Approximate Homomorphisms and Derivations on Normed Lie Triple Systems by Hark-Mahn Kim, Juri Lee

“…We investigate the generalized Hyers-Ulam stability of homomorphisms and derivations on normed Lie triple systems for the following generalized Cauchy-Jensen additive equation r0f((s∑j=1pxj+t∑j=1dyj)/r0)=s∑j=1p‍f(xj)+t∑j=1d‍f(yj), where r0,s, and  t are nonzero real numbers. As a results, we generalize some stability results concerning this equation.…”
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Global Behavior of the Max-Type Difference Equation xn+1=max⁡{1/xn,An/xn−1} by Taixiang Sun, Bin Qin, Hongjian Xi, Caihong Han

“…We study global behavior of the following max-type difference equation xn+1=max⁡{1/xn,An/xn−1}, n=0,1,…, where {An}n=0∞ is a sequence of positive real numbers with 0≤inf⁡An≤sup⁡An<1. The special case when {An}n=0∞ is a periodic sequence with period k and An∈(0,1) for every n≥0 has been completely investigated by Y. …”
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Fuzzy Shortest Path Problem Based on Level 𝜆-Triangular LR Fuzzy Numbers by S. Elizabeth, L. Sujatha

“…In this paper, algorithms are proposed for the fuzzy shortest path problem, where the arc length of the network takes imprecise numbers, instead of real numbers, namely, level 𝜆-triangular LR fuzzy numbers. …”
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Dynamical Behavior and Expressions of Solutions of a Class of Higher-Order Nonlinear Difference Equations by Ghada AlNemer, Lama Sh. Aljoufi, A. M. Ahmed, Samir Al Mohammady, M. Zakarya, H. M. Rezk

“…The aim of this article is to get the forms of the solutions of the following nonlinear higher-order difference equations χs+1=χs−3k+1/±1±Πl=1kχs−3l+1,s=0,1,2,…, where the initial conditions χ−j,j=0,1,2,…,3k−1 and k∈1,2,… are arbitrary real numbers. Also, we examine stability, boundedness, oscillation, and the periodic nature of these solutions.…”
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On the Global Asymptotic Stability and 4-Period Oscillation of the Third-Order Difference Equation by M. E. Erdogan

“…The main objective of this paper is to study the global behavior and oscillation of the following third-order rational difference equation xn+1=αxnxn−1xn−2/βxn−12+γxn−22, where the initial conditions x−2,x−1,x0 are nonzero real numbers and α,β,γ are positive constants such that α≤β+γ. …”
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Global Stability of a Rational Difference Equation by Guo-Mei Tang, Lin-Xia Hu, Gang Ma

“…We consider the higher-order nonlinear difference equation 𝑥𝑛+1=(𝑝+𝑞𝑥𝑛−𝑘)/(1+𝑥𝑛+𝑟𝑥𝑛−𝑘),𝑛=0,1,… with the parameters, and the initial conditions 𝑥−𝑘,…,𝑥0 are nonnegative real numbers. We investigate the periodic character, invariant intervals, and the global asymptotic stability of all positive solutions of the above-mentioned equation. …”
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The Multivariate Müntz-Szasz Problem in Weighted Banach Space on Rn by Xiangdong Yang

“…,λkn)}k=1∞ a sequence of real numbers in R+n. The completeness of monomials {tλk} in Cα is investigated, where Cα is the weighted Banach spaces which consist of complex continuous functions f defined on Rn with f(t) exp(-α(t)) vanishing at infinity in the uniform norm.…”
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Novel Refinements via n–Polynomial Harmonically s–Type Convex Functions and Application in Special Functions by Saad Ihsan Butt, Saima Rashid, Muhammad Tariq, Miao-Kun Wang

“…Finally, we illustrate the applicability of this new investigation in special functions (hypergeometric function and special mean of real numbers).…”
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On the Rational Recursive Sequence xn+1=(A+∑i=0kαixn−i)/(B+∑i=0kβixn−i) by E. M. E. Zayed, M. A. El-Moneam

“…,x−1,x0 are arbitrary positive real numbers, while k is a positive integer number.…”
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The Solution and Dynamic Behaviour of Difference Equations of Twenty-First Order by Ibrahim Tarek Fawzi Abdelhamid, Dağıstan Şimşek, Burak Oğul

