Quantifying uncertainty in robust datasets is essential in decision analysis. Merging such data with the concepts of information theory opens various aspects of uncertainty. The additional degree of uncertainty can be addressed by picture fuzzy divergences. This study precisely handles such datasets by introducing a novel picture fuzzy divergence measure (PFDM) using generalized f-divergence. The validity of the measure has been proved, and some properties are discussed. Furthermore, some information inequalities are established for classical dissimilarity measures. These inequalities offer critical mathematical boundaries for analyzing and comparing various fuzzy information measures. Additionally, the application of the measure is discussed for market behaviour trends and pattern recognition problems. The obtained results aims to minimize the divergence and maximize the result accuracy and the measures successfully quantify the variations within fuzzy sets.
This paper investigates the strong convergence of Noor iteration for nonexpansive operators in $L^p$ spaces, where $1 < p < \infty$. By exploiting the $p$-uniform convexity of $L^p$, we derive explicit $p$-dependent constants in the asymptotic regularity inequalities and obtain quantitative convergence rates. We establish sufficient conditions for strong convergence, including the case of affine operators, demi-compact operators, and norm convergence. As an application, we analyze the $p$-Laplace equation for $p>1$ and validate our theoretical findings through comprehensive numerical experiments. The numerical results demonstrate the efficiency of the method and the importance of parameter selection across different nonlinearity regimes. Our work provides a quantitative refinement of known results in the literature and offers practical insights for solving nonlinear partial differential equations.
This paper studies a Hartree-type wave equation featuring a distributed delay term and memory effects governed by a past history. The problem is formulated with coupling through fractional boundary conditions. Under suitable assumptions and for negative initial energy, we prove that solutions blow up in finite time.
This paper aims to present a new iterative method for solving the split feasibility problem with multiple output sets for generalized demimetric mappings and solution sets of a generalized equilibrium problem in the real Banach spaces. The strong convergence of the sequence generated by our method is proven under certain conditions. We also give a numerical example to support our main result. The results of this paper extend and improve some recent corresponding results announced by many other authors.
In this paper, we deal with the asymptotic behaviour of a semiconductor Boltzmann equation by using the sigma convergence method. We first prove that the scaled model is well-posed in the usual Lebesgue space of square integrable functions, and we perform the a priori estimates. Then, assuming that the coefficients of the model are highly oscillating in space variable, we show that in the non-vanishing flux case, the homogenized problem is equivalent at first order, to a hyperbolic process modified by a perturbation of viscosity, and the diffusion term appears at second order. In the vanishing flux case, we obtain a diffusion model.
In this paper, the convergence analysis of the Chebyshev wavelet of the second kind is thoroughly carried out. Operational matrices for integration and product operations of the second kind Chebyshev wavelet are constructed, and these matrices are utilized to obtain solutions to the differential equations. A theorem related to the proposed operational matrix method is established. Solutions of the differential equations considered in this paper resemble their exact solutions. The characteristics of second kind Chebyshev wavelet are utilized to transform differential equations into systems of algebraic equations, which are solved very efficiently using a suitable method.
This paper focuses on the essential role of the quasi-conformal curvature tensor in developing the theoretical foundation and applications of quasi-contact metric geometry. The quasi-conformal curvature tensor of NC10-manifolds using the space associated with G structures (AGS-space) has been investigated. By deriving explicit expressions for the tensor components, the necessary and sufficient conditions for considering the quasi-conformal NC10-manifold as flat quasi-conformal have been determined. Noteworthy, it indicated that any flat quasi-conformal NC10-manifold is locally isometric to the product of the Ka & uml;hler manifold and the real line, thus connecting abstract tensor properties to classical geometric structures. Moreover, the conditions for the NC10-manifold that yield the ?]-Einstein structure are established. New analogues of Gray's identities for the quasi-conformal curvature tensor have been introduced for NC10-manifold.
In this paper, we propose a novel HIV/AIDS epidemic treatment model to reduce the number of HIV cases. We divide infected individuals into four compartments, that is, a compartment of infected individuals who are unaware of their HIV status and do not show any symptoms, a compartment of infected individuals who are aware of their status but do not show any symptoms, infected individuals in the asymptomatic compartment and a treatment compartment that receives infected individuals who are aware of their status, whether they are sick or not. The basic reproduction number R0 for the proposed model is computed using the next generation matrix (NGM). Using a corollary of Gershgorin's circle theorem, the results show that the disease-free equilibrium (DFE) is locally asymptotically stable (LAS) if R-0 < 1 and the endemic equilibrium (EE) is locally asymptotically stable if R-0> 1. We also proved by means of the Lyapunov method that the disease-free equilibrium is globally asymptotically stable if R-0 < 1. Finally, numerical simulations of the model are conducted to support the theoretical results and also to investigate the sensitivity of certain parameters using HIV/AIDS data from the Democratic Republic of the Congo (DRC).
The aim of this paper is to study the multipliers of Bloch-type and Zygmund-type spaces of holomorphic functions on the unit ball Bn subset of Cn. For the classical Bloch space, such multipliers were characterized by Zhu. Subsequently, Galindo and Lindstr"om extended this investigation to the infinite-dimensional setting for the specific weight omega(z) = 1-|z|2.
