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Fixed-point results for convex orbital operators 凸轨道算子的不动点结果
IF 2 3区 数学
Demonstratio Mathematica Pub Date : 2023-01-01 DOI: 10.1515/dema-2022-0184
O. Popescu
{"title":"Fixed-point results for convex orbital operators","authors":"O. Popescu","doi":"10.1515/dema-2022-0184","DOIUrl":"https://doi.org/10.1515/dema-2022-0184","url":null,"abstract":"Abstract The aim of this article is to introduce a new type of operator similar to those of A. Petruşel and G. Petruşel type (Fixed point results for decreasing convex orbital operators, J. Fixed Point Theory Appl. 23 (2021), no. 35) and prove some fixed-point theorems which generalize and complement several results in the theory of nonlinear operators.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49348940","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
On split generalized equilibrium problem with multiple output sets and common fixed points problem 多输出集分裂广义平衡问题及公共不动点问题
IF 2 3区 数学
Demonstratio Mathematica Pub Date : 2023-01-01 DOI: 10.1515/dema-2022-0251
E. C. Godwin, O. Mewomo, T. O. Alakoya
{"title":"On split generalized equilibrium problem with multiple output sets and common fixed points problem","authors":"E. C. Godwin, O. Mewomo, T. O. Alakoya","doi":"10.1515/dema-2022-0251","DOIUrl":"https://doi.org/10.1515/dema-2022-0251","url":null,"abstract":"Abstract In this article, we introduce and study the notion of split generalized equilibrium problem with multiple output sets (SGEPMOS). We propose a new iterative method that employs viscosity approximation technique for approximating the common solution of the SGEPMOS and common fixed point problem for an infinite family of multivalued demicontractive mappings in real Hilbert spaces. Under mild conditions, we prove a strong convergence theorem for the proposed method. Our method uses self-adaptive step size that does not require prior knowledge of the operator norm. The results presented in this article unify, complement, and extend several existing recent results in the literature.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47645313","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Pell-Lucas polynomials for numerical treatment of the nonlinear fractional-order Duffing equation 用Pell-Lucas多项式数值处理非线性分数阶Duffing方程
IF 2 3区 数学
Demonstratio Mathematica Pub Date : 2023-01-01 DOI: 10.1515/dema-2022-0220
A. A. El-Sayed
{"title":"Pell-Lucas polynomials for numerical treatment of the nonlinear fractional-order Duffing equation","authors":"A. A. El-Sayed","doi":"10.1515/dema-2022-0220","DOIUrl":"https://doi.org/10.1515/dema-2022-0220","url":null,"abstract":"Abstract The nonlinear fractional-order cubic-quintic-heptic Duffing problem will be solved through a new numerical approximation technique. The suggested method is based on the Pell-Lucas polynomials’ operational matrix in the fractional and integer orders. The studied problem will be transformed into a nonlinear system of algebraic equations. The numerical expansion containing unknown coefficients will be obtained numerically via applying Newton’s iteration method to the claimed system. Convergence analysis and error estimates for the introduced process will be discussed. Numerical applications will be given to illustrate the applicability and accuracy of the proposed method.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47765589","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A numerical Haar wavelet-finite difference hybrid method and its convergence for nonlinear hyperbolic partial differential equation 非线性双曲型偏微分方程的数值Haar小波-有限差分混合方法及其收敛性
IF 2 3区 数学
Demonstratio Mathematica Pub Date : 2023-01-01 DOI: 10.1515/dema-2022-0203
W. Lei, Muhammad Ahsan, Waqas Khan, Zaheer Uddin, Masood Ahmad
{"title":"A numerical Haar wavelet-finite difference hybrid method and its convergence for nonlinear hyperbolic partial differential equation","authors":"W. Lei, Muhammad Ahsan, Waqas Khan, Zaheer Uddin, Masood Ahmad","doi":"10.1515/dema-2022-0203","DOIUrl":"https://doi.org/10.1515/dema-2022-0203","url":null,"abstract":"Abstract In this research work, we proposed a Haar wavelet collocation method (HWCM) for the numerical solution of first- and second-order nonlinear hyperbolic equations. The time derivative in the governing equations is approximated by a finite difference. The nonlinear hyperbolic equation is converted into its full algebraic form once the space derivatives are replaced by the finite Haar series. Convergence analysis is performed both in space and time, where the computational results follow the theoretical statements of convergence. Many test problems with different nonlinear terms are presented to verify the accuracy, capability, and convergence of the proposed method for the first- and second-order nonlinear hyperbolic equations.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44217083","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Normal ordering associated with λ-Stirling numbers in λ-shift algebra λ平移代数中与λ-Stirling数相关的正规序
