New generalized fuzzy metrics and fixed point theorem in fuzzy metric space

In this paper, in fuzzy metric spaces (in the sense of Kramosil and Michalek (Kibernetika 11:336-344, 1957)) we introduce the concept of a generalized fuzzy metric which is the extension of a fuzzy metric. First, inspired by the ideas of Grabiec (Fuzzy Sets Syst. 125:385-389, 1989), we define a new G-contraction of Banach type with respect to this generalized fuzzy metric, which is a generalization of the contraction of Banach type (introduced by M Grabiec). Next, inspired by the ideas of Gregori and Sapena (Fuzzy Sets Syst. 125:245-252, 2002), we define a new GV-contraction of Banach type with respect to this generalized fuzzy metric, which is a generalization of the contraction of Banach type (introduced by V Gregori and A Sapena). Moreover, we provide the condition guaranteeing the existence of a fixed point for these single-valued contractions. Next, we show that the generalized pseudodistance J:X×X→[0,∞) (introduced by Włodarczyk and Plebaniak (Appl. Math. Lett. 24:325-328, 2011)) may generate some generalized fuzzy metric NJ on X. The paper includes also the comparison of our results with those existing in the literature

Kannan-type cyclic contraction results in 22-Menger space

summary:In this paper we establish Kannan-type cyclic contraction results in probabilistic 2-metric spaces. We use two different types of $t$-norm in our theorems. In our first theorem we use a Hadzic-type $t$-norm. We use the minimum $t$-norm in our second theorem. We prove our second theorem by different arguments than the first theorem. A control function is used in our second theorem. These results generalize some existing results in probabilistic 2-metric spaces. Our results are illustrated with an example

Multivalued generalizations of fixed point results in fuzzy metric spaces

This paper attempts to prove fixed and coincidence point results in fuzzy metric space using multivalued mappings. Altering distance function and multivalued strong {bn}-fuzzy contraction are used in order to do that. Presented theorems are generalization of some well known single valued results. Two examples are given to support the theoretical results

Construction of Self-Adjoint Berezin-Toeplitz Operators on Kahler Manifolds and a Probabilistic Representation of the Associated Semigroups

We investigate a class of operators resulting from a quantization scheme attributed to Berezin. These so-called Berezin-Toeplitz operators are defined on a Hilbert space of square-integrable holomorphic sections in a line bundle over the classical phase space. As a first goal we develop self-adjointness criteria for Berezin-Toeplitz operators defined via quadratic forms. Then, following a concept of Daubechies and Klauder, the semigroups generated by these operators may under certain conditions be represented in the form of Wiener-regularized path integrals. More explicitly, the integration is taken over Brownian-motion paths in phase space in the ultra-diffusive limit. All results are the consequence of a relation between Berezin-Toeplitz operators and Schrodinger operators defined via certain quadratic forms. The probabilistic representation is derived in conjunction with a version of the Feynman-Kac formula.Comment: AMS-LaTeX, 30 pages, no figure

Common Fixed Point Theorems of Integral Type in Menger Pm Spaces

In this paper, we propose integral type common fixed point theorems in Menger spaces satisfying common property (E.A). Our results generalize several previously known results in Menger as well as metric spaces. Keywords: Menger space; Common property (E.A); weakly compatible pair of mappings and t-norm