-quantum data conversion process between the two iterations of QNM, thereby constructing the whole process of QNM. The complexity of QNM in each iteration is [Formula: see text]. Through numerical simulation, we find that when [Formula: see text], QNM is still effective, so the complexity of QNM is sublinear with [Formula: see text], which provides quantum advantage compared with the optimal classical algorithm.

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