Banach's contraction principle has been improved and extensively studied on several generalized metric spaces. Recently, complex-valued $S$-metric spaces have been introduced and studied for this purpose. In this paper, we investigate some generalized fixed point results on a complete complex valued $S$-metric space. To do this, we prove some common fixed point (resp. fixed point) theorems usin...

3 Convex functions on symmetric spaces 11 3.1 Geometric preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.1.1 Metric spaces with curvature bounds . . . . . . . . . . . . . . 11 3.1.2 Hadamard spaces . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.1.3 Symmetric spaces of noncompact type . . . . . . . . . . . . . 15 3.1.4 Auxiliary results . . . . . . . . . . . . . . . ....

We interpret the global Hadamard condition for a two-point distribution of a Klein-Gordon neutral scalar quantum field model on an arbitrary globally hyperbolic curved space-time in terms of distinguished parametrices (of Duistermaat and Hörmander) and a wave front set spectrum condition. Microlocal results by Duistermaat and Hörmander such as the propagation of singularities theorem and the un...

We give upper bounds on the Walsh coefficients of functions for which the derivative of order at least one has bounded variation of fractional order. Further, we also consider the Walsh coefficients of functions in periodic and non-periodic reproducing kernel Hilbert spaces. A lower bound which shows that our results are best possible is also shown. Mathematical Subject Classification (2000): P...

Fixing a complete Riemannian metric g on Rn, we show that a local diffeomorphism f : Rn → Rn is bijective if the height function f · v (standard inner product) satisfies the Palais-Smale condition relative to g for each for each nonzero v ∈ Rn. Our method substantially improves a global inverse function theorem of Hadamard. In the context of polynomial maps, we obtain new criteria for invertibi...

The existence of fixed point in orthogonal metric spaces has been initiated by Eshaghi and et. al [7]. In this paper, we prove existence and uniqueness theorem of fixed point for mappings on $varepsilon$-connected orthogonal metric space. As a consequence of this, we obtain the existence and uniqueness of fixed point for analytic function of one complex variable. The paper concludes with some i...