Bulletin of the Transilvania University of Brasov. Series III: Mathematics and Computer Science

A new hybrid conjugate gradient method as a convex combination methods

2025-06-05T12:52:36+00:00

The conjugate gradient (CG) method is a widely employed algorithm for solving large-scale unconstrained optimization problems due to its fast convergence and efficient memory usage. In this paper, we suggest a new hybrid nonlinear conjugate gradient method, which the conjugate gradient coefficient β_k is a convex combination of β_k^NPRP and β_k^DY . The parameter θ_k is computed in such a way that the conjugacy condition is satisfied. With the strong Wolfe line search, the descent property and global convergence of the new hybrid method are proved. The numerical results also show that our method is robust and efficient.

Covering C4⨁e by the same label

2025-06-05T13:09:09+00:00

In this paper we have proven a result for a covered graph with at least one subgraph C₄⨁e. We have also mentioned some observations and conditions for a graph containing C₄⨁e. An algorithm along with the flowchart, that describes the impact of covering a specified C₄⨁e with a common label is described by us.

Spatio-temporal video restoration technique using a 3d anisotropic diffusion-based scheme

2025-06-05T13:21:15+00:00

A spatio-temporal video filtering approach is proposed in this article. The video restoration technique introduced here removes successfully the signalindependent noises, such as the additive white Gaussian noise, that deteriorate the frame sequences. The proposed framework is based on a novel 3D fourth-order nonlinear reaction-diffusion model that reduces the additive white Gaussian noise (AWGN) considerably, overcomes the side-effects and deals properly with the inter-frame correlation problem. A rigorous mathematical treatment is performed on this model, its validity being investigated. A numerical approximation algorithm that solves this nonlinear partial differential equation (PDE)-based model is then provided in this paper and applied successfully in the video denoising tests that are also described here.

Existence and stability of solutions for fuzzy fractional multi-pantograph differential equations with ψ-Caputo derivative

2025-06-04T13:51:31+00:00

In the current work, we examine a novel type of fuzzy fractional multipantograph differential equations involving ψ-Caputo derivative. Firstly, we establish the existence result by using Schaefer fixed point theorem and then the uniqueness is proved by using Banach fixed point theorem. Secondly, with aid of generalized Gr¨onwall inequality, we investigative the Ulam–Hyers–Mittag-Leffler stability of solution for the problem under consideration. Lately, two examples are provided to illustrate the theoretical results.

Numerical solution for stochastic mixed nonlinear Schodinger equation

2025-06-04T14:26:12+00:00

In this paper, a numerical study of a mixed nonlinear stochastic Schr¨odinger equation in the case of an additive white noise and with mixed concaveconvex, sub-super nonlinearities is developed. The influence of the stochastic part on the deterministic solutions such as stationary states and blow-up solutions is investigated. Numerical examples are provided with error estimates.

An approach to reverse Minkowski type inequality with k-weighted fractional integral operator

2025-06-04T14:46:31+00:00

In this research, we present an innovative approach to the reverse Minkowski type inequality using the k-weighted fractional integral operator _a+J_v^ψ. This operator has two positive summation parameters, 1 ≤ p ≤ q < ∞, and our approach yields new results based on the selection of the function ψ.

Solutions for a nonlocal elliptic equation with critical Sobolev exponent and singular term

2025-06-04T14:58:33+00:00

In this paper, we consider a class of nonhomogeneous fractional elliptic equations involving critical Hardy Sobolev exponents as follows {(−Δ)su − μ u |x|2s = |u|2∗ s−2u + λ u |x|2s−α + f(x), x ∈ Ω, u = 0 x ∈ ∂Ω, where Ω ⊂ RN is a bounded domain, 0 < s < 1, λ > 0 is a parameter. We prove the existence of multiple solutions using the variational methods and the Nehari manifold decomposition.

Common fixed point via new type of implicit relations

2025-06-04T15:20:46+00:00

This paper focuses on three things. Firstly, we define a new type of implicit relations which covers a multitude of contractive conditions in one go. Secondly, we use this implicit relation to prove a new common fixed point theorem for four occasionally weakly biased maps of type (A) in a dislocated metric space. This theorem improves some results existing in the fixed point theory’s environment. Thirdly, we will provide an example to illustrate our main theorem and to expound the credibility and generality of our result.

