In this paper, we introduce the notion of a rectangular S-b-metric space which extends the rectangular metric space given by Branciari [3]. We establish some fixed point theorems in this new structure. We provide some applications of our results in differential and integral equations.
In this paper, we consider the Korteweg-de Vries equation with internal time-varying delay feedback. We prove exponential stability results using an appropriate Lyapunov functional, without imposing any assumptions on the length of the spatial domain. Finally, we present numerical simulations to illustrate the stability results obtained.
Two fixed point theorems for alpha-admissible mappings satisfying contractive conditions of integral type with w-distance in a complete metric space are demonstrated. The results obtained in this paper improve and generalize some well-known results in the literature. An example is given.
In the present work, using the Matkowski type contraction, we discuss the existence of fixed point results within the framework of orthogonal c-metric spaces. Our results extend and generalize several well-known findings that are already present in the literature. Furthermore, as an application, we investigate solution to a nonlinear integral equation.
This paper investigates fixed point theorems in bipolar R-metric space by introducing the concepts of F-R-contractive and F-R-expansive maps. We first establish a fixed point theorem for F-R-contractive map, then extend our results to F-R-expansive map. Our findings reveal that under certain conditions, these results can be reduced to novel fixed point results for expansive maps in bipolar metric space. This aligns with existing literature, underscoring the relevance, and applicability of our findings in broader contexts.
In the present work, using generalized k-Fibonacci numbers, generalized k-Fibonacci points on the plane are constructed. Applying inverse stereographic projection (ISP), the images of these points and their recurrence relations on the sphere are obtained. Rotation of the special generalized k-Fibonacci points located on the positive x-axis is considered, and the relation between the ISPs of those points is derived. As a further application, the generalized k-Fibonacci curve, which passes through the generalized k-Fibonacci points, is considered. Under the ISP, the images of these curves, which form spherical spirals, are obtained. Moreover, two different types of deformations are employed, the first one is the deformation of the curves and the second one is the deformation of the surfaces. In the first case, it is shown that there exist special forms of deformation such that, after the deformation of the generalized k-Binet-Fibonacci spirals, they still pass through the generalized k-Fibonacci points. In the second case, the deformation of the sphere itself is examined. With the help of this new type of deformation, k-Fibonacci points and generalized k-Binet-Fibonacci spirals are transformed onto various new deformed spherical geometries. The mathematical background of all these procedures is explicitly established, and illustrative cases such as spheroidal and pinecone-shaped deformed spherical objects are analyzed in detail.
In this paper, we explore a property of polynomial operators related to a question first posed by Walter Rudin, a distinguished mathematician famous for his textbooks on Mathematical Analysis. The original question was whether surjective bilinear operators on complex spaces, like their linear counterparts, are necessarily open at the origin. This question took just over 50 years to be completely answered (see Introduction), but similar questions remain for the more general class of polynomial operators. In particular, we show that polynomial operators, unlike their bilinear cousins, do not have an open mapping theorem, except for the case where the range has dimension 1. We also consider the topic of Repelling Points for polynomial operators, which is related to the existence or nonexistence of an open mapping theorem, and see how this notion further distinguishes the general class of polynomial operators from multilinear operators.
The purpose of this short note is to present a new generalization of Bolzano's and Darboux's Intermediate Value Theorems.
In this paper, we introduce a modified form of fuzzy numbers and investigate its implications for the Hyers-Ulam stability of the following generalized fuzzy number-valued functional equation in Banach spaces: uf(ax + by) +vf(cx-dy)=rf(x) +sf(y), where f denotes a fuzzy number-valued mapping on a Banach space, a, b, c, d > 0, and u, v, r, s E R with u + v not equal 0. The obtained results extend and generalize several existing stability results for fuzzy number-valued functional equations.
