Adrian Nicolae Branga

• PhD
• Professor (Associate) at Lucian Blaga University of Sibiu

In this article we present an algorithm, software implementation and some numerical experiments for an optimization method applied to unimodal functions, which depends on a conveniently chosen free parameter. This algorithm contains as a particular case the method of golden section, for a certain choice of the parameter. Numerical results showed th...

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In this article, we will solve optimization problems from the financial and economic field with constants, infinite-horizon iterative techniques and elements from fixed point theory. We will resort to Ćirić contractions in Banach space and the main result consists of the existence of a fixed point to solve an important class of infinite-horizon ite...

Starting from an inequality presented by professor A. Lupas (1973), which shown that the intermediate point of the logarithmic function in Lagrange’s theorem is between the arithmetic mean and the geometric mean of the the limits of the interval on which the function is defined, in this paper we will find a sharp estimation of the intermediate poin...

In this paper, we introduce the concept of (F, G)-perturbed contraction in a metric space and we establish some fixed point theorems which extends the results from Branga, A. N. Olaru, I. M. Some Fixed Point Results in Spaces with Perturbed Metrics. Carpathian J. Math. 38 (2022), no. 3, 641-654 and Olaru, I. M.; Secelean, N. A. A new approach of so...

In this paper, we have provided some fixed point results for self-mappings fulfilling generalized contractive conditions on altered metric spaces. In addition, some applications of the main results to continuous data dependence of the fixed points of operators defined on these spaces were shown.

"n this paper, the concept of perturbed metric was introduced within the metric spaces and some fixed point results were established for self-mappings satisfying such contractive conditions, using Picard operators technique and generalized contractions. Moreover, some applications of the main result to continuous data dependence of the fixed points...

In this paper, applying the theory of fixed points in complete gauge spaces, we establish some conditions for the existence and uniqueness of monotonic and positive solutions for nonlinear systems of ordinary differential equations. Moreover, the paper contains an application of the theoretical results to the study of a class of systems of nonlinea...

In this paper, the concept of F-contraction was generalized for cone metric spaces over topological left modules and some fixed point results were obtained for self-mappings satisfying a contractive condition of this type. Some applications of the main result to the study of the existence and uniqueness of the solutions for certain types of integra...

In this paper, we establish some conditions for the existence and uniqueness of the monotonic solutions for nonhomogeneous systems of first-order linear differential equations, by using a result of the fixed points theory for sequentially complete gauge spaces.

Numerical methods. Seminar lecture notes and practical laboratory work

In this paper, we introduce the concept of cone metric space over a topological left module and we establish some coincidence and common fixed point theorems for self-mappings satisfying a condition of Lipschitz type. The main results of this paper provide extensions as well as substantial generalizations and improvements of several well known resu...

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In this paper, we prove some coincidence and common fixed point theorems for self-maps satisfying contractive conditions in a \(D^*\)-quasimetric space.

Advanced numerical computation (in Romanian)

Numerical methods (in Romanian)

In this paper, using the quadrature formulas of Bouzitat type, we present an improvement of Fejer's inequality and also some applications. 2010 Mathematics Subject Classification: 33C45.

In this paper we introduce the notion of b-K-metric space and prove some common fixed point theorems in complete b-K-metric space.

In the introduction of this paper is presented the definition of the generalized spline functions as solutions of a variational problem and are shown some theorems regarding to the existence and uniqueness. The main result of this article consists in a remarkable equality verified by the generalized spline elements, based on the properties of the s...

We obtain a quadrature formula with higher degree of exactness. This formula is a generalization of some classical quadrature rules.

Functional analysis and approximation theory (in Romanian)

Approximation and optimization by spline functions (in Romanian)

A necessary and sufficient condition for characterization of spline functions

In the introduction of this paper is presented the denition of the generalized spline functions as solutions of a variational problem and are shown some theorems regarding to the existence and uniqueness. The main result of this article consist in a structural theorem of the generalized spline functions based on the properties of the spaces, operat...

In the introduction of this paper, the definition of generalized spline functions as solutions of a variational problem is presented and some theorems regarding existence, uniqueness and characterization are shown. The main result of this article consists in a best approximation property satisfied by generalized spline functions in the context of t...

Our aim in this paper is to find some developments in Chebyshev series and using these to prove that min Qn2e |n k Q nk p = k e Tnk p, where e Tn(x) = 1 2n¡1 cos(n arccos x) is the n-th Chebyshev monic polyno- mial.

The Radon transform and applications (in Romanian)

Contributions to the theory of spline functions and applications (in Romanian)

Optimal approximation of linear functionals using natural splines of Hermite type

Programming problems (in Romanian)

Numerical analysis: algorithms and problems (in Romanian)

The C/C++ programming language: theory and programs (in Romanian)

The aim of this paper is to present a new proof to the formula of divided differences with multiple nodes corresponding to a product of two functions.

Let Δ n :t 0 ≤t 1 ≤⋯t n be a division on the real line, where n∈ℕ * and t 0 ,t 1 ,⋯,t n ∈ℝ. We denote by B i,k (x), k=0,⋯,n-1, i=0,⋯,n-1-k, x∈ℝ, the functions B-spline corresponding to the division Δ n . Our aim here is to prove a new fundamental property of b-splines.

The aim of this paper is to find the inverse of a matrix of Vandermonde type using the fundamental polynomials of Hermite interpolation. This result enables us to express Hermite’s interpolating polynomial in the basis e k (x)=x k , k=01,2⋯ and, further, to obtain the coefficients of the quadrature formula, of Turán type.

The main result of this paper is an inequality for the generalized spline functions based on the properties of the space, operator and interpolatory set used in the definition.

In this paper we introduce the notion of b-cone metric space over topological vector space (for short b-TVS cone metric space) and prove some common fixed point theorems in complete b-cone metric spaces over topological vector spaces. These results generalize, extend and unify several well-known recent related results in literature. 2000 Mathematic...