Hermitian-Toeplitz determinants for a subclass of analytic functions

2025-06-04T15:27:54+00:00

In this study, we obtain sharp bounds for the second Hermitian- Toeplitz determinants of a subclass of analytics functions in the open unit disk.

Quantum approach on convolution of harmonic univalent mappings

2025-06-04T15:35:35+00:00

In this paper, we construct a new family of locally univalent and sensepreserving harmonic mappings T_c,q[f] by using quantum approach in the open unit disk D. We prove that the convolution of a harmonic convex mapping T_c,q[f] with a right half-plane mapping is q-convex in the direction of the real axis provided that the convolution is locally univalent and sense-preserving. Further, we show that the convolution of T_c,q[f] with a vertical strip mapping is also q-convex in the direction of the real axis. In particular, the results in this paper generalize or improve (in certain cases) the corresponding results obtained by recent researchers.

Finslerian hypersurfaces of a Finsler space with deformed Douglas infinite series metric

2025-06-05T11:33:18+00:00

In present paper we studied the geometrical properties of Finslerian hypersurfaces and its reducibility of Cartan C− tensor in various forms for a Finsler space Fⁿ equipped with deformed Infinite series metric. Further we obtained the value of main scalar I for the hypersurface in a two-dimensional case.

Coefficient bounds for a family of bi-univalent functions involving telephone numbers

2025-06-05T11:43:36+00:00

In the present paper, we introduce and investigate a new family FΣ(γ, λ, δ; ϑ) of holomorphic and bi-univalent functions by using the generalized telephone numbers which defined in the open unit disk Λ. We find upper bounds for the initial Taylor-Maclaurin coefficients and Fekete-Szeg¨o inequality for functions in this family. We also indicate certain special cases and consequences for our results.

Exponential Kantorovich-Stancu operators

2025-06-05T12:01:37+00:00

In this paper we will obtain some Bernstein-Kantorovich operators modified in Stancu sense which preserve exponential function e^μx, where μ > 0. Concerning these operators we prove they verify Korovkin’s theorem conditions and also that they approximate functions from a weighted L^p space. Moreover, we will obtain a Voronovskaya theorem and some quantitative estimates of approximation using the first order modulus of continuity. Also, we will prove some estimates concerning the approximation of functions from a weighted L^p space using Peetre’s K-functional. Finally, we will obtain an estimate which involves the first order modulus of continuity and the second order modulus of smoothness by using the equivalence relation between these moduli and the corresponding K-functionals.

Common local spectral properties for the operators AC and BD

2025-06-05T12:17:46+00:00

In [6], Chen and Abdolyousefi studied the common spectral properties of operators AC and BD satisfying (AC)²A = ACDBA = DBACA = (DB)²A; (AC)²D = ACDBD = DBACD = (DB)²D. In this note, we continue studying the common local spectral properties of these operators. We show that AC and BD shared the single-valued extension property, the Bishop property (β), the property (β_ϵ), the decomposition property (δ), and decomposability. Furthermore, we investigate the closedness of the analytic core and the quasinilpotent part. We also examine the Dunford’s property (C) and the property (Q).

Extremal functions and approximate inversion formulas for weighted Hardy spaces

2025-06-05T12:31:17+00:00

In this paper we consider the weighted Hardy space H_β. This space which gives a generalization of some Hilbert spaces of analytic functions on the unit disk like, the Hardy space H , the weighted Bergman space B_ν and the weighted Dirichlet space D_ν, it plays a background to our contribution. Especially, we examine the extremal functions for the primitive operator Pf(z) := R [0,z] f(w)dw, where [0, z] = {tz, t ∈ [0, 1]}; and we deduce approximate inversion formulas for the operator P on the weighted Hardy space H_β.

Some remarks related to the Raabe-Duhamel test

2025-06-05T12:42:33+00:00

We precise, for some classes of series with positive terms, the expression R_n which appears in the application of the Raabe-Duhamel test and its limit R, in relationship to the expression of the general term.