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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]

The aim of this paper is to introduce the notion of interpolative fuzzy Z-contractive condition for a pair of self maps in a fuzzy metric space, which enlarges, unifies and generalizes the existing fuzzy contractions (by Gregori et al. [6]), contraction (by Mihet [11]), fuzzy Z-contractions (by Shukla et al. ([19]) and Tirado contraction (by Tirado [20]), which are for only one self map. Using this, we establish a unique common fixed point theorem for two self maps satisfying condition (S), which was introduced by Shukla et al. in [19] through weak compatibility. As an applications, we discuss fixed point theorem for Fredholm non-linear integral equation. The article also includes an example, which shows the validity of our results. [ABSTRACT FROM AUTHOR]

In this article, we introduce generalized cyclic contractions in the context of metric-like spaces and prove some new fixed point results concerning these contractions. Our results, extend and unify several results in existing literature. We present suitable examples to make our findings worth mentioning. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of F--G--contraction mappings in F-metric spaces endowed with a graph and give some fixed point results for such contractions. Our results are generalization of some famous theorem in metric spaces to F--metric spaces endowed with a graph. Also, we give some examples that support obtained theoretical results. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to establish the uniqueness and existence of the common fixed point under generalized contractive conditions in b -metric spaces with supportive examples. We also approximate the common fixed point by Jungck–Picard and Picard iteration procedures along with the P property of the mappings. Further, (T , f) -stability of Jungck–Picard iterative and T -stability of Picard iterative schemes are proved. [ABSTRACT FROM AUTHOR]

The purpose of this short note is to consider much shorter and nicer proofs about fixed point results on b-metric spaces via b-simulation function introduced very recently by Demma et al. [M. Demma, R. Saadati, P. Vetro, Fixed point results on b-metric space via Picard sequences and b-simulation functions, Iranian J. Math. Sci. Infor. 11 (1) (2016) 123-136]. [ABSTRACT FROM AUTHOR]

In this paper, we present a new type of contraction calledW-contraction in fuzzy metric space. Utilizing this contraction, we establish a unique fixed point theorem for self-map in the structure of fuzzy metric space which turns out to be generalization of fuzzy contraction given by Gregori et al. [8]. As an application of our result, we study the existence and uniqueness of the solution to nonlinear ordinary differential equations. The article also includes an example which shows the validity of our results. [ABSTRACT FROM AUTHOR]

In this paper is introduced a new type of generalization of metric spaces called Sb metric space. For this new kind of spaces it has been proved a common fixed point theorem for four mappings which satisfy generalized contractive condition. We also present example to confirm our theorem. [ABSTRACT FROM AUTHOR]

This paper presents a new and general class of α - K ψ - s-contractions, involving α-admissible and - s simulation mappings considered in the setting of b-metric-like spaces. By applying this set of contractions associated with applications to integral equation, we unify, generalize, and increase the fixed point results range in the literature. [ABSTRACT FROM AUTHOR]

In this paper, the concept of a cone bv(s)-metric space over Banach algebra is introduced as a generalization of metric spaces, rectangular metric spaces, b-metric spaces, rectangular b-metric spaces, v-generalized metric spaces, cone b-metric spaces over Banach algebra and rectangular cone b-metric spaces over Banach algebra. We also give Banach and, Kannan fixed point results in cone bv(s)-metric spaces over Banach algebra. Some examples are provided as well. [ABSTRACT FROM AUTHOR]

The aim of this paper is to initiate the study of best proximity point and optimal coincidence point results of some a Pata-proximal admissible contraction of type-I and type-II in the framework of complete metric space. Some examples are presented to support the results obtained herein. Our results unify, extend and generalize various existing results in literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of a pair (f, h) called upper class of type II and αβ-contractive mappings. We obtain that all the corresponding established results of Hussain et al. [7] are immediately consequences of our main result. Our main result generalizes and modifies several existing results in literature. Also, an example is given to support the main result. [ABSTRACT FROM AUTHOR]

In this paper we see the personality of man through his comprehension as a moral entity. An entity that emerges, thinks morally and/or behaves morally, inseparable from the society in which he lives as a moral being, and by its moral thinking and/or behaviour further defines the morals of the whole society. Accordingly, we present (post)modern society as a society of tolerance of value ambiguity. In that kind of society we perceive medical situation as moral situation and define the role of medical ethics in the field of biomedicine. In that kind of society politics is perceived as one of the social spheres where different varieties of systems of values of individuals or groups are publicly embraced, touched, or terribly unhappily pursued... all in the name of understanding man and his world. In order to prevent the victory of Thanatos, who prevails in the contemporary concept of politics and in postmodern global society, we suggest implementing applied bioethics as a form of metapolitics as an answer. We explain the idea of bioethics and suggest bioethical education as the operationalisation of metapolitics through bioethics as orientation knowledge, in both medicine and politics.

In this article, we apply common fixed point results in incomplete metric spaces to examine the existence of a unique common solution for the following systems of Urysohn integral equations and Volterra-Hammerstein integral equations, respectively: [Formula: see text] where [Formula: see text]; [Formula: see text] and [Formula: see text], [Formula: see text] and [Formula: see text] where [Formula: see text], [Formula: see text], u , [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], [Formula: see text], are real-valued measurable functions both in s and r on [Formula: see text].

In this paper we consider, discuss, improve and generalize recent b-(E.A)-property results for mappings in b-metric spaces established by Ozturk and Turkoglu (J Nonlinear Convex Anal 16(10):2059-2066, 2015). Thus, all our results are with much shorter proofs. One example is given to support the result.