Consider the space of weighted binomial matrices in the Nakano sequence space of soft functions. We have offered some geometric and topological structures of the multiplication operator acting on ...this space and its associated operator ideal. The existence of a fixed point of the Kannan contraction operator in this prequasioperator ideal is confirmed. Finally, we discuss many applications of solutions to nonlinear stochastic dynamical matrix systems and illustrative examples of our findings.
In the framework of complete metric spaces, the major objective of this paper is to investigate if a common coincidence point exists for more than two fuzzy mappings meeting the criteria of hybrid ...fuzzy contractions of Nadler’s type in connection with the Hausdorff metric. Fascinating examples are also provided to show how the strategy can be used. For the presence of a common
α
-fuzzy fixed point of three and four fuzzy mappings, we have derived sufficient requirements. Further prior observations are offered as corollaries from the relevant literature. Some implications that are clear in this mode and widely covered in literature are expanded upon and included in our study.
The sufficient settings of the space generated by absolute type-weighted gamma matrices of rank p in the Nakano complex functions of the formal power series, as well as its associated ...prequasioperators’ ideal equipped with definite functions, are defined and explained in this paper. Assorted prequasinorms are shown to have the Fatou characteristic. Some of its geometric and topological features and the prequasioperators’ ideal that goes with it are talked about. These structures have a relationship with the fixed points of the Kannan contraction and nonexpansive mappings. By looking at real-world examples and how they are used, it is shown that there are solutions for nonlinear dynamical systems of the Kannan type.
The applications of non-zero self distance function have recently been discovered in both symmetric and asymmetric spaces. With respect to invariant point results, the available literature reveals ...that the idea has only been examined for crisp mappings in either symmetric or asymmetric spaces. Hence, the aim of this paper is to introduce the notion of invariant points for non-crisp set-valued mappings in metric-like spaces. To this effect, the technique of κ-contraction and Feng-Liu’s approach are combined to establish new versions of intuitionistic fuzzy functional equations. One of the distinguishing ideas of this article is the study of fixed point theorems of intuitionistic fuzzy set-valued mappings without using the conventional Pompeiu–Hausdorff metric. Some of our obtained results are applied to examine their analogues in ordered metric-like spaces endowed with an order and binary relation as well as invariant point results of crisp set-valued mappings. By using a comparative example, it is observed that a few important corresponding notions in the existing literature are complemented, unified and generalized.
In this paper, the notion of generalized quasi-weakly contractive operators in metric-like spaces is introduced, and new conditions for the existence of fixed points for such mappings are ...investigated. A non-trivial example which highlights the novelty of our principal idea is constructed. It is observed comparatively that the proposed concepts herein subsume some important results in the corresponding literature. As an application, one of our obtained findings is utilized to setup novel criteria for the existence of solutions to two-point boundary value problems of a second order differential equation. To attract new researchers in the directions examined in this article, a significant number of corollaries are pointed out and discussed.
It is a fact that $ C^* $-algebra-valued metric space is more general and hence the results in this space are proper improvements of their corresponding ideas in standard metric spaces. With this ...motivation, this paper focuses on introducing the concepts of $ C^* $-algebra-valued $ F $-contractions and $ C^* $-algebra-valued $ F $-Suzuki contractions and then investigates novel criteria for the existence of fixed points for such mappings. It is observed that the notions examined herein harmonize and refine a number of existing fixed point results in the related literature. A few of these special cases are highlighted and analyzed as some consequences of our main ideas. Nontrivial comparative illustrations are constructed to support the hypotheses and indicate the preeminence of the obtained key concepts. From application viewpoints, one of our results is applied to discuss new conditions for solving a Volterra-type integral equation.
The recent years have witnessed a wealth of research on energy harvesting technologies. To maximize the output power, vibration-based energy harvesters are normally designed to exhibit natural ...frequencies that match those of the excitation. This has spurred interest into the design of devices that possess tunable natural frequencies to cope with sources which exhibit varying frequencies. In this work, an energy harvester is proposed in the form of a base excited cantilever treated with a piezoelectric layer. The cantilever carries a tip mass in the form of a magnet which is placed in close proximity to a stationary magnet with opposite polarity. Different values of axial tensions, and hence different natural frequencies, are obtained by adjusting the gap between the magnets. A dynamic model to predict the system performance is presented and verified experimentally. Based on the findings of this paper, natural frequencies ranging from 3.19 to 12
Hz were achieved.
The use of vibration-based techniques in damage identification has recently received considerable attention in many engineering disciplines. While various damage indicators have been proposed in the ...literature, those relying only on changes in the natural frequencies are quite appealing since these quantities can conveniently be acquired. Nevertheless, the use of natural frequencies in damage identification is faced with many obstacles, including insensitivity and non-uniqueness issues. The aim of this article is to develop a viable damage identification scheme based only on changes in the natural frequencies and to attempt to overcome the challenges typically encountered. The proposed methodology relies on building a finite element model (FEM) of the structure under investigation. An improved particle swarm optimization algorithm is proposed to facilitate updating the FEM in accordance with experimentally determined natural frequencies in order to predict the damage location and extent. The method is tested on beam structures and was shown to be an effective tool for damage identification.
