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In 1964, A. I. Perov generalized the Banach contraction principle introducing, following the work of ¯D. Kurepa, a new approach to fixed point problems, by defining generalized metric spaces (also known as vector valued metric spaces), and providing some actual results for the first time. Using the recent approach of coordinate representation for a generalized metric of Jachymski and Klima, we verify in this article some natural properties of generalized metric spaces, already owned by standard metric spaces. Among other results, we show that the theorems of Nemytckii (1936) and Edelstein (1962) are valid in generalized metric spaces, as well. A new application to fractional differential equations is also presented. At the end we state a few open questions for young researchers. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the existence of best proximity points of certain mappings via simulation functions in the frame of complete metric-like spaces. Some consequences and examples are given of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we utilize the family F and the notion of ω-distance in an ordered G-metric space and introduce (F, ω)-contractions in order to derive some fixed point results. We also discuss the problems of Ulam-Hyers stability, well-posedness and limit shadowing property. In order to illustrate the use of our results, we apply them to nonlinear integral equations, as well as to some three-point fractional integral boundary value problems, both with numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, we define a generalized c-distance in tvs-cone b-metric spaces and introduce some results about its properties. Then we prove some new fixed point and common fixed point results (with the underlying cone which is not normal). Respective results concerning mappings without periodic points are also deduced. Some examples are presented to validate our obtained results. An application to system of Fredholm integral equations is presented. [ABSTRACT FROM AUTHOR]

In this paper, the coincidence point problem of Nadler type is treated for two mappings (one single-valued and one multi-valued) in a metric space. A generalized (α; θ; f)-contractive condition is assumed, together with α-completeness of the space, α-continuity of the multi-valued mapping and α-compatibility of the two mappings. The results are applied to metric spaces endowed with a graph or with a binary relation. [ABSTRACT FROM AUTHOR]

In this paper, several results are presented on common fixed points using (φ1-φ2-φ3)-contraction condition including rational expressions in orbitally 0-complete partial metric spaces. A counterexample illustrates that the results are distinct from some known ones. It is also observed that the work of Kadelburg and Radenovic [Kadelburg, Z., Radenovic, S.: Fixed points under α-α conditions in ordered partial metric spaces, Intern. J. Anal. Appl. 5, 91{101 (2014)] is a particular case of the present investigation. As applications of our results, we prove two theorems for the existence of solutions of certain system of Volterra type integral equations, as well as for a nonlinear fractional differential equation. [ABSTRACT FROM AUTHOR]