Saber Mansour

We establish the existence and uniqueness of solutions to a class of second-order nonlinear boundary value problems involving impulses, delay, and possible singularities. The approach leverages the recent notion of paired-Chatterjea-type contractions. Under a smallness condition ensuring the associated integral operator is a Banach contraction with constant $\mu <{\displaystyle \frac{1}{3}}$, we show that it is also a Chatterjea, and hence, a paired-Chatterjea contraction. By the fixed point theorem of Chand, this guarantees at most two fixed points; a supplementary uniqueness argument then ensures a unique solution in the Banach space $P{C}^1\left([a,b]\right)$.

In this paper, we study the irreducibility of polynomials of the form \( f(X) + p^k g(X) \), where \( f(X) \) and \( g(X) \) are polynomials with integer coefficients, \( p \) is a prime number, and \( k \) is a positive integer. Unlike previous results, we do not require \( f(X) \) and \( g(X) \) to be relatively prime or impose any conditions on \( \gcd(k, \deg g) \). We prove that, for all but finitely many primes \( p \), the polynomial \( f(X) + p^k g(X) \) is either irreducible over \( \mathbb{Q} \) or factors into polynomials whose degrees are multiples of \( \gcd(k, \deg g) \). This generalizes and extends earlier work on the irreducibility of such polynomials.

In the following numerical novel, we develop a new fractional integral operator that incorporates polynomials \(n\)-fractional with \(s\)-like preinvexity, thus expanding the notion of fractional calculus. This new operator provides a more comprehensive framework for examining the behavior of functions exhibiting generalized preinvexity properties which are crucial in many optimization problems. We investigate the existence, uniqueness, and stability of this fractional integral as well as its basic characteristics. In addition, we provide a number of inequalities that show how useful this operator is in the context of applied sciences and mathematical analysis. Our results not only advance the theory of fractional calculus but also pave the way for future investigations into integral inequalities and fractional optimization.

The aims of this paper are (a) to introduce the concept of the 0-complete m-metric spaces, (b) to obtain the results for $m^w$-Caristi mapping using Kirk’s approach, (c) to investigate the problem of non-cooperative equilibrium (abbreviated as NCE) in two- and three-person games in the structure of game theory and find the solution by employing coupled and tripled fixed-point results within the framework of 0-complete m-metric spaces (m-metric spaces, respectively), and (d) to establish some coupled fixed-point results which extend the scope of metric fixed point theory. We provide some examples to support the concepts and results presented in this paper. As an application of our results in this paper, we obtain the existence of a solution for a nonlinear integral equation.

This paper performed an investigation into the s-embedding of the Lie superalgebra $\overrightarrow{(}{S}^{1\mid 1})$, a representation of smooth vector fields on a (1,1)-dimensional super-circle. Our primary objective was to establish a precise definition of the s-embedding, effectively dissecting the Lie superalgebra into the superalgebra of super-pseudodifferential operators ( $S\psi D\odot$) residing on the super-circle $S^{1|1}$. We also introduce and rigorously define the central charge within the framework of $\overrightarrow{(}{S}^{1\mid 1})$, leveraging the canonical central extension of $S\psi D\odot$. Moreover, we expanded the scope of our inquiry to encompass the domain of fuzzy Lie algebras, seeking to elucidate potential connections and parallels between these ostensibly distinct mathematical constructs. Our exploration spanned various facets, including non-commutative structures, representation theory, central extensions, and central charges, as we aimed to bridge the gap between Lie superalgebras and fuzzy Lie algebras. To summarize, this paper is a pioneering work with two pivotal contributions. Initially, a meticulous definition of the s-embedding of the Lie superalgebra $\overrightarrow{(}{S}^{1|1})$ is provided, emphasizing the representationof smooth vector fields on the (1,1)-dimensional super-circle, thereby enriching a fundamental comprehension of the topic. Moreover, an investigation of the realm of fuzzy Lie algebras was undertaken, probing associations with conventional Lie superalgebras. Capitalizing on these discoveries, we expound upon the nexus between central extensions and provide a novel deformed representation of the central charge.

In this manuscript, using the idea of $ b $-simulation functions, certain common fixed point results via generalized $ \Im_b $-contractions are investigated in the context of b-metric spaces. These findings generalize and supplement various numbers of established results from the existing literature. Examples and applications are also provided for the authenticity of the presented work. Besides, we ensure the existence of a unique common solution for systems of Volterra-Hammerstein integral and Urysohn integral equations, respectively, by applying the established results.

In this manuscript, we give strong convergence results for a fixed point of a subfamily of an evolution family on a convex and closed subset $ \mathcal{D} $ of a Banach space $ \mathsf{B} $. An example is also provided which shows the applications of evolution families and our main results. At the end, an open problem is given.

In this article, the notion of Hausdorff fuzzy $ b $-metric space is studied. Some fixed point results for multivalued mappings using Geraghty type contractions in $ G $-complete fuzzy $ b $-metric spaces are established. To strengthen the results, an illustrative example is furnished. A fuzzy integral inclusion is constructed as an application of fixed point result which shows the validity of the proved results. The presented outcomes are the generalization of the existing results in literature.