A Fixed Point Approach to the Hyers-Ulam-Rassias Stability Problem of Pexiderized Functional Equation in Modular Spaces

In this paper, we consider pexiderized functional equations for studying their Hyers-Ulam-Rassias stability. This stability has been studied for a variety of mathematical structures. Our framework of discussion is a modular space. We adopt a fixed-point approach to the problem in which we use a generalized contraction mapping principle in modular spaces. The result is illustrated with an example.

On Invariant Approximations in Modular Spaces

This article is devoted to presenting results on invariant approximations over a non-star-shsped weakly compact subset of a complete modular space by introduced a new notion called S-star-shaped with center f: if be a mapping and , . Then the existence of common invariant best approximation is proved for Banach operator pair of mappings by combined the hypotheses with Opial’s condition or demi-closeness condition

Nadler’s Theorem on Incomplete Modular Space

This manuscript is focused on the role of convexity of the modular, and some fixed point results for contractive correspondence and single-valued mappings are presented. Further, we prove Nadler’s Theorem and some fixed point results on orthogonal modular spaces. We present an application to a particular form of integral inclusion to support our proposed version of Nadler’s theorem.

Common fixed point theorems for several multivalued mappings on proximinal sets in regular modular space

In this paper, we found a common fixed point for several multivalued mappings on proximinal sets in regular modular metric space. Also, we introduced the notions of conjoint F-proximinal contraction as well as conjoint F-proximinal contraction of Hardy–Rogers-type for several multivalued mappings. Furthermore, we enhanced our results by giving an application in integral equations.

Approximating Damped Vibrations of Large Space Structures

It is possible to use data recorded by onboard acceleration sensors to verify mathematical models of large modular space structures in terms of simulating dynamic processes. The paper investigates an approach to approximating damped oscillations caused by dynamic impacts during operation. Initially, we approximate the response of the structure by summing damped harmonics derived from analysing the frequency spectrum of the dynamic process; then we use the Levenberg --- Marquardt algorithm in the parameter space of the harmonic set to find the best match between the real dynamic process and its approximation. We propose a modification of the approach considered which involves employing single harmonics to perform successive approximations of the function of time to be fitted. We show that it is possible to apply the approach proposed to identifying the frequency and dissipative parameters of the structure under consideration. The paper presents the results of testing the approach proposed via artificially generated noisy acceleration functions of time with known parameters, which were reconstructed with a sufficient degree of accuracy. A real-world example provided comprises the results of analysing the ISS accelerometer readings recorded against the background of damped vibrations in its structure that were caused by burns of its attitude control engines

Strongly Summable Vector-Valued Sequence Spaces Defined by 2-modular

Summability is an important concept in sequence spaces. One summability concept is strongly Cesaro summable. In this paper, we study a subset of the set of all vector-valued sequence in 2-modular space. Some facts that we investigated in this paper include linearity, the existence of modular and completeness with respect to these modular.

Convexity property and fixed-point theorems in CΩ-modular space

The purpose of this study is to introduce a new concept of the modular space, which is CΩ-modular space, and then some of the convex properties are discussed. We also study finding fixed-point in CΩ-modular space.