IF 2 3区 数学
Demonstratio Mathematica Pub Date : 2023-01-01 DOI: 10.1515/dema-2022-0250
Taekyun Kim, Dae San Kim, H. Kim
{"title":"Normal ordering associated with λ-Stirling numbers in λ-shift algebra","authors":"Taekyun Kim, Dae San Kim, H. Kim","doi":"10.1515/dema-2022-0250","DOIUrl":"https://doi.org/10.1515/dema-2022-0250","url":null,"abstract":"Abstract It is known that the Stirling numbers of the second kind are related to normal ordering in the Weyl algebra, while the unsigned Stirling numbers of the first kind are related to normal ordering in the shift algebra. Recently, Kim-Kim introduced a λ lambda -analogue of the unsigned Stirling numbers of the first kind and that of the r r -Stirling numbers of the first kind. In this article, we introduce a λ lambda -analogue of the shift algebra (called λ lambda -shift algebra) and investigate normal ordering in the λ lambda -shift algebra. From the normal ordering in the λ lambda -shift algebra, we derive some identities about the λ lambda -analogue of the unsigned Stirling numbers of the first kind.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47413036","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Kinematic-geometry of a line trajectory and the invariants of the axodes 直线轨迹的运动几何和轴的不变量
3区 数学
Demonstratio Mathematica Pub Date : 2023-01-01 DOI: 10.1515/dema-2022-0252
Yanlin Li, Fatemah Mofarreh, Rashad A. Abdel-Baky
{"title":"Kinematic-geometry of a line trajectory and the invariants of the axodes","authors":"Yanlin Li, Fatemah Mofarreh, Rashad A. Abdel-Baky","doi":"10.1515/dema-2022-0252","DOIUrl":"https://doi.org/10.1515/dema-2022-0252","url":null,"abstract":"Abstract In this article, we investigate the relationships between the instantaneous invariants of a one-parameter spatial movement and the local invariants of the axodes. Specifically, we provide new proofs for the Euler-Savary and Disteli formulas using the E. Study map in spatial kinematics, showcasing its elegance and efficiency. In addition, we introduce two line congruences and thoroughly analyze their spatial equivalence. Our findings contribute to a deeper understanding of the interplay between spatial movements and axodes, with potential applications in fields such as robotics and mechanical engineering.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135181565","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
A class of strongly convergent subgradient extragradient methods for solving quasimonotone variational inequalities 一类求解拟单调变分不等式的强收敛次梯度外延方法
IF 2 3区 数学
Demonstratio Mathematica Pub Date : 2023-01-01 DOI: 10.1515/dema-2022-0202
H. Rehman, P. Kumam, Murat Ozdemir, I. Yildirim, W. Kumam
{"title":"A class of strongly convergent subgradient extragradient methods for solving quasimonotone variational inequalities","authors":"H. Rehman, P. Kumam, Murat Ozdemir, I. Yildirim, W. Kumam","doi":"10.1515/dema-2022-0202","DOIUrl":"https://doi.org/10.1515/dema-2022-0202","url":null,"abstract":"Abstract The primary goal of this research is to investigate the approximate numerical solution of variational inequalities using quasimonotone operators in infinite-dimensional real Hilbert spaces. In this study, the sequence obtained by the proposed iterative technique for solving quasimonotone variational inequalities converges strongly toward a solution due to the viscosity-type iterative scheme. Furthermore, a new technique is proposed that uses an inertial mechanism to obtain strong convergence iteratively without the requirement for a hybrid version. The fundamental benefit of the suggested iterative strategy is that it substitutes a monotone and non-monotone step size rule based on mapping (operator) information for its Lipschitz constant or another line search method. This article also provides a numerical example to demonstrate how each method works.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":"56 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67143964","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Analytical and numerical analysis of damped harmonic oscillator model with nonlocal operators 非局部算符阻尼谐振子模型的解析与数值分析
IF 2 3区 数学
Demonstratio Mathematica Pub Date : 2023-01-01 DOI: 10.1515/dema-2022-0230
N. Alharthi, A. Atangana, B. Alkahtani
