We prove versions of Ekeland, Takahashi and Caristi principles in preordered quasi-metric spaces, the equivalence between these principles, as well their to some completeness results for underlying space. These extend proved S.~Cobza\c{s}, Topology Appl. \textbf{265} (2019), 106831, 22, spaces. The key tools are Picard sequences special set-valued mappings on a space $X$, defined terms preorder...

Convex like properties, without vector space structure are intensively used in the minimax theory Since Ky Fan has proved the first minimax theorem for concave-convexlike functions, several authors have proposed other extensions or generalizations for the convexity. In this paper we propose a survey of the recent studies concerning convexity and invexity in optimization theory. In fact, in the ...

Cone-valued lower semicontinuous maps are used to generalize Cristi-Kirik’s fixed point theorem to Cone metric spaces. The cone under consideration is assumed to be strongly minihedral and normal. First we prove such a type of fixed point theorem in compact cone metric spaces and then generalize to complete cone metric spaces. Some more general results are also obtained in quasicone metric spaces.

The paper is concerned with a very general version of Caristi’s coincidence theorem, in topological spaces (X, τ) satisfying some completeness conditions with respect to a function p : X ×X → [0,∞), and having as consequence Caristi’s fixed point theorem. The general result is applied to various concrete situations quasi-metric spaces, bornological spaces to obtain versions of Ekeland’s variati...