On fixed points and convergence results of sequences generated by uniformly convergent and point-wisely convergent sequences of operators in Menger probabilistic metric spaces

Altres ajuts: The authors thank the reviewers for their useful comments and to University Jorge Tadeo Lozano by its support through Grant 644-11-14.In the framework of complete probabilistic Menger metric spaces, this paper investigates some relevant properties of convergence of sequences built through sequences of operators which are either uniformly convergent to a strict k -contractive operator, for some real constant k ∈ (0, 1), or which are strictly k -contractive and point-wisely convergent to a limit operator. Those properties are also reformulated for the case when either the sequence of operators or its limit are strict -contractions. The definitions of strict (k and ) contractions are given in the context of probabilistic metric spaces, namely in particular, for the considered probability density function. A numerical illustrative example is discussed

Existence of common fixed points for linear combinations of contractive maps in enhanced probabilistic metric spaces

In this paper, we introduce the concept of enhanced probabilistic metric space (briefly EPM-space) as a type of probabilistic metric space. Also, we investigate the existence of fixed points for a (finite or infinite) linear combination of different types of contractive mappings in EPM-spaces. Furthermore, we investigate about the convergence of sequences (generated by a finite or infinite family of contractive mappings) to a common fixed point. The useful application of this research is the study of the stability of switched dynamic systems, where we study the conditions under which the iterative sequences generated by a (finite or infinite) linear combination of mappings (contractive or not), converge to the fixed point. Also, some examples are given to support the obtained results. In the end, a number of figures give us an overview of the examples

α-admissible Prešić type operators and fixed points

In this paper, we introduce α-admissible mappings on product spaces and obtain fixed point results for α-admissible Prešić type operators. Our results extend, unify and generalize some known results of the literature. We also provide examples which illustrate the results proved herein and show that how the new results are different from the existing ones

Reflections of a Mathematician

In this lecture, an attempt is made to convey in a broad sense about mathematics and its applications and the impact it has made outside its own domain. While doing so, we try to dispel the belief (held in certain quarters) that there are two types of mathematics, namely useful mathematics and not so useful mathematics. An attempt is also made to reflect on the role of mathematics in industry along with the challenges of teaching of mathematics in the current environment