New fixed-point results for countably condensing operators defined on Frechet spaces axe presented. Applications to integral inclusions are also discussed. (C) 2001 Elsevier Science Ltd. All rights reserved.
New fixed-point results for countably condensing operators defined on Frechet spaces axe presented. Applications to integral inclusions are also discussed. (C) 2001 Elsevier Science Ltd. All rights reserved.
In this note, we present fixed-point results for contractive maps in the sense of Bose and Mukherjee defined on complete gauge spaces. (C) 2001 Elsevier Science Ltd. All rights reserved.
In this note, we present fixed-point results for contractive maps in the sense of Bose and Mukherjee defined on complete gauge spaces. (C) 2001 Elsevier Science Ltd. All rights reserved.
In this article, we essentially extend the Baillon fixed-point theorem from [1]. We illustrate the significance of our result by suitable example and compare it with earlier known ones. (C) 2000 Elsevier Science Ltd. ...
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In this article, we essentially extend the Baillon fixed-point theorem from [1]. We illustrate the significance of our result by suitable example and compare it with earlier known ones. (C) 2000 Elsevier Science Ltd. All rights reserved.
This article presents a survey of papers published on controllability of nonlinear systems, including nonlinear delay systems, by means of fixed-point principles.
This article presents a survey of papers published on controllability of nonlinear systems, including nonlinear delay systems, by means of fixed-point principles.
In this paper, we prove a new minimization theorem by using the generalized Ekeland variational principle. We apply our minimization theorem to obtain some fixed-point theorems. Our results extend, improve, and unify ...
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In this paper, we prove a new minimization theorem by using the generalized Ekeland variational principle. We apply our minimization theorem to obtain some fixed-point theorems. Our results extend, improve, and unify many known results due to Kui, Ekeland, Takahashi, Caristi, Ciric, and others.
We prove a fixed-point theorem that generalizes and simplifies a number of results in the theory of F-contractions. We show that all of the previously imposed conditions on the operator can be either omitted or relaxe...
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We prove a fixed-point theorem that generalizes and simplifies a number of results in the theory of F-contractions. We show that all of the previously imposed conditions on the operator can be either omitted or relaxed. Furthermore, our result is formulated in the more general context of b-metric spaces and phi-contractions. We also point out that the framework of F-contractions can be reformulated in an equivalent way that is both closer in spirit to the classical syntax of Banach-type fixedpointtheorems, and also more natural and easier to deal with in the proofs.
Lawvere's fixedpoint theorem captures the essence of diagonalization arguments. Cantor's theorem, Gödel's incompleteness theorem, and Tarski's undefinability of truth are all instances of the con...
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Lawvere's fixedpoint theorem captures the essence of diagonalization arguments. Cantor's theorem, Gödel's incompleteness theorem, and Tarski's undefinability of truth are all instances of the contrapositive form of the theorem. It is harder to apply the theorem directly because non-trivial examples are not easily found, in fact, none exist if excluded middle holds. We study Lawvere's fixed-point theorem in synthetic computability, which is higher-order intuitionistic logic augmented with the Axiom of Countable Choice, Markov's principle, and the Enumeration axiom, which states that there are countably many countable subsets of N. These extra-logical principles are valid in the effective topos, as well as in any realizability topos built over Turing machines with an oracle, and suffice for an abstract axiomatic development of a computability theory. We show that every countably generated ω-chain complete pointed partial order (ωcppo) is countable, and that countably generated ωcppos are closed under countable products. Therefore, Lawvere's fixed-point theorem applies and we obtain fixedpoints of all endomaps on countably generated ωcppos. Similarly, the Knaster-Tarski theorem guarantees existence of least fixedpoints of continuous endomaps. To get the best of both theorems, namely that all endomaps on domains (ωcppos generated by a countable set of compact elements) have least fixedpoints, we prove a synthetic version of the Myhill-Shepherdson theorem: every map from an ωcpo to a domain is continuous. The proof relies on a new fixed-point theorem, the synthetic Recursion Theorem, so called because it subsumes the classic Kleene-Rogers Recursion Theorem. The Recursion Theorem takes the form of Lawvere's fixedpoint theorem for multi-valued endomaps.
This article explores the stochastic predator-prey model. This model offers a probabilistic framework for understanding the dynamics of interacting species. The stochastic predator-prey model is a practical tool for p...
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This article explores the stochastic predator-prey model. This model offers a probabilistic framework for understanding the dynamics of interacting species. The stochastic predator-prey model is a practical tool for predicting the intricate balance of survival between predators and their prey in the face of nature's unpredictability. This study introduces a new measure of noncompactness and applies it to investigate solutions in nonlinear stochastic equations. Additionally, we present a numerical method using block pulse functions and demonstrate its convergence through the new measure of noncompactness for solving the system of stochastic integrals. Finally, the proposed method is employed to solve a numerical example.
This research article deals with stochastic dynamical systems governed by fractional order stochastic anti-periodic boundary value problems with Poisson-jump. We consider two systems which involve Caputo derivative an...
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This research article deals with stochastic dynamical systems governed by fractional order stochastic anti-periodic boundary value problems with Poisson-jump. We consider two systems which involve Caputo derivative and generalized Caputo derivative. We give some sufficient conditions for the existence and uniqueness of the solution for considered systems via fixedpoint technique. We present an application in the form of an example and validate the conditions with the help of numerical simulation.
We prove a variety of fixed-point theorems for groups acting on CAT(0) spaces. fixedpoints are obtained by a bootstrapping technique, whereby increasingly large subgroups are proved to have fixedpoints: specific con...
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We prove a variety of fixed-point theorems for groups acting on CAT(0) spaces. fixedpoints are obtained by a bootstrapping technique, whereby increasingly large subgroups are proved to have fixedpoints: specific configurations in the subgroup lattice of Γ are exhibited and Helly-type theorems are developed to prove that the fixed-point sets of the subgroups in the configuration intersect. In this way, we obtain lower bounds on the smallest dimension FixDim ( Γ ) + 1 in which various groups of geometric interest can act on a complete CAT(0) space without a global fixedpoint. For automorphism groups of free groups, we prove FixDim ( Aut ( F n ) ) ≥ ⌊ 2 n / 3 ⌋ .
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