In this paper we present new iterative algorithms in convex metric spaces. We show that these iterative schemes are convergent to the fixed point of a single-valued contraction operator. Then we make the comparison of their rate of convergence. Additionally, numerical examples for these iteration processes are given.

‎In this paper‎, ‎we study weighted composition operators between Lipschitz algebras of complex-valued bounded functions on metric spaces‎, ‎not necessarily compact‎. ‎We give necessary and sufficient conditions for the injectivity and the surjectivity of these operators‎. ‎We also obtain sufficient and necessary conditions for a weighted composition operator between these spaces to be compact.

‎ Let $(X,d)$ be a metric space and $Jsubseteq (0,infty)$ be a nonempty set. We study the structure of the arbitrary intersection of vector-valued Lipschitz algebras, and define a special Banach subalgebra of $cap{Lip_gamma (X,E):gammain J}$, where $E$ is a Banach algebra, denoted by $ILip_J (X,E)$. Mainly, we investigate $C-$character amenability of $ILip_J (X,E)$.

This paper deals with tripled fixed point theorem, and the approach is based on Perov-type fixed point theorem for contractions in metric spaces endowed with vector-valued metrics. We are also study Ulam-Hyers stability results for the tripled fixed points of a triple of contractive type single-valued and respectively multi-valued operators on complete metric spaces.

In this work, we introduce new approximation operators for univariate setvalued functions with general compact images. We adapt linear approximation methods for real-valued functions by replacing linear combinations of numbers with new metric linear combinations of finite sequences of compact sets, thus obtaining ”metric analogues” operators for set-valued functions. The new metric linear combi...

The Hölder setting of the metric subregularity property of set-valued mappings between general metric or Banach/Asplund spaces is investigated in the framework of the theory of error bounds for extended real-valued functions of two variables. A classification scheme for the general Hölder metric subregularity criteria is presented. The criteria are formulated in terms of several kinds of primal...

Very recently, Ma et al. (Fixed Point Theory Appl. 2014:206, 2014) introduced C∗-algebra-valued metric spaces as a new concept. Also, Ma and Jiang (Fixed Point Theory Appl. 2015:222, 2015), generalizing this concept, introduced C∗-algebra-valued b-metric spaces. In both frameworks, these and other authors proved some fixed point results. We show in this paper that all these results (as well as ...