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11. On a generalization of a Greguš fixed point theorem

Creator:
Ćirić, Ljubomir
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
convex metric space, nonexpansive type mapping, and fixed point
Language:
English
Description:
Let $C$ be a closed convex subset of a complete convex metric space $X$. In this paper a class of selfmappings on $C$, which satisfy the nonexpansive type condition $(2)$ below, is introduced and investigated. The main result is that such mappings have a unique fixed point.
Rights:
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12. On the heights of power digraphs modulo $n$

Creator:
Ahmad, Uzma and Syed, Husnine
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
iteration digraph, height, Carmichael lambda function, fixed point, and regular digraph
Language:
English
Description:
A power digraph, denoted by $G(n,k)$, is a directed graph with $\mathbb Z_{n}=\{0,1,\dots ,n-1\}$ as the set of vertices and $E=\{(a,b)\colon a^{k}\equiv b\pmod n\}$ as the edge set. In this paper we extend the work done by Lawrence Somer and Michal Křížek: On a connection of number theory with graph theory, Czech. Math. J. 54 (2004), 465–485, and Lawrence Somer and Michal Křížek: Structure of digraphs associated with quadratic congruences with composite moduli, Discrete Math. 306 (2006), 2174–2185. The heights of the vertices and the components of $G(n,k)$ for $n\geq 1$ and $k\geq 2$ are determined. We also find an expression for the number of vertices at a specific height. Finally, we obtain necessary and sufficient conditions on $n$ such that each vertex of indegree $0$ of a certain subdigraph of $G(n,k)$ is at height $q\geq 1$.
Rights:
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13. On the set of solutions of some nonconvex nonclosed hyperbolic differential inclusions

Creator:
Cernea, Aurelian
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
hyperbolic, differential inclusions, fixed point, and solution set
Language:
English
Description:
We consider a class of nonconvex and nonclosed hyperbolic differential inclusions and we prove the arcwise connectedness of the solution set.
Rights:
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14. Properties of differences of meromorphic functions

Creator:
Chen, Zong-Xuan and Zhon, Kwang Ho
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
meromorphic function, difference, divided difference, zero, and fixed point
Language:
English
Description:
Let $f$ be a transcendental meromorphic function. We propose a number of results concerning zeros and fixed points of the difference $g(z)=f(z+c)-f(z)$ and the divided difference $g(z)/f(z)$.
Rights:
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15. Risk-sensitive Markov stopping games with an absorbing state

Creator:
López-Rivero, Jaicer, Cavazos-Cadena, Rolando, and Cruz-Suárez, Hugo
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
hitting time, fixed point, equilibrium equation, bounded rewards, monotone operator, and certainty equivalent
Language:
English
Description:
This work is concerned with discrete-time Markov stopping games with two players. At each decision time player II can stop the game paying a terminal reward to player I, or can let the system to continue its evolution. In this latter case player I applies an action affecting the transitions and entitling him to receive a running reward from player II. It is supposed that player I has a no-null and constant risk-sensitivity coefficient, and that player II tries to minimize the utility of player I. The performance of a pair of decision strategies is measured by the risk-sensitive (expected) total reward of player I and, besides mild continuity-compactness conditions, the main structural assumption on the model is the existence of an absorbing state which is accessible from any starting point. In this context, it is shown that the value function of the game is characterized by an equilibrium equation, and the existence of a Nash equilibrium is established.
Rights:
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16. Some fixed point theorems in logarithmic convex structures

Creator:
Moazzen, Alireza, Cho, Yoel-Je, Park, Choonkil, and Eshaghi Gordji, Madjid
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
fixed point, logarithmic convex structure, and convex metric space
Language:
English
Description:
In this paper, we introduce the concept of a logarithmic convex structure. Let X be a set and D : X × X → [1, ∞) a function satisfying the following conditions: (i) For all x, y ∈ X, D(x, y) ≥ 1 and D(x, y) = 1 if and only if x = y. (ii) For all x, y ∈ X, D(x, y) = D(y, x). (iii) For all x, y, z ∈ X, D(x, y) ≤ D(x, z)D(z, y). (iv) For all x, y, z ∈ X, z ≠ x, y and λ ∈ (0, 1), D(z, W(x, y, λ)) ≤ D λ (x, z)D 1−λ (y, z), D(x, y) = D(x, W(x, y, λ))D(y, W(x, y, λ)), where W : X ×X ×[0, 1] → X is a continuous mapping. We name this the logarithmic convex structure. In this work we prove some fixed point theorems in the logarithmic convex structure.
Rights:
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17. Stability in linear neutral difference equations with variable delays

