1.1. Introducton to Banach Spaces Definition 1.1. Let X be a K–vector space. A functional p ∶ X → [0,+∞) is called a seminorm, if (a) p(λx) = ∣λ∣p(x), ∀λ ∈ K, x ∈X, (b) p(x + y) ≤ p(x) + p(y), ∀x, y ∈X. Definition 1.2. Let p be a seminorm such that p(x) = 0 ⇒ x = 0. Then, p is a norm (denoted by ∥ ⋅ ∥). Definition 1.3. A pair (X, ∥ ⋅ ∥) is called a normed linear space. Lemma 1.4. Each normed sp...

in this paper, tripled coincidence points of mappings satisfying  -contractive conditions in the framework of partially ordered gb-metric spaces are obtained. our results extend the results of aydi et al. [h. aydi, e. karapnar and w. shatanawi, tripled xed point results in generalized metric space, j. applied math., volume 2012, article id 314279, 10 pages]. moreover, some examples of the mai...

We develop a new model of a spinning particle in Brans-Dicke space-time using a metric-compatible connection with torsion. The particle's spin vector is shown to be Fermi-parallel (by the Levi-Civita connection) along its worldline (an autoparallel of the metric-compatible connection) when neglecting spin-curvature coupling.

Let F be a finite field with q elements. A k dimensional subspace C of the vector space Fn of all n-tuples over F is called a linear code of length n and dimension k. Algebraically, C is just a k-dimensional vector space over F. However, as a particular subspace of Fn, C inherits some metric properties. Specifically, for every v E Fn, the weight of v, denoted by wt( v), is defined to be the num...

The time-optimal trajectory for an airplane from some starting point to some final point is studied by many authors. Here, we consider the extension of robot planer motion of Dubins model in three dimensional spaces. In this model, the system has independent bounded control over both the altitude velocity and the turning rate of airplane movement in a non-obstacle space. Here, in this paper a g...

In [Fuzzy Sets and Systems 27 (1988) 385-389], M. Grabiec in- troduced a notion of completeness for fuzzy metric spaces (in the sense of Kramosil and Michalek) that successfully used to obtain a fuzzy version of Ba- nachs contraction principle. According to the classical case, one can expect that a compact fuzzy metric space be complete in Grabiecs sense. We show here that this is not the case,...

To any finite collection of smooth real vector fields Xj in R we associate a metric in the phase space T ∗Rn. The relation between the asymptotic behavior of this metric and hypoellipticity of ∑ X j , in the smooth, real analytic, and Gevrey categories, is explored. To Professor P. Lelong, on the occasion of his 85th birthday.

We develop a new model of a spinning particle in Brans-Dicke space-time using a metric-compatible connection with torsion. The particle's spin vector is shown to be Fermi-parallel (by the Levi-Civita connection) along its worldline (an autoparallel of the metric-compatible connection) when neglecting spin-curvature coupling.

The sequential $p$-convergence in a fuzzy metric space, in the sense of George and Veeramani, was introduced by D. Mihet as a weaker concept than convergence. Here we introduce a stronger concept called $s$-convergence, and we characterize those fuzzy metric spaces in which convergent sequences are $s$-convergent. In such a case $M$ is called an $s$-fuzzy metric. If $(N_M,ast)$ is a fuzzy metri...

The Horrocks-Mumford bundle E is a famous stable complex vector bundle of rank 2 on 4-dimensional complex projective space. By construction, E has a natural Hermitian metric h1. On the other hand, stability implies the existence of a Hermitian-Einstein metric in E which is unique up to a positive scalar. Now the obvious question is if h1 is in fact the Hermitian-Einstein metric. In this note we...