scholarly journals F-evolution algebra

Filomat ◽  
2016 ◽  
Vol 30 (10) ◽  
pp. 2637-2652 ◽  
Author(s):  
Uygun Jamilov ◽  
Manuel Ladra
Keyword(s):  
Fixed Point ◽  
Banach Algebra ◽  
Necessary Conditions ◽  
Zero Point ◽  
Limit Set ◽  
Volterra Type ◽  
Quadratic Stochastic Operator ◽  
Stochastic Operator ◽  
Evolution Algebra ◽  
Upper Estimate

We consider the evolution algebra of a free population generated by an F-quadratic stochastic operator. We prove that this algebra is commutative, not associative and necessarily power-associative. We show that this algebra is not conservative, not stationary, not genetic and not train algebra, but it is a Banach algebra. The set of all derivations of the F-evolution algebra is described. We give necessary conditions for a state of the population to be a fixed point or a zero point of the F-quadratic stochastic operator which corresponds to the F-evolution algebra. We also establish upper estimate of the ?-limit set of the trajectory of the operator. For an F-evolution algebra of Volterra type we describe the full set of idempotent elements and the full set of absolute nilpotent elements.

scholarly journals Regularity of Geometric quadratic stochastic operator generated by 2-partition of infinite points

2020 ◽  
Vol 16 (3) ◽  
pp. 281-285
Author(s):  
Siti Nurlaili Karim ◽  
Nur Zatul Akmar Hamzah ◽  
Nasir Ganikhodjaev
Keyword(s):  
Fixed Point ◽  
State Space ◽  
Unique Fixed Point ◽  
Limiting Behavior ◽  
Countable State Space ◽  
Quadratic Stochastic Operator ◽  
Stochastic Operator ◽  
Countable State ◽  
Regular Transformation

In this research, we construct a class of quadratic stochastic operator called Geometric quadratic stochastic operator generated by arbitrary 2-partition  of infinite points on a countable state space , where . We also study the limiting behavior of such operator by proving the existence of the limit of the sequence  through the convergence of the trajectory to a unique fixed point. It is established that such operator is a regular transformation.

scholarly journals THE ASYMPTOTIC BEHAVIOR OF TRAJECTORIES OF DISSIPATIVE QUADRATIC STOCHASTIC OPERATORS ON 2D SIMPLEX

2012 ◽  
Vol 09 ◽  
pp. 293-298
Author(s):  
FARRUH SHAHIDI ◽  
ABU OSMAN MD TAP
Keyword(s):  
Fixed Point ◽  
Asymptotic Behavior ◽  
Fixed Points ◽  
Unique Fixed Point ◽  
Limit Behavior ◽  
Quadratic Stochastic Operator ◽  
Stochastic Operator ◽  
Quadratic Stochastic Operators ◽  
The Face

In the present paper we study limit behavior of dissipative quadratic stochastic operators on 2D simplex. We show that dissipative quadratic stochastic operator, which is not linear, is either regular or has infinitely many fixed points. If dissipative quadratic stochastic operator is regular, it is shown that its unique fixed point is either a vertex of the simplex or the center of the face of the simplex.

EXISTENCE OF SOLUTION FOR A VOLTERRA TYPE INTEGRAL EQUATION USING DARBO-TYPE F-CONTRACTION

2021 ◽  
Vol 10 (6) ◽  
pp. 2687-2710
Author(s):  
F. Akutsah ◽  
A. A. Mebawondu ◽  
O. K. Narain
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Existence Of Solution ◽  
Volterra Type ◽  
Complete Metric Spaces ◽  
Type Integral ◽  
New Type

In this paper, we provide some generalizations of the Darbo's fixed point theorem and further develop the notion of $F$-contraction introduced by Wardowski in (\cite{wad}, D. Wardowski, \emph{Fixed points of a new type of contractive mappings in complete metric spaces,} Fixed Point Theory and Appl., 94, (2012)). To achieve this, we introduce the notion of Darbo-type $F$-contraction, cyclic $(\alpha,\beta)$-admissible operator and we also establish some fixed point and common fixed point results for this class of mappings in the framework of Banach spaces. In addition, we apply our fixed point results to establish the existence of solution to a Volterra type integral equation.