Creator:
Ardjouni, Abdelouaheb and Djoudi, Ahcene
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
fixed point, stability, neutral difference equation, and variable delay
Language:
English
Description:
In this paper we use the fixed point method to prove asymptotic stability results of the zero solution of a generalized linear neutral difference equation with variable delays. An asymptotic stability theorem with a sufficient condition is proved, which improves and generalizes some results due to Y. N. Raffoul (2006), E. Yankson (2009), M. Islam and E. Yankson (2005).
Rights:
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18. Strong convergence theorems of $k$-strict pseudo-contractions in Hilbert spaces

Creator:
Qin, Xiaolong, Kang, Shin Min, and Shang, Meijuan
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Hilbert space, nonexpansive mapping, strict pseudo-contraction, iterative algorithm, and fixed point
Language:
English
Description:
Let $K$ be a nonempty closed convex subset of a real Hilbert space $H$ such that $K\pm K\subset K$, $T\: K\rightarrow H$ a $k$-strict pseudo-contraction for some $0\leq k<1$ such that $F(T)=\{x\in K\: x=Tx\}\neq \emptyset $. Consider the following iterative algorithm given by $$ \forall x_1\in K,\quad x_{n+1}=\alpha _n\gamma f(x_n)+\beta _nx_n+((1-\beta _n)I-\alpha _n A)P_KSx_n,\quad n\geq 1, $$ where $S\: K\rightarrow H$ is defined by $Sx=kx+(1-k)Tx$, $P_K$ is the metric projection of $H$ onto $K$, $A$ is a strongly positive linear bounded self-adjoint operator, $f$ is a contraction. It is proved that the sequence $\{x_n\}$ generated by the above iterative algorithm converges strongly to a fixed point of $T$, which solves a variational inequality related to the linear operator $A$. Our results improve and extend the results announced by many others.
Rights:
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19. Suzuki type fuzzy Z-contractive mappings and fixed points in fuzzy metric spaces

Creator:
Gopal, Dhananjay and Martínez-Moreno, Juan
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
fuzzy metric space, fixed point, fuzzy Z-contractive mapping, and Suzuki type fuzzy Z-contractive mappings
Language:
English
Description:
In this paper, we propose the concept of Suzuki type fuzzy Z-contractive mappings, which is a generalization of Fuzzy Z-contractive mappings initiated in the article [S. Shukla, D. Gopal, W. Sintunavarat, A new class of fuzzy contractive mappings and fixed point theorems, Fuzzy Sets and Systems 350 (2018)85-95]. For this type of contractions suitable conditions are framed to ensure the existence of fixed point in G-complete as well as M-complete fuzzy metric spaces. A comprehensive set of examples are furnished to demonstrate the validity of the obtained results.
Rights:
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20. The classification of finite groups by using iteration digraphs

Creator:
Ahmad, Uzma and Moeen, Muqadas
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, iterační metody, mathematics, iterative methods (mathematics), 2-group, generalized quaternion group, iteration digraph, cycle, indegree, fixed point, regular digraph, 13, and 51
Language:
English
Description:
A digraph is associated with a finite group by utilizing the power map f: G → G defined by f(x) = xkfor all x \in G, where k is a fixed natural number. It is denoted by γG(n, k). In this paper, the generalized quaternion and 2-groups are stud- ied. The height structure is discussed for the generalized quaternion. The necessary and sufficient conditions on a power digraph of a 2-group are determined for a 2-group to be a generalized quaternion group. Further, the classification of two generated 2-groups as abelian or non-abelian in terms of semi-regularity of the power digraphs is completed., Uzma Ahmad, Muqadas Moeen., and Obsahuje seznam literatury
Rights:
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