Some generalizations of Ekeland-type variational principle with applications to equilibrium problems and fixed point theory

Characterizations of partial metric completeness in terms of weakly contractive mappings having fixed point

“…Several authors have recently contributed to a vigorous development of the theory of fixed point for some classes of generalized metric spaces, as cone metric spaces, quasi-metric spaces and partial metric spaces (see [1,2,3,4,5,6,9,13,15,17,18,23,26], etc.). In particular, Romaguera [23], and Acar, Altun and Romaguera [2], have obtained characterizations of 0-complete and complete partial metric spaces, respectively, in the style of the aforementioned Kirk characterization of metric completeness.…”

Ekeland’s Variational Principle and Minimization Takahashi’s Theorem in Generalized Metric Spaces

“…Definition 8. Let M be a nonempty subset of metric space (see [29]). Assume that H : M × M −→ R is a real valued function and γ ∈ Γ .…”

Common fixed point results for quasi-contractions of Ciric type in b-metric spaces with Qt-functions

“…(2) If condition (q2) in Definition is replaced by the following stronger condition: (q2 ) for any x ∈ X, P(x, ·) : X → [0, ∞) is K-lower semi-continuous, then the Qt-function is called a wt-distance on X; see [15]. It is easy to see that every b-metric is a wt-distance and every wt-distance is a Qt-function; see [15] and [17]. Now, we give some properties of a Qt-function which are similar to the properties of a wtdistance, see, for example, [15].…”