Hyers Stability and Multi-Fuzzy Banach Algebra

In this paper, we define multi-fuzzy Banach algebra and then prove the stability of involution on multi-fuzzy Banach algebra by fixed point method. That is, if f:A→A is an approximately involution on multi-fuzzy Banach algebra A, then there exists an involution H:A→A which is near to f. In addition, under some conditions on f, the algebra A has multi C*-algebra structure with involution H.

Sets of Fractional Operators and Numerical Estimation of the Order of Convergence of a Family of Fractional Fixed-Point Methods

Considering the large number of fractional operators that exist, and since it does not seem that their number will stop increasing soon at the time of writing this paper, it is presented for the first time, as far as the authors know, a simple and compact method to work the fractional calculus through the classification of fractional operators using sets. This new method of working with fractional operators, which may be called fractional calculus of sets, allows generalizing objects of conventional calculus, such as tensor operators, the Taylor series of a vector-valued function, and the fixed-point method, in several variables, which allows generating the method known as the fractional fixed-point method. Furthermore, it is also shown that each fractional fixed-point method that generates a convergent sequence has the ability to generate an uncountable family of fractional fixed-point methods that generate convergent sequences. So, it is presented a method to estimate numerically in a region Ω the mean order of convergence of any fractional fixed-point method, and it is shown how to construct a hybrid fractional iterative method to determine the critical points of a scalar function. Finally, considering that the proposed method to classify fractional operators through sets allows generalizing the existing results of the fractional calculus, some examples are shown of how to define families of fractional operators that satisfy some property to ensure the validity of the results to be generalized.

Fixed points and stability of A class of Stochastic dynamical system driven by Brownian motion

In real life, many models and systems are affected by random phenomena. For this reason, experts and scholars propose to describe these stochastic processes with Brownian motion respectively. In this paper we consider a kind of stochastic Vollterra dynamical systems of nonconvolution type and give some new conditions to ensure that the zero solution is asymptotically stable in mean square by means of fixed point method. The theorems of asymptotically stability in mean square with a necessary conditions are proved. Some results of related papers are improved.

Оn the Analysis of Certain Flotation Processes with Velocities Depending on Time and Height of the Column

— The present paper is an extension of the previous paper of the author where the flotation column dynamics has been investigated. Here we consider the case when particle sedimentation rate and bubble lifting speed depend on time and position in the column. We use the methods for examining the transmission lines set out in the papers mentioned in the References. We formulate a mixed problem for the system describing the processes in the column and present it in a suitable operator form. Then we prove an existence - uniqueness of generalized solution by the fixed point method. We show an explicit approximated solution as a step in the sequence of successive approximations.

SIMULASI PERBANDINGAN TITIK JEPIT TIANG MENGGUNAKAN VIRTUAL FIXED POINT DAN LATERAL SPRING DI DERMAGA “KNP”

The jetty is the most important facility in the port because it is connected between the sea and the land. The jetty structure consists of the upper structure (beams, plates and pile caps) and the lower structure (piles). The upper structure uses reinforced concrete as the base material and the lower structure can use steel or concrete material. In designing the piles on the jetty, the depth of the fixed point is not at the seabed depth, but below the seabed. It is necessary to conduct research on the depth of the pile fixed point at KNP jetty Southeast Sulawesi. Based on the OCDI 2002 (Overseas Coastal Area Development Institute of Japan) using the virtual fixed point method (1/β), the depth of the fixed point on the KNP jetty is 24 m, meanwhile according to the lateral spring method the KNP jetty has a fixed point depth of 25,6 m. and by adding a lateral spring to the pile in the virtual fixed point method, it can also make the model more efficient with a smaller deflection of 6,43% for deflection due to earthquake in the x direction and 7,25% for deflection due to earthquake in y direction. ABSTRAKDermaga merupakan fasilitas yang paling penting pada pelabuhan karena menghubungkan antara laut dan daratan. Struktur dermaga terdiri dari struktur atas (balok, pelat dan pile cap) dan struktur bawah (tiang pancang). Struktur atas menggunakan bahan dasar beton bertulang dan struktur bawah dapat menggunakan bahan baja atau beton. Dalam mendesain tiang pancang pada dermaga, kedalaman titik jepit tidak berada pada kedalaman seabed tetapi berada dibawah seabed. Perlu dilakukan penelitian tentang kedalaman titik jepit tiang pancang. Studi kasus yang dibahas pada penelitian ini adalah dermaga yang berlokasi di Kendari, Sulawesi Tenggara. Dermaga tersebut dikenal dengan nama dermaga “KNP”. Berdasarkan OCDI (Overseas Coastal Area Development Institute of Japan) tahun 2002 dengan menggunakan metode virtual fixed point (1/β) memiliki kedalaman titik jepit pada dermaga “KNP” sebesar 24 m, sedangkan menurut metode pegas lateral pada dermaga “KNP” memiliki kedalaman titik jepit sebesar 25,6 m dan dengan menambahkan pegas lateral pada tiang pancang dalam metode virtual fixed point juga dapat membuat model lebih efisien dengan defleