Fixed point theorems of Rothe and Altman types about convex-power condensing operator and application

Zhang, Guowei; Zhang, Tongshan; Zhang, Tie

doi:10.1016/j.amc.2009.04.033

Cited by 8 publications

(5 citation statements)

References 14 publications

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“…In [25], Sun and Zhang introduced the definition of convex-power condensing operator with respect to the Kuratowski measure of noncompactness and proved a fixed point theorem which extended the well-known Sadovskii's fixed point theorem and a fixed point theorem in Liu et al [21]. In [26], G. Zhang et al established some fixed point theorems of Rothe and Altman types about convex-power condensing operators with respect to the Kuratowski measure of noncompactness. These results were applied to a differential equation of one order with integral boundary conditions.…”

Section: Theorem 11 Let M Be a Nonempty Closed Convex Subset Of A Bamentioning

confidence: 97%

Sadovskii-Krasnosel’skii type fixed point theorems in Banach spaces with application to evolution equations

Ezzinbi

Taoudi

2014

J. Appl. Math. Comput.

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In this work, we introduce the concept of a convex-power condensing mapping T with respect to another mapping S as a generalization of condensing and convex-power condensing mappings. Some fixed point theorems for the sum T + S with S is a strict contraction and T is convex-power condensing with respect to S are established. The cases where S is nonexpansive or expansive are also considered. Our fixed point results encompass the well known Sadovskii's fixed point theorem and a number of its generalizations. To show the usefulness and the applicability of our fixed point results we investigate the existence of mild solutions to a broad class of neutral differential equations.

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Section: Theorem 11 Let M Be a Nonempty Closed Convex Subset Of A Bamentioning

confidence: 97%

Sadovskii-Krasnosel’skii type fixed point theorems in Banach spaces with application to evolution equations

Ezzinbi

Taoudi

2014

J. Appl. Math. Comput.

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“…(2) If we take Ω = {x 0 } with x 0 ∈ C in Definition 1.3 we obtain a multivalued version of [20] (see also [24]) for the weak topology.…”

Section: Remark 12mentioning

confidence: 99%

Fixed Point Theorems for General Classes of Maps Acting on Topological Vector Spaces

Agarwal

O’Regan

Taoudi

2011

Asian-European J. Math.

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We present new fixed point theorems for multivalued U k c -admissible maps acting on locally convex topological vector spaces. The considered multivalued maps need not be compact. We merely assume that they are weakly compact and map weakly compact sets into relatively compact sets. Our fixed point results are obtained under Schauder, Leray-Schauder and Furi-Pera type conditions. These results are useful in applications and extend earlier works.

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“…Fixed point theorems give as answer to the question whether a solution exists, i.e., a system can be steered to a final state 𝑥(𝑡 1 ) (the state 𝑥(𝑡 1 ) can be reached). Rothe's fixed point theorem has already been used in [48] for integer order nonlinear differential equation with integral boundary conditions, in [26] for semilinear system of ordinary differential equations, and in [39] for the Caputo fractional-order semilinear systems with delays in the control. The Darbo fixed point theorem has been used for studying controllability of the integer-order nonlinear differential systems in [6] and for the Caputo fractional-order nonlinear implicit systems with delays in [29].…”

Section: Introductionmentioning

confidence: 99%

On the constrained and unconstrained controllability of semilinear Hilfer fractional systems

2023

Archives of Control Sciences

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In the paper finite-dimensional semilinear dynamical control systems described by fractional-order state equations with the Hilfer fractional derivative are discussed. The formula for a solution of the considered systems is presented and derived using the Laplace transform. Bounded nonlinear function 𝑓 depending on a state and controls is used. New sufficient conditions for controllability without constraints are formulated and proved using Rothe's fixed point theorem and the generalized Darbo fixed point theorem. Moreover, the stability property is used to formulate constrained controllability criteria. An illustrative example is presented to give the reader an idea of the theoretical results obtained. A transient process in an electrical circuit described by a system of Hilfer type fractional differential equations is proposed as a possible application of the study.

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Fixed point theorems of Rothe and Altman types about convex-power condensing operator and application

Cited by 8 publications

References 14 publications

Sadovskii-Krasnosel’skii type fixed point theorems in Banach spaces with application to evolution equations

Sadovskii-Krasnosel’skii type fixed point theorems in Banach spaces with application to evolution equations

Fixed Point Theorems for General Classes of Maps Acting on Topological Vector Spaces

On the constrained and unconstrained controllability of semilinear Hilfer fractional systems

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