In this paper, the model updating problem for quadratic asymmetric vibration systems with no spillover (MUP-QAV) is considered. The original quadratic asymmetric vibration systems are updated to new systems such that some "troublesome" eigenpairs are replaced by newly measured or given ones, while the remaining eigenpairs are kept unchanged. Firstly, some necessary and sufficient conditions are derived so that the updated system can preserve no spill-over. Then a set of parameter solutions of the MUP-QAV is characterized using only a few eigenpairs to be replaced. A gradient-based optimization algorithm is proposed for the minimum norm solution of the MUP-QAV. Finally, a necessary and sufficient condition is provided so that the sparsity structures of the system matrices and the no spill-over property are preserved simultaneously. The performance of the proposed algorithm is illustrated by some numerical examples.
Infinitely many smooth and compactly supported solutions to the steady ideal MHD equations have been constructed from some solutions of the steady incompressible Euler equations.
This paper presents generalization of a best proximity point theorem by utilizing a Suzuki-type setting, which extends Banach's contraction principle to the scenario of non-self mappings. Furthermore, our results define the completeness of the metric space with some different sufficient conditions.
This paper seeks to establish a comprehensive analysis of zero-free regions for lacunary type polynomials. These polynomials have coefficients with specific constraints, either concerning their real and imaginary parts. Additionally, the study aims to determine bounds on the number of zeros within a designated annular region.
In this work, we consider a regularized sinc-collo cation method for solving Fredholm integral equations of the first kind, which is known to be an ill-posed problem. This numerical method is a combination of the Sinc-Collo cation method with a Tikhonov regularization procedure. We show the convergence results of this new technique, and we give some numerical examples to demonstrate the validity and applicability of the proposed method.
The dynamics of CD4(+)T cells and infected virus particles are described by a system of nonlinear ordinary differential equations and that mathematical model describes the behaviour of states for HIV infections in the presence of immune boosting nutrition and antiretroviral drugs. In this study, the constant control strategies are introduced for comparison with the optimal control strategy to minimize the treatment cost of HIV infections. The aim of this paper is to find the optimal immunotherapeutic treatment and compare them to various treatment strategies of HIV infections.
Some new types of special curves, such as xi(-)-helix, xi(-)(1)-helix, & micro;(-)-helix, nu(-)-helix and Wk-Darboux helices in the Myller configuration M(C, xi(-), pi) are defined and studied where k is an element of {n, r, o}. The necessary and sufficient conditions for a curve in M(C,xi(-) , pi) to be classified as a special helix are established. Additionally, the axes of these helices are presented, and the relationships between them are discussed.
Let G be a graph with no isolated vertices. A k-coupon coloring of G is an assignment of colors from [k] = {1, 2, ... , k} to the vertices of G such that the neighborhood of every vertex of G contains vertices of all colors from [k]. The maximum k for which a k-coupon coloring exists is called the coupon coloring number of G, and is denoted by chi(c)(G). In this paper, we investigate the coupon coloring of graphs generated by applying various unary operations on various graph classes.
In this study, we aim to convert a given doubly substochastic matrix A into a semi doubly stochastic matrix D by adding some columns. We show that by adding a minimum (cardinal) number of columns, a doubly substochastic matrix A is transformed into a semi doubly stochastic matrix D. Such a minimum cardinality is called the semi sub-defect of A. Additionally, we obtain a general formula for the semi sub-defect of I x J doubly substochastic matrices. Our findings also demonstrate that for any increasable matrix A, the semi sub-defects of A and its transpose, A(t), are equal.
This article discusses the solvability of a weakly singular integral equation with a logarithm kernel. These equations are defined within the function space C[0,l], which consists of real-valued functions. The primary methodological framework employed in our proofs is the concept of a measure of noncompactness in conjunction with the theorem of Petryshyn. Furthermore, we illustrate the practical significance of our findings by presenting a series of applications related to nonlinear singular integral equations. These examples serve to demonstrate the efficacy and applicability of our theoretical results, thereby contributing to the broader understanding of such integral equations in mathematical analysis.
We prove a necessary optimality condition of Euler-Lagrange type for the calculus of variations with Omega derivatives, which turns out to be sufficient under joint convexity of the Lagrangian.