We develop a multiplicative/logarithmic counterpart of the convexthe scalar level, we establish comparison inequalities for strictly increasing log-convex functions on the logarithmic scale. We also record a derivative-weighted estimate expressed via the logarithmic derivative r = (log phi)', and we clarify parameter regimes where this derivative factor can improve the universal constant. Concrete applications are presented for the function tt and the Gamma function Gamma. We then extend the scalar comparison to commuting positive definite matrices under unitarily invariant norms with the universal constant v(1-v) tau(1-tau) . For the non-commuting case, we obtain "envelope" bounds via spectral pinching onto finite-dimensional abelian subalgebras, and we include a Heinz-centered quantitative estimate in the pinched abelian setting, combining a Lipschitz control for g = log o phi with the Heinz norm inequality under unitarily invariant norms.
This paper investigates a weighted Kirchhoff-type equation driven by the fractional p(x, & centerdot;)-Laplacian operator. The proposed model captures both nonlocal interactions and variable exponent effects, which naturally arise in several applied contexts. Under suitable structural assumptions, we analyze the associated nonlocal boundary value problem with Dirichlet conditions. By employing topological degree methods, we prove the existence of weak solutions, thereby extending and enriching existing results on Kirchhoff-type problems involving fractional and variable exponent operators.
This work analyzes certain features of the Karry-Kalim-Adnan transform and discusses its q-analogues in a quantum calculus theory. It discusses a number of characteristics of the q-Karry-Kalim-Adnan transform and its application to a wide range of functions, including q-trigonometric, q-hyperbolic and q-exponential functions and some q-polynomials. Moreover, it utilizes first-and second-order qinitial value problems to illustrate advantages of our proposed q-transform analogues. Over and above, the paper proves the q-convolution theorem and provides a table to further ease the q-transform technique in solving various q-initial value problems.
Based on the geometric correspondence between Lagrangian and Legendrian submanifolds, we construct Legendrian 2-submanifolds in the standard contact Euclidean Five-space R-5 satisfying the self-similarity equation H+theta xi= alpha F-perpendicular to(alpha > 0), with particular focus on their self-expander solutions under Legendrian mean curvature flow. This paper mainly generalizes Theorem C of the work by Joyce-Lee-Tsui [10].
The aim of this paper is to investigate the existence of weak solutions to the following Kirchhoff-type problem: {M([u](p )(sp)) (-triangle)(s) (p)(u) = f (x, u) in Omega u = 0 in R-n\Omega, where Omega subset of R-n , 0 < s < 1 < p
For a class of hypersingular integral operators, we establish optimal uniform bounds for their norms on the Hardy space H1(R). Our results extend the classical result of Fefferman-Stein for the phase function 1/y to phase functions of the form 1/P(y) where P is an arbitrary real polynomial. It is revealed that the presence and absence of a constant term in P play a crucial role in the outcome.
In this paper, we introduce and study hybrinomials defined by application of orthogonal polynomials. Using selected orthogonal polynomials and hybrid numbers operators, we define Hermite, Laguerre, Legendre and Chebyshev type hybrinomials and present some properties of them.
The study of blow-up phenomena in fractional diffusion equations is of great interest due to its numerous applications and the fact that these types of problems are encountered in several areas of science and engineering. This article is concerned with the blow-up solutions of a one-dimensional time-fractional heat equation, where the time derivative is defined in the sense of the Caputo fractional formula, subject to a nonlinear Neumann boundary condition of a power-type function. Firstly, global existence and blow-up are studied. Under a restricted condition on the nonlinear boundary term, it is proved that every positive solution blows up in finite time; otherwise, positive solutions are continued globally. Secondly, we prove that the blow-up phenomenon can occur only on the boundary.
We consider the problem of damping a control system with delay described by first-order functional-differential equations on a temporal tree. The delay in the system is time-proportional and propagates through the internal vertices. The problem of minimizing the energy functional with account of the probabilities of the scenarios corresponding to different edges is studied. We establish the equivalence of this variational problem to a certain boundary value problem for second-order functional-differential equations on the tree, possessing both the global contractions and the global extensions, and prove the unique solvability of both problems. In particular, it is established that the optimal trajectory obeys Kirchhoff-type conditions at the internal vertices.
Using the Lipschitz continuity of a class of viscosity solutions, we find a kind of viscosity solution for some higher-order partial differential equations containing the special Lagrangian operator. Additionally, we extend this analysis to equations that simultaneously contain the special Lagrangian and some other operators including Laplacian.
This article discuss about a numerical study to find the solution of second order reaction diffusion singular perturbation problem with non-local boundary conditions using cubic B-spline functions and collocation technique. Shishkin mesh is used to construct layer adapted meshes. The non-local boundary conditions are discretized using Trapezoidal rule. The study establishes that the discussed scheme's result is uniformly convergent up to second order in the supremum norm. To establish the efficiency of the discussed method, two numerical examples are presented along with their results in the form of tables and figures.
