Ioan A. Rus
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View article: Weakly Picard mappings: Retraction-displacement condition, quasicontraction notion and weakly Picard admissible perturbation
Weakly Picard mappings: Retraction-displacement condition, quasicontraction notion and weakly Picard admissible perturbation Open
Let (X, d) be a metric space, f : X → X be a mapping and G(·, f (·)) be an admissible perturbation of f. In this paper we study the following problems: In which conditions imposed on f and G we have the following: (DDE) data dependence est…
View article: Identification of Vegetation Surfaces and Volumes by Height Levels in Reservoir Deltas Using UAS Techniques—Case Study at Gilău Reservoir, Transylvania, Romania
Identification of Vegetation Surfaces and Volumes by Height Levels in Reservoir Deltas Using UAS Techniques—Case Study at Gilău Reservoir, Transylvania, Romania Open
The hydrophilic vegetation from reservoir deltas sustains rapid expansions in surface and important increases in vegetal mass against a background of a significant influx of alluvium and nutrients from watercourses. It contributes to reser…
View article: Monitoring Forest Cover Dynamics Using Orthophotos and Satellite Imagery
Monitoring Forest Cover Dynamics Using Orthophotos and Satellite Imagery Open
The assessment of changes in forest coverage is crucial for managing protected forest areas, particularly in the face of climate change. This study monitored forest cover dynamics in a 6535 ha mountain area located in north-west Romania as…
View article: Around metric coincidence point theory
Around metric coincidence point theory Open
Let $(X,d)$ be a complete metric space, $(Y,\rho)$ be a metric space and $f,g:X\to Y$ be two mappings. The problem is to give metric conditions which imply that, $C(f,g):=\{x\in X\ |\ f(x)=g(x)\}\not=\emptyset$. In this paper we give an ab…
View article: The Evolution of Cluj Fortress From Extramuros Area and the Imprint of the Geosite in the Geographical Landscape of Cluj-Napoca City
The Evolution of Cluj Fortress From Extramuros Area and the Imprint of the Geosite in the Geographical Landscape of Cluj-Napoca City Open
"The Evolution of Cluj Fortress from Extramuros Area and the Imprint of the Geosite in the Geographical Landscape of Cluj-Napoca City. Cluj Fortress was built by the military garrison of the Habsburg Empire to have a defensive role in trag…
View article: Fixed point structures on a set-mapping pair and cartesian product
Fixed point structures on a set-mapping pair and cartesian product Open
In this paper we study the following problem (Problem 4.2 in, I.A. Rus, Sets with structure, mappings and fixed point property: fixed point structures, Fixed Point Theory 23, No. 2 (2022), 689-706): Let (𝒰, 𝒮, M ) be a fixed point structur…
View article: Automated versus Manual Mapping of Gravel Pit Lakes from South-Eastern Romania for Detailed Morphometry and Vegetation
Automated versus Manual Mapping of Gravel Pit Lakes from South-Eastern Romania for Detailed Morphometry and Vegetation Open
In recent years, the accelerated development of the remote sensing domain and the improvement of the resolution and frequency of satellite images allowed the increase in the accuracy of the evaluation of morphometric characteristics and th…
View article: Machine Learning and Remote Sensing Application for Extreme Climate Evaluation: Example of Flood Susceptibility in the Hue Province, Central Vietnam Region
Machine Learning and Remote Sensing Application for Extreme Climate Evaluation: Example of Flood Susceptibility in the Hue Province, Central Vietnam Region Open
Floods are the most frequent natural hazard globally and incidences have been increasing in recent years as a result of human activity and global warming, making significant impacts on people’s livelihoods and wider socio-economic activiti…
View article: Applications of fibre contraction principle to some classes of functional integral equations
Applications of fibre contraction principle to some classes of functional integral equations Open
Let a < c < b real numbers, (B, |•|) a (real or complex) Banach space, H ∈ C([a, b]×[a, c]× B, B), K ∈ C([a, b] 2 × B, B), g ∈ C([a, b], B), A : C([a, c], B) → C([a, c], B) and B : C([a, b], B) → C([a, b], B).In this paper we study the fol…
View article: Fixed point equations with abstract Volterra operators on spaces of functions of several variables
Fixed point equations with abstract Volterra operators on spaces of functions of several variables Open
Several notions of abstract Volterra operators on spaces of functions of one variable are well known. In this paper, we introduce various notions of abstract Volterra operators in spaces of functions of several variables. Some fixed point …
View article: On a Fredholm-Volterra integral equation
On a Fredholm-Volterra integral equation Open
"In this paper we give conditions in which the integral equation $$x(t)=\displaystyle\int_a^c K(t,s,x(s))ds+\int_a^t H(t,s,x(s))ds+g(t),\ t\in [a,b],$$ where $a<c<b$, $K\in C([a,b]\times [a,c]\times \mathbb{B},\mathbb{B})$, $H\in C([a,b]\t…
View article: Some variants of fibre contraction principle and applications: from existence to the convergence of successive approximations
Some variants of fibre contraction principle and applications: from existence to the convergence of successive approximations Open