“…We explore the dynamics of adhering to rational difference formula$$ \psi_{m+1}=\frac{\psi_{m-20}}{\pm 1 \pm \psi_{m-2}\psi_{m-5}\psi_{m-8}\psi_{m-11}\psi_{m-14}\psi_{m-17}\psi_{m-20}}, \quad m \in \mathbb{N}_{0} $$where the initials are arbitrary nonzero real numbers. Specifically, we examine global asymptotically stability. …”
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Metrics for Multiset-Theoretic Subgraphs by Ray-Ming Chen

“…The method mainly utilizes the minimal matching between any two multisets of positive real numbers by comparing the multiple edges with respect to their corresponding vertices. …”
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Remarks on complexities and entropies for singularity categories by Takahashi, Ryo

“…In this paper, we find real numbers $t$ such that the complexity $\delta _t(G,X)$ in the sense of Dimitrov, Haiden, Katzarkov and Kontsevich vanishes for any split generator $G$ of $\mathsf {D_{sg}}(R)$ and any object $X$ of $\mathsf {D_{sg}}(R)$. …”
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Asymptotic Stability for a Class of Nonlinear Difference Equations by Chang-you Wang, Shu Wang, Zhi-wei Wang, Fei Gong, Rui-fang Wang

“…We study the global asymptotic stability of the equilibrium point for the fractional difference equation xn+1=(axn-lxn-k)/(α+bxn-s+cxn-t), n=0,1,…, where the initial conditions x-r,x-r+1,…,x1,x0 are arbitrary positive real numbers of the interval (0,α/2a),l,k,s,t are nonnegative integers, r=max⁡⁡{l,k,s,t} and α,a,b,c are positive constants. …”
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Global Character of a Six-Dimensional Nonlinear System of Difference Equations by Mehmet Gümüş, Yüksel Soykan

“…The aim of this paper is to study the dynamical behavior of positive solutions for a system of rational difference equations of the following form: un+1=αun-1/β+γvn-2p, vn+1=α1vn-1/β1+γ1un-2p, n=0,1,…, where the parameters α,β,γ,α1,β1,γ1,p and the initial values u-i,v-i for i=0,1,2 are positive real numbers.…”
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On Caputo–Fabrizio Fractional Integral Inequalities of Hermite–Hadamard Type for Modified h-Convex Functions by Xiaobin Wang, Muhammad Shoaib Saleem, Kiran Naseem Aslam, Xingxing Wu, Tong Zhou

“…Moreover, we also present some application of our results to special means of real numbers.…”
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On Stability Analysis of Higher-Order Rational Difference Equation by Abdul Khaliq, H. S. Alayachi, M. S. M. Noorani, A. Q. Khan

“…With initial values w−p,w−p+1,…,w−r,w−r+1,…,w−1, and w0 are positive real numbers. Some numerical examples are given to verify our theoretical results.…”
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Convergence of weighted sums of independent random variables and an extension to Banach space-valued random variables by W. J. Padgett, R. L. Taylor

“…Let {Xk} be independent random variables with EXk=0 for all k and let {ank:n≥1, k≥1} be an array of real numbers. In this paper the almost sure convergence of Sn=∑k=1nankXk, n=1,2,…, to a constant is studied under various conditions on the weights {ank} and on the random variables {Xk} using martingale theory. …”
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Periodic Solutions of a System of Nonlinear Difference Equations with Periodic Coefficients by Durhasan Turgut Tollu

“…This paper is dealt with the following system of difference equations xn+1=an/xn+bn/yn,yn+1=cn/xn+dn/yn, where n∈ℕ0=ℕ∪0, the initial values x0 and y0 are the positive real numbers, and the sequences ann≥0, bnn≥0, cnn≥0, and dnn≥0 are two-periodic and positive. …”
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k -Fractional Variants of Hermite-Mercer-Type Inequalities via s-Convexity with Applications by Saad Ihsan Butt, Jamshed Nasir, Shahid Qaisar, Khadijah M. Abualnaja

“…As an application viewpoint, certain estimates in respect of special functions and special means of real numbers are also illustrated to demonstrate the applicability and effectiveness of the suggested scheme.…”
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On the Multiplicity of Solutions for the Discrete Boundary Problem Involving the Singular ϕ-Laplacian by Zihua Qiu

“…In order to apply the critical point theory, we extend the domain of the singular operator to the whole real numbers. Instead, we consider an auxiliary problem associated with the original one. …”
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