One algorithm for testing annulling of mixed trigonometric polynomial functions on boundary points

This paper considers one problem of modern automated theorem provers. While there are many different numerical methods for computation of real roots of polynomials, theorem provers require higher level of assurances of result correctness. In this paper is shown one method that circumvents limitations of application of Sturm’s theorem for such tasks

A Unified Approach and Related Fixed-Point Theorems for Suzuki Contractions

This paper aims to give an extended class of contractive mappings combining types of Suzuki contractions α-admissible mapping and Wardowski F-contractions in b-metric-like spaces. Our results cover and generalize many of the recent advanced results on the existence and uniqueness of fixed points and fulfill the Suzuki-type nonlinear hybrid contractions on various generalized metrics

Possibilities of BLOB (Binary Large OBject) and CLOB (Character Large Object) Integration Into the Core of IoT and Using the SQL Platform for Distributing a Large Amount of Data to HTML, JAVA, and PHP Platforms

This chapter identifies and describes the key concepts and techniques for BLOB and CLOB integration into the IoT core. Data system centralization has sped up the solution of problems with large amounts of data storage and processing, particularly if the data is large by its nature. In that sense, everyday stream of photos, audio and video content, large textual data files led to new concepts BLOB and CLOB. Adequate examples of stored procedures, views, C#, JAVA, HTML5 i PHP languages, follow the establishing communication methods. Finally, the chapter will illustrate two practical examples of IoT: the example for pagination on a large database with million BLOB and CLOB objects, and the example for dynamic mechatronic system of a fire truck with feedback

A Suzuki-type multivalued contraction on weak partial metric spaces and applications

Abstract Based on a recent paper of Beg and Pathak (Vietnam J. Math. 46(3):693–706, 2018), we introduce the concept of Hq+ $\mathcal{H}_{q}^{+}$-type Suzuki multivalued contraction mappings. We establish a fixed point theorem for this type of mappings in the setting of complete weak partial metric spaces. We also present an illustrated example. Moreover, we provide applications to a homotopy result and to an integral inclusion of Fredholm type. Finally, we suggest open problems for the class of 0-complete weak partial metric spaces, which is more general than complete weak partial metric spaces

On F-Contractions: A Survey

D. Wardowski proved in 2012 a generalization of Banach Contraction Principle by introducing F-contractions in metric spaces. In the next ten years. a great number of researchers used Wardowski's approach, or some of its modifications, to obtain new fixed point results for single- and multivalued mappings in various kinds of spaces. In this review article. we present a survey of these investigations, including some improvements, in particular concerning conditions imposed on function F entering the contractive condition