arXiv subjects

Mădălina Păcurar

Publications and source records attributed to Mădălina Păcurar.

4 recordsLinked to original sources

arXiv2024

Recent developments in the fixed point theory of enriched contractive mappings. A survey

The aim of this note is threefold: first, to present a few relevant facts about the way in which the technique of enriching contractive mappings was introduced; secondly, to expose the main contributions in the area of enriched mappings established by the authors and their collaborators by using this technique; and third, to survey some related developments in the very recent literature which were authored by other researchers.

math.FA↗

arXiv2019

Fixed point theorems for Kannan type mappings with applications to split feasibility and variational inequality problems

The aim of this paper in to introduce a large class of mappings, called {\it enriched Kannan mappings}, that includes all Kannan mappings and some nonexpansive mappings. We study the set of fixed points and prove a convergence theorem for Kransnoselskij iteration used to approximate fixed points of enriched Kannan mappings in Banach spaces. We then extend further these mappings to the class of enriched Bianchini mappings. Examples to illustrate the effectiveness of our results are also given. As applications of our main fixed point theorems, we present two Kransnoselskij projection type algorithms for solving split feasibility problems and variational inequality problems in the class of enriched Kannan mappings and enriched Bianchini mappings, respectively.

math.FA↗

arXiv2019

Approximating fixed points of enriched contractions in Banach spaces

We introduce a large class of mappings, called enriched contractions, which includes, amongst many other contractive type mappings, the Picard-Banach contractions and some nonexpansive mappings. We show that any enriched contraction has a unique fixed point and that this fixed point can be approximated by means of an appropriate Kransnoselskij iterative scheme. Several important results in fixed point theory are shown to be corollaries or consequences of the main results in this paper. We also study the fixed points of local enriched contractions, asymptotic enriched contractions and Maia type enriched contractions. Examples to illustrate the generality of our new concepts and the corresponding fixed point theorems are also given.

math.FA↗

arXiv2019

Approximating fixed points of enriched Chatterjea contractions by Krasnoselskij iterative method in Banach spaces

Using the technique of enrichment of contractive type mappings by Krasnoselskij averaging, introduced in [Berinde, V., {\it Approximating fixed points of enriched nonexpansive mappings by Krasnoselskij iteration in Hilbert spaces}, Carpathian J. Math. {\bf 35} (2019), no. 3, 277-288.], we introduce the class of enriched Chatterjea contractions and prove general fixed point theorems for such contractions in the setting of a Banach space. Examples to illustrate the richness of the new class of contractions and the relationship between enriched Banach contractions, enriched Kannan contractions and enriched Kannan contractions are also given.

math.FA↗