{"title":"Analytical and numerical analysis of damped harmonic oscillator model with nonlocal operators","authors":"N. Alharthi, A. Atangana, B. Alkahtani","doi":"10.1515/dema-2022-0230","DOIUrl":"https://doi.org/10.1515/dema-2022-0230","url":null,"abstract":"Abstract Nonlocal operators with different kernels were used here to obtain more general harmonic oscillator models. Power law, exponential decay, and the generalized Mittag-Leffler kernels with Delta-Dirac property have been utilized in this process. The aim of this study was to introduce into the damped harmonic oscillator model nonlocalities associated with these mentioned kernels and see the effect of each one of them when computing the Bode diagram obtained from the Laplace and the Sumudu transform. For each case, we applied both the Laplace and the Sumudu transform to obtain a solution in a complex space. For each case, we obtained the Bode diagram and the phase diagram for different values of fractional orders. We presented a detailed analysis of uniqueness and an exact solution and used numerical approximation to obtain a numerical solution.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43076939","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On some geometric results for generalized k-Bessel functions 关于广义k-贝塞尔函数的一些几何结果
IF 2 3区 数学
Demonstratio Mathematica Pub Date : 2023-01-01 DOI: 10.1515/dema-2022-0235
Evrim Toklu
{"title":"On some geometric results for generalized k-Bessel functions","authors":"Evrim Toklu","doi":"10.1515/dema-2022-0235","DOIUrl":"https://doi.org/10.1515/dema-2022-0235","url":null,"abstract":"Abstract The main aim of this article is to present some novel geometric properties for three distinct normalizations of the generalized k k -Bessel functions, such as the radii of uniform convexity and of α alpha -convexity. In addition, we show that the radii of α alpha -convexity remain in between the radii of starlikeness and convexity, in the case when α ∈ [ 0 , 1 ] , alpha in {[}0,1], and they are decreasing with respect to the parameter α . alpha . The key tools in the proof of our main results are infinite product representations for normalized k k -Bessel functions and some properties of real zeros of these functions.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":"56 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41547161","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the existence of nonnegative radial solutions for Dirichlet exterior problems on the Heisenberg group Heisenberg群上Dirichlet外问题非负径向解的存在性
IF 2 3区 数学
Demonstratio Mathematica Pub Date : 2023-01-01 DOI: 10.1515/dema-2022-0193
M. Jleli
{"title":"On the existence of nonnegative radial solutions for Dirichlet exterior problems on the Heisenberg group","authors":"M. Jleli","doi":"10.1515/dema-2022-0193","DOIUrl":"https://doi.org/10.1515/dema-2022-0193","url":null,"abstract":"Abstract We investigate the existence and nonexistence of nonnegative radial solutions to exterior problems of the form Δ H m u ( q ) + λ ψ ( q ) K ( r ( q ) ) f ( r 2 − Q ( q ) , u ( q ) ) = 0 {Delta }_{{{mathbb{H}}}^{m}}uleft(q)+lambda psi left(q)Kleft(rleft(q))fleft({r}^{2-Q}left(q),uleft(q))=0 in B 1 c {B}_{1}^{c} , under the Dirichlet boundary conditions u = 0 u=0 on ∂ B 1 partial {B}_{1} and lim r ( q ) → ∞ u ( q ) = 0 {mathrm{lim}}_{rleft(q)to infty }uleft(q)=0 . Here, λ ≥ 0 lambda ge 0 is a parameter, Δ H m {Delta }_{{{mathbb{H}}}^{m}} is the Kohn Laplacian on the Heisenberg group H m = R 2 m + 1 {{mathbb{H}}}^{m}={{mathbb{R}}}^{2m+1} , m > 1 mgt 1 , Q = 2 m + 2 Q=2m+2 , B 1 {B}_{1} is the unit ball in H m {{mathbb{H}}}^{m} , B 1 c {B}_{1}^{c} is the complement of B 1 {B}_{1} , and ψ ( q ) = ∣ z ∣ 2 r 2 ( q ) psi left(q)=frac{| z{| }^{2}}{{r}^{2}left(q)} . Namely, under certain conditions on K K and f f , we show that there exists a critical parameter λ ∗ ∈ ( 0 , ∞ ] {lambda }^{ast }in left(0,infty ] in the following sense. If 0 ≤ λ < λ ∗ 0le lambda lt {lambda }^{ast } , the above problem admits a unique nonnegative radial solution u λ {u}_{lambda } ; if λ ∗ < ∞ {lambda }^{ast }lt infty and λ ≥ λ ∗ lambda ge {lambda }^{ast } , the problem admits no nonnegative radial solution. When 0 ≤ λ < λ ∗ 0le lambda lt {lambda }^{ast } , a numerical algorithm that converges to u λ {u}_{lambda } is provided and the continuity of u λ {u}_{lambda } with respect to λ lambda , as well as the behavior of u λ {u}_{lambda } as λ → λ ∗ − lambda to {{lambda }^{ast }}^{-} , are studied. Moreover, sufficient conditions on the the behavior of f ( t , s ) fleft(t,s) as s → ∞ sto infty are obtained, for which λ ∗ = ∞ {lambda }^{ast }=infty or λ ∗ < ∞ {lambda }^{ast }lt infty . Our approach is based on partial ordering methods and fixed point theory in cones.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49023204","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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