Let (X 1 , →) and (X 2 , →) be two L-spaces, U be a nonempty subset ofthe problem is in which additional conditions T is a weakly Picard operator ?In this paper we study this problem in the case when the convergence structures on X 1 and X…
View article: Set-theoretical aspect of the fixed point theory: some examples
Set-theoretical aspect of the fixed point theory: some examples Open
In this paper we revisit some of my own contributions to the fixed point theory, contributions which are related to set-theoretical terms. My intention is to do this in a unitary way. New notions and results are given. Open problems are al…
View article: Theoretical and numerical considerations on Bratu-type problems
Theoretical and numerical considerations on Bratu-type problems Open
"In this paper we present an heuristic introduction to Bratu problem and we give some variants of Bratu's theorem (G. Bratu, Sur les \'equations int\'egrales non lin\'eaires, Bulletin Soc. Math. France, 42(1914), 113-142). Using the positi…
View article: Asymptotic regularity, fixed points and successive approximations
Asymptotic regularity, fixed points and successive approximations Open
Let (M,d) be a metric space. In this paper we survey some of the most relevant results which relate the three concepts involved in the title: a) the asymptotic regularity; b) the existence (and uniqueness) of fixed points and c) the conver…
View article: Frum-Ketkov operators which are weakly Picard
Frum-Ketkov operators which are weakly Picard Open
In this paper, we will give sufficient conditions ensuring that a Frum-Ketkov operator is weakly Picard. Some generalized Frum-Ketkov operators are also studied.
View article: Some variants of contraction principle in the case of operators with Volterra property: step by step contraction principle
Some variants of contraction principle in the case of operators with Volterra property: step by step contraction principle Open
Following the idea of T.A. Burton, of progressive contractions, presented in some examples (T.A. Burton, \emph{A note on existence and uniqueness for integral equations with sum of two operators: progressive contractions}, Fixed Point Theo…
View article: Fixed point theory in terms of a metric and of an order relation
Fixed point theory in terms of a metric and of an order relation Open
We consider a nonempty set X endowed with a metric d an order relation and an operator f : X → X, which satisfies two main assumptions:(1) f is generalized monotone with respect to ;(2) f is a (generalized) contraction with respect to d on…
View article: Fixed point theory for nonself generalized contractions in Kasahara spaces
Fixed point theory for nonself generalized contractions in Kasahara spaces Open
In this paper we extend some results of V. Berinde, Şt. Măruşter and I.A. Rus ( Saturated contraction principles for nonself operators, generalizations and applications , Filomat, 31:11(2017), 3391-3406), which were given in metric spaces,…
View article: Convergence results for fixed point iterative algorithms in metric spaces
Convergence results for fixed point iterative algorithms in metric spaces Open
In this paper we give some conditions on fn and f which imply the convergence of algorithm (2). In this way we improve some results given in [Rus, I. A., An abstract point of view on iterative approximation of fixed points: impact on the t…
View article: Stability of Picard operators under operator perturbations
Stability of Picard operators under operator perturbations Open
In this paper we study the following problems: I. Let ( M, d ) be a complete metric space and f, g : M → M be two operators. We suppose that: (a) f is a Picard operator with its unique fixed point x * f ; (b) there exists η > 0 such that d…
View article: "Homogeneous" second order differential equation: zeros separation principles
"Homogeneous" second order differential equation: zeros separation principles Open
In this paper we study the following problems: \medskip \noindent\underline{Problem 1}. Let $I\subset \mathbb{R}$ be an open interval and $F:\mathbb{R}^3\times I\to \mathbb{R}$ be a continuous function with, $F(0,0,0,x)=0$, for all $x\in I…
View article: Some problems in the fixed point theory
Some problems in the fixed point theory Open
In this paper we present some of my favorite problems, all the time open, in the fixed point theory. Theseproblems are in connection with the following two: Which properties have the fixed point equations for which an iterative algorithm i…
View article: Some remarks on the notations and terminology in the ordered set theory
Some remarks on the notations and terminology in the ordered set theory Open
By various examples we illustrate that the ordered set theory is far away from having unitary notations and terminology. Some suggestions for unifiying the terminology are also presented.
View article: Saturated contraction principles for non self operators, generalizations and applications
Saturated contraction principles for non self operators, generalizations and applications Open
Let (X; d) be a metric space, Y ? X a nonempty closed subset of X and let f : Y ? X be a non self operator. In this paper we study the following problem: under which conditions on f we have all of the following assertions: 1. The operator …
View article: Some fixed point theorems for nonself generalized contraction
Some fixed point theorems for nonself generalized contraction Open
In this paper we give a new proof of a result by S. Reich and A.