scholarly journals Extended partial b-metric spaces and some fixed point results

Filomat ◽  
2018 ◽  
Vol 32 (8) ◽  
pp. 2837-2850 ◽  
Author(s):  
V. Parvaneh ◽  
Z. Kadelburg
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Metric Spaces ◽  
Volterra Type ◽  
Fundamental Lemma ◽  
Contractive Mappings ◽  
Type Integral ◽  
Convergence Of Sequences ◽  
Weakly Contractive

In this paper, we introduce the concept of extended partial b-metric space. We demonstrate a fundamental lemma for the convergence of sequences in such spaces. Then we prove some fixed point results for weakly contractive mappings in the setup of ordered extended partial b-metric spaces. An example is given to verify the effectiveness and applicability of our main results. An application of these results to Volterra-type integral equations is provided at the end.

On solutions of a stochastic integral equation of the volterra type with applications for chemotherapy

1988 ◽  
Vol 25 (02) ◽  
pp. 257-267 ◽  
Author(s):  
D. Szynal ◽  
S. Wedrychowicz
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Stochastic Model ◽  
Asymptotic Behaviour ◽  
Existence Of Solutions ◽  
Stochastic Integral ◽  
Volterra Type ◽  
Stochastic Integral Equation

This paper deals with the existence of solutions of a stochastic integral equation of the Volterra type and their asymptotic behaviour. Investigations of this paper use the concept of a measure of non-compactness in Banach space and fixed-point theorem of Darbo type. An application to a stochastic model for chemotherapy is also presented.

Non-linear matrix integral equations of Volterra type in queueing theory

1973 ◽  
Vol 10 (03) ◽  
pp. 644-651 ◽  
Author(s):  
Peter Purdue
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Unique Solution ◽  
Queueing Theory ◽  
Branching Process ◽  
Linear Matrix ◽  
Volterra Type ◽  
Matrix Integral ◽  
Non Linear

The use of a branching process argument in complex queueing situations often leads to a discussion of a non-linear matrix integral equation of Volterra type. By the use of a fixed point theorem we show these equations have a unique solution.

Conditions for the Uniqueness of the Fixed Point in Kakutani's Theorem

1981 ◽  
Vol 24 (3) ◽  
pp. 351-357 ◽  
Author(s):  
Helga Schirmer
Keyword(s):  
Fixed Point ◽  
Euclidean Space ◽  
Convex Set ◽  
Necessary Conditions ◽  
Unique Fixed Point

AbstractKakutani's Theorem states that every point convex and use multifunction ϕ defined on a compact and convex set in a Euclidean space has at least one fixed point. Some necessary conditions are given here which ϕ must satisfy if c is the unique fixed point of ϕ. It is e.g. shown that if the width of ϕ(c) is greater than zero, then ϕ cannot be lsc at c, and if in addition c lies on the boundary of ϕ(c), then there exists a sequence {xk} which converges to c and for which the width of the sets ϕ(xk) converges to zero. If the width of ϕ(c) is zero, then the width of ϕ(xk) converges to zero whenever the sequence {xk} converges to c, but in this case ϕ can be lsc at c.

scholarly journals Dislocated quasi cone b-metric space over Banach algebra and contraction principles with application to functional equations

2019 ◽  
Vol 17 (1) ◽  
pp. 1065-1081
Author(s):  
Reny George ◽  
Hossam A. Nabwey ◽  
Jelena Vujaković ◽  
R. Rajagopalan ◽  
Selva Vinayagam
Keyword(s):  
Fixed Point ◽  
Banach Algebra ◽  
Common Fixed Point ◽  
Metric Space ◽  
Functional Equations ◽  
Fixed Point Theorems ◽  
Identical Pair ◽  
Common Fixed Point Theorems

Abstract In this paper we introduce dislocated and dislocated quasi version of a cone b-metric space over a Banach algebra as well as weak semi α-admissible and α-identical pair of mappings and prove common fixed point theorems for a pair of α-identical and weak α-admissible mappings in the aforesaid spaces. Our results are supported with suitable examples and an application to a system of m-tupled functional equations.

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