On Some New Contractive Conditions in Complete Metric Spaces

One of the main goals of this paper is to obtain new contractive conditions using the method of a strictly increasing mapping F:(0,+∞)→(−∞,+∞). According to the recently obtained results, this was possible (Wardowski’s method) only if two more properties (F2) and (F3) were used instead of the aforementioned strictly increasing (F1). Using only the fact that the function F is strictly increasing, we came to new families of contractive conditions that have not been found in the existing literature so far. Assuming that α(u,v)=1 for every u and v from metric space Ξ, we obtain some contractive conditions that can be found in the research of Rhoades (Trans. Amer. Math. Soc. 1977, 222) and Collaco and Silva (Nonlinear Anal. TMA 1997). Results of the paper significantly improve, complement, unify, generalize and enrich several results known in the current literature. In addition, we give examples with results in line with the ones we obtained.

A look at nonexpansive mappings in non-Archimedean vector spaces

In a spherically complete ultrametric space every nonexpansive self-mapping T has a fixed point ̄x or a minimal invariant ball B(̄x, d(̄x, T(̄x)). We show how we can approximate this fixed center ̄x in a non-Archimedean vector space. And, we give a synthetic study for increasing mapping in non-Archimedean local fields.

On \({\mathcal{F}}\)-Contractions for Weak α-Admissible Mappings in Metric-Like Spaces

In the paper, we consider some fixed point results of F-contractions for triangular α-admissible and triangular weak α-admissible mappings in metric-like spaces. The results on F-contraction type mappings in the context of metric-like spaces are generalized, improved, unified, and enriched. We prove the main result but using only the property (F1) of the strictly increasing mapping F:0,+∞→−∞,+∞. Our approach gives a proper generalization of several results given in current literature.

On Iteration of Bijective Functions with Discontinuities

We present three different types of bijective functions f : I → I on a compact interval I with finitely many discontinuities where certain iterates of these functions will be continuous. All these examples are strongly related to permutations, in particular to derangements in the first case, and permutations with a certain number of successions (or small ascents) in the second case. All functions of type III form a direct product of a symmetric group with a wreath product. It will be shown that any iterative root F : J → J of the identity of order k on a compact interval J with finitely many discontinuities is conjugate to a function f of type III, i.e., F = φ−1 ∘ f ∘ φ where φ is a continuous, bijective, and increasing mapping between J and [0, n] for some integer n.

UAV-Based Structural Damage Mapping: A Review

Structural disaster damage detection and characterization is one of the oldest remote sensing challenges, and the utility of virtually every type of active and passive sensor deployed on various air- and spaceborne platforms has been assessed. The proliferation and growing sophistication of unmanned aerial vehicles (UAVs) in recent years has opened up many new opportunities for damage mapping, due to the high spatial resolution, the resulting stereo images and derivatives, and the flexibility of the platform. This study provides a comprehensive review of how UAV-based damage mapping has evolved from providing simple descriptive overviews of a disaster science, to more sophisticated texture and segmentation-based approaches, and finally to studies using advanced deep learning approaches, as well as multi-temporal and multi-perspective imagery to provide comprehensive damage descriptions. The paper further reviews studies on the utility of the developed mapping strategies and image processing pipelines for first responders, focusing especially on outcomes of two recent European research projects, RECONASS (Reconstruction and Recovery Planning: Rapid and Continuously Updated Construction Damage, and Related Needs Assessment) and INACHUS (Technological and Methodological Solutions for Integrated Wide Area Situation Awareness and Survivor Localization to Support Search and Rescue Teams). Finally, recent and emerging developments are reviewed, such as recent improvements in machine learning, increasing mapping autonomy, damage mapping in interior, GPS-denied environments, the utility of UAVs for infrastructure mapping and maintenance, as well as the emergence of UAVs with robotic abilities.