Abstract In this article, we present several Geršhgorin-type theorems for Z 1 {Z}_{1} -eigenvalues of tensors, which improve the results provided by Wang et al. (Some upper bounds on Z t {Z}_{t} -eigenvalues of tensors, Appl. Math. Comput. 329 (2018), 266–277). Bounds for the largest Z 1 {Z}_{1} -eigenvalue of nonnegative tensors are given. Furthermore, based on the Geršhgorin-type theorems, we introduce some sufficient criteria for the positivity of even order tensors.

Abstract Narayana numbers are well-known and have many applications in the field of combinatorics. The Narayana numbers form a triangular array, where the sum of the nth row is the nth Catalan number. Here we normalize the Narayana numbers by dividing each entry in the nth row by the nth Catalan number. Now each row of these normalized Narayana numbers defines a discrete probability distribution. We investigate two new properties of these normalized Narayana numbers: instead of summing along the rows, we derive the limit of the sums along the columns and the limit of the sums along the short diagonals.

Abstract The circular Pythagorean fuzzy set is an expansion of the circular intuitionistic fuzzy set (CIFS), in which each component is represented by a circle. Nevertheless, even though CIFS improves the intuitionistic fuzzy set representation, it is still restricted to the inflexible intuitionistic fuzzy interpretation triangle (IFIT) space, where the square sum of membership and nonmembership in a circular Pythagorean fuzzy environment and the sum of membership and nonmembership in a circular intuitionistic fuzzy environment cannot exceed one. To overcome this restriction, we provide a fresh extension of the CIFS called the circular n,m -rung orthopair fuzzy set (C n,m -ROFS), which allows the IFIT region to be expanded or contracted while maintaining the features of CIFS. Consequently, decision makers can assess items over a wider and more flexible range when using a C n,m -ROFS, allowing for the making of more delicate decisions. In addition, we define several basic algebraic and arithmetic operations on C n,m -ROFS, such as intersection, union, multiplication, addition, and scalar multiplication, and we discuss their key characteristics together with some of the known relations over C n,m -ROFS. In addition, we present and study the new circular n,m -rung orthopair fuzzy weighted average/geometric aggregation operators and their properties. Further, a strategy for resolving multicriteria decision-making problems in a C n,m -ROF environment is provided. The suggested strategy is tested on two situations: the best teacher selection problem and the best school selection problem. To confirm and illustrate the efficacy of the suggested methodology, a comparative analysis with the intuitionistic fuzzy weighted average, intuitionistic fuzzy weighted geometric, q-rung orthopair fuzzy weighted averaging, q-rung orthopair fuzzy geometric averaging, circular PFWA max {{\rm{PFWA}}}_{{\rm{\max }}} , and circular PFWA min {{\rm{PFWA}}}_{{\rm{\min }}} operators approaches is also carried out. Ultimately, in the final section, there are discussions and ideas for future research.

Abstract This paper is concerned with an asymptotic equation which models uni-directional and weakly nonlinear waves for the variational sine-Gordon equation describing the motion of long waves on a neutral dipole chain in the continuum limit. Based on the Young measure theory, we prove the global existence of dissipative weak solutions to its initial-boundary problem by establishing the precompactness of the viscosity approximate solution sequence. The convergence rate of the vanishing viscosity approximations is also estimated.

Abstract In this work, we prove some fixed point results in generalized Banach spaces ( G B S {\mathfrak{G}}{\mathfrak{B}}{\mathfrak{S}} s) in the sense of Perov using the vector degree of nondensifiability tools. The given result generalizes Darbo’s and Krasnoselskii’s theorems, which are connected with the vector measure of noncompactness. An existence result for coupled Caputo fractional delay differential equations in the G B S C ( [ − τ , T ] , R ) × C ( [ − τ , T ] , R ) {\mathfrak{G}}{\mathfrak{B}}{\mathfrak{S}}\hspace{0.33em}{\mathcal{C}}\left(\left[-\tau ,T],{\mathbb{R}})\times {\mathcal{C}}\left(\left[-\tau ,T],{\mathbb{R}}) is given to show the significance and the applicability of our theoretical results.

Abstract In this study, we introduce a kind of Stancu variant of the complex Bernstein-Durrmeyer-type operators in movable compact disks. Their approximation properties for analytic functions in the movable compact disks are investigated.

Abstract This research aims to derive novel soliton solutions for a complex hyperbolic Schrödinger equation with a truncated M-fractional derivative. The selected equation is pivotal for its application in modeling various physical phenomena, such as nonlinear wave propagation in optical fibers and plasma physics, where conventional methods may fall short. We employed the modified generalized Kudryashov method and the modified exponential function method to obtain these solutions. These methods were chosen due to their effectiveness in solving nonlinear partial differential equations and their novelty in the context of this equation. The solutions obtained are stable solitons, localized wave packets that maintain their shape while propagating, and they are represented through trigonometric and hyperbolic functions. These solutions are significant for their potential applications in understanding and predicting wave behavior in optical and plasma systems. Additionally, we utilized software to analyze the wave functions, generating 3-D and 2-D contour plots based on specific parameters. These visualizations are essential for comprehending the solutions’ physical configurations and dynamic processes in practical scenarios. The results confirm that the proposed methods are efficient for the analytic treatment of a wide variety of nonlinear partial differential equations with truncated M-fractional derivatives, enhancing our ability to model and analyze complex physical systems.

Abstract In this paper, we establish the sharp Fekete–Szegö inequalities of functional type over a new class of holomorphic mappings on the unit ball in a complex Banach space. This class includes some important widely studied classes. We offer simpler proofs and require less restrictive assumptions than those found in recent literature. Finally we show that some important previous results follows from ours by choosing suitable parameters.

Abstract In this article, we present two new algorithms referred to as the improved modified gradient-based iterative (IMGI) algorithm and its relaxed version (IMRGI) for solving the complex conjugate and transpose (CCT) Sylvester matrix equations, which often arise from control theory, system theory, and so forth. Compared with the gradient-based iterative (GI) (A.-G. Wu, L.-L. Lv, and G.-R. Duan, Iterative algorithms for solving a class of complex conjugate and transpose matrix equations, Appl. Math. Comput. 217 (2011), 8343–8353) and the relaxed GI (RGI) (W.-L. Wang, C.-Q. Song, and S.-P. Ji, Iterative solution to a class of complex matrix equations and its application in time-varying linear system, J. Appl. Math. Comput. 67 (2021), 317–341) algorithms, the proposed ones can make full use of the latest information and need less computations, which leads to higher computational efficiency. With the real representation of a complex matrix as a tool, we establish sufficient and necessary conditions for the convergence of the IMGI and the IMRGI algorithms. Finally, some numerical examples are given to illustrate the effectiveness and advantages of the proposed algorithms.

Abstract In this article, we study the inviscid limit of the solution to the Cauchy problem of a one-dimensional viscous conservation law, where the second-order term is nonlinear. Under the assumption that the inviscid equation admits a piecewise smooth solution with two noninteracting entropy shocks, we prove that the solution of the viscous equation converges uniformly to the piecewise smooth inviscid solution away from the shocks, even the strength of shocks is not small.