The main objective of the paper is to state newly fixed point theorems for set-valued mappings in the framework of 0-complete partial metric spaces which speak about a location of a fixed point with respect to an initial value of the set-valued mapping by using some $C$-class functions. The results proved herein generalize, modify and unify some recent results of the existing literature. As an ...

We introduce variational inequality problems on Hilbert $C^*$-modules and we prove several existence results for variational inequalities defined on closed convex sets. Then relation between variational inequalities, $C^*$-valued metric projection and fixed point theory  on  Hilbert $C^*$-modules is studied.

We discuss new applications of advanced tools of variational analysis and generalized differentiation to a number of important problems in optimization theory, equilibria, optimal control, and feedback control design. The presented results are largely based on the recent work by the author and his collaborators. Among the main topics considered and briefly surveyed in this paper are new calculu...

The aim of this paper is to prove a common fixed point theorem for variants of weak compatible maps in a complex valued metric space. As a consequence, we extend and generalize the theorem of Branciari [3] for 2812 a pair of weakly compatible mappings satisfying a general contractive condition of integral type in complex valued metric space. At last, we prove two results by using E.A. property ...

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.