scholarly journals Trajectories of set valued integrals

1985 ◽  
Vol 31 (3) ◽  
pp. 389-411 ◽  
Author(s):  
Nikolaos S. Papageorgiou
Keyword(s):  
Banach Space ◽  
Mosco Convergence ◽  
Convergence And Stability ◽  
Algebraic Properties ◽  
Stability Results ◽  
Convergence Of Sets

The purpose of this paper is to study the trajectory multifunction Φ(·) determined by the indefinite set valued integral of a measurable Banach space valued multifunction F(·), that is for all t ∈ [0, T], , where the set valued integral is interpreted in the sense of Aumann. We study the topological and algebraic properties of SΦ equaling the set of selectors of Φ(·) whose primitive is an integrable selector of F(·). We also determine several useful properties that Φ(·) possesses and finally we present some convergence and stability results using the Kuratowski-Mosco convergence of sets.

scholarly journals Convergence theorems for Banach space valued integrable multifunctions

1987 ◽  
Vol 10 (3) ◽  
pp. 433-442 ◽  
Author(s):  
Nikolaos S. Papageorgiou
Keyword(s):  
Banach Space ◽  
Convergent Sequence ◽  
Mosco Convergence ◽  
Convergence Theorems ◽  
Aumann Integral ◽  
Convergence Results ◽  
Measurable Multifunctions ◽  
Dominated Convergence ◽  
Convergence Of Sets

In this work we generalize a result of Kato on the pointwise behavior of a weakly convergent sequence in the Lebesgue-Bochner spacesLXP(Ω) (1≤p≤∞). Then we use that result to prove Fatou's type lemmata and dominated convergence theorems for the Aumann integral of Banach space valued measurable multifunctions. Analogous convergence results are also proved for the sets of integrable selectors of those multifunctions. In the process of proving those convergence theorems we make some useful observations concerning the Kuratowski-Mosco convergence of sets.

scholarly journals Properties of the trajectories of set-valued integrals in banach spaces

1990 ◽  
Vol 41 (2) ◽  
pp. 271-281
Author(s):  
Nikolaos S. Papageorgiou
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Separable Banach Space ◽  
Hausdorff Metric ◽  
Density Theorem ◽  
Mosco Convergence ◽  
Convexity Theorem ◽  
Convergence Theorems ◽  
Convergence Of Sets ◽  
Differentiability Properties

Let F: T → 2x \ {} be a closed-valued multifunction into a separable Banach space X. We define the sets and We prove various convergence theorems for those two sets using the Hausdorff metric and the Kuratowski-Mosco convergence of sets. Then we prove a density theorem of CF and a corresponding convexity theorem for F(·). Finally we study the “differentiability” properties of K(·). Our work extends and improves earlier ones by Artstein, Bridgland, Hermes and Papageorgiou.

scholarly journals Some results of the Picard-Krasnoselskii hybrid iterative process

Filomat ◽  
2019 ◽  
Vol 33 (2) ◽  
pp. 359-365
Author(s):  
Aynur Şahin
Keyword(s):  
Banach Space ◽  
Functional Equation ◽  
Strong Convergence ◽  
Hyperbolic Space ◽  
General Class ◽  
Iterative Process ◽  
Convergence And Stability ◽  
Stability Results

In this paper, we establish the strong convergence and stability results of Picard-Krasnoselskii hybrid iterative process for a general class of contractive-like operators in a hyperbolic space. Additionally, we apply this iterative process to obtain the solution of a functional equation in a Banach space.

scholarly journals Convergence and Stability Results of Modified CUIA Iterative Scheme for Hyperbolic Convex Metric space

2021 ◽  
Vol 2089 (1) ◽  
pp. 012040
Author(s):  
Surjeet Singh Chauhan Gonder ◽  
Khushboo Basra
Keyword(s):  
Fixed Points ◽  
Integral Equations ◽  
Metric Space ◽  
Iterative Scheme ◽  
Real Life ◽  
Convex Metric Space ◽  
Convergence And Stability ◽  
Life Problems ◽  
Stability Results ◽  
Differential And Integral Equations

Abstract The iterative fixed points have numerous applications in locating the solution of some real-life problems which can be modelled into linear as well as nonlinear differential and integral equations. In this manuscript, first of all, a new iterative scheme namely Modified CUIA iterative scheme is introduced. We first prove a theorem to check the convergence of this iteration for Hyperbolic Convex metric space. The result is then supported with one example. Further, another theorem is proved establishing the weak T stability of modified CUIA iterative scheme on the above space.

scholarly journals Nonlinear Evolution Equations with Exponentially Decaying Memory: Existence via Time Discretisation, Uniqueness, and Stability

2020 ◽  
Vol 20 (1) ◽  
pp. 89-108 ◽  
Author(s):  
André Eikmeier ◽  
Etienne Emmrich ◽  
Hans-Christian Kreusler
Keyword(s):  
Banach Space ◽  
Integral Operator ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Inner Product ◽  
Initial Value ◽  
Time Discretisation ◽  
Volterra Integral Operator ◽  
Stability Results

AbstractThe initial value problem for an evolution equation of type {v^{\prime}+Av+BKv=f} is studied, where {A:V_{A}\to V_{A}^{\prime}} is a monotone, coercive operator and where {B:V_{B}\to V_{B}^{\prime}} induces an inner product. The Banach space {V_{A}} is not required to be embedded in {V_{B}} or vice versa. The operator K incorporates a Volterra integral operator in time of convolution type with an exponentially decaying kernel. Existence of a global-in-time solution is shown by proving convergence of a suitable time discretisation. Moreover, uniqueness as well as stability results are proved. Appropriate integration-by-parts formulae are a key ingredient for the analysis.

scholarly journals Convergence and Stability of New Approximation Algorithms for Certain Contractive-Type Mappings

2021 ◽  
Vol 2 ◽  
pp. 1
Author(s):  
Imo Kalu Agwu ◽  
Donatus Ikechi Igbokwe
Keyword(s):  
Approximation Algorithms ◽  
Fixed Points ◽  
Iterative Scheme ◽  
Type Condition ◽  
Iterative Schemes ◽  
Convergence And Stability ◽  
Contractive Type ◽  
Stability Results

We present new fixed points algorithms called multistep H-iterative scheme and multistep SH-iterative scheme. Under certain contractive-type condition, convergence and stability results were established without any imposition of the ’sum conditions’, which to a large extent make some existing iterative schemes so far studied by other authors in this direction practically inefficient. Our results complement and improve some recent results in literature.

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