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Article
Mathematics
Mohamed M. A. Metwali et al.
Summary: In this article, a new compactness criterion is proved in the Lebesgue spaces Lp(R+), 1 <= p < infinity, and this criterion is used to construct a measure of noncompactness in these spaces. The conjunction of this measure with the Hausdorff measure is also proved for sets that are compact in finite measure. By applying this measure and a modified version of the Darbo fixed point theorem, the existence of monotonic integrable solutions for n-Hammerstein integral equations (n >= 2) is proven.
TURKISH JOURNAL OF MATHEMATICS
(2023)
Article
Multidisciplinary Sciences
Ehsan Lotfali Ghasab et al.
Summary: This paper introduces the concepts of rectangular Menger probabilistic metric (RMPM) space and rectangular Menger probabilistic b-metric (RMPbM) space as generalizations of the Menger probabilistic metric space and the Menger probabilistic b-metric space, respectively. Some nonunique fixed-point and coupled-fixed-point results for contractive mappings are provided. The findings extend and improve outcomes presented in the existing literature. The main results are illustrated with examples, and validated by means of an application to a system of integral equations. The importance of spaces with non-Hausdorff topology is high, as is the case of computer science, with the Tarskian approach to programming language semantics.
Article
Mathematics
Ali Ganjbakhsh Sanatee et al.
Summary: This paper defines the concepts of phi-contraction and point-wise phi-contraction in modular metric space. It also provides some conditions to guarantee the existence and uniqueness of fixed points for self-mappings in modular metric spaces. Finally, an application to Caratheodory's type anti-periodic boundary value problem is presented.
JOURNAL OF ANALYSIS
(2023)
Article
Vijai Kumar Pathak et al.
Discontinuity, Nonlinearity, and Complexity
(2023)
Article
Mathematics, Applied
Supriya Kumar Paul et al.
Summary: In this paper, we establish the existence and uniqueness of the solution for nonlinear integral equations involving the RLFO in the Banach space C([0; beta];R) under certain conditions. The requirements for the existence and uniqueness of solutions are established using the Leray-Schauder alternative and Banach's fixed point theorem. We also analyze the H-U-R and H-U stability of the integral equations involving the RLFO in the space C([0; beta];R). Additionally, we propose an effective and efficient computational method based on Laguerre polynomials for obtaining approximate numerical solutions of these integral equations. Five examples are provided to illustrate the method.
Article
Mathematics
Radu Precup et al.
Summary: Using various mathematical theorems, the paper proves the existence of stationary solutions to Fokker-Planck equations and systems with nonlinear reaction terms. Additionally, it demonstrates through the Ekeland variational principle the uniqueness of the solution and Nash equilibrium in system cases associated with energy functionals.
POTENTIAL ANALYSIS
(2022)
Article
Mathematics
Vijai Kumar Pathak et al.
Summary: The main objective of this paper is to discover the existence of fractional order non-linear Hadamard functional integral equations on [1, a] using the theory of measure of non-compactness and fixed point theory in Banach space. An example is provided to demonstrate the validity and practicality of the proposed existence result.
Article
Mathematics, Interdisciplinary Applications
Vijai Kumar Pathak et al.
Summary: This paper investigates the existence of the solution to mixed-type non-linear fractional functional integral equations in biological population dynamics. The key findings of the article rely on theoretical concepts related to fractional calculus and the Hausdorff measure of non-compactness. The author uses Darbo's fixed-point theorem in the Banach space and provides numerical examples to demonstrate the applicability of the findings to the theory of fractional integral equations.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Applied
Lakshmi Narayan Mishra et al.
Summary: In this article, we investigate the existence of solutions for a class of nonlinear functional integral equations on the Banach space C[0, 1]. We use the technique of the generalized Darbo's fixed-point theorem associated with the measure of noncompactness (MNC) to prove our existence result. Additionally, we provide two examples of the applicability of the established existence result in the theory of functional integral equations. Furthermore, we construct an efficient iterative algorithm to compute the solution of one of the examples, using the modified homotopy perturbation (MHP) method associated with Adomian decomposition. We also present the convergence condition and an upper bound of errors.
Article
Mathematics, Applied
Ehsan Lotfali Ghasab et al.
Summary: The main purpose of this paper is to define the concept of an e-distance on a Menger PGM space, introduce its properties, and prove some coupled fixed point results in a complete PGM space. Several examples and an application are considered to support the definitions and main results.
Article
Mathematics, Applied
Shahram Banaei et al.
COMPUTATIONAL & APPLIED MATHEMATICS
(2020)
Article
Mathematics, Applied
Z. Sadeghi et al.
JOURNAL OF FIXED POINT THEORY AND APPLICATIONS
(2018)
Article
Mathematics
Xiao-lan Liu et al.
Article
Mathematics
Tayyab Kamran et al.
Article
Mathematics, Applied
Jacek Jachymski
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2010)
Article
Mathematics, Applied
Ljubomir Ciric
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2010)
Article
Mathematics, Applied
Lj. B. Ciric et al.
TOPOLOGY AND ITS APPLICATIONS
(2009)
Article
Mathematics, Applied
Binayak S. Choudhury et al.
ACTA MATHEMATICA SINICA-ENGLISH SERIES
(2008)
Article
Mathematics, Applied
D Mihet
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2005)
Article
Mathematics
H Maagli
POTENTIAL ANALYSIS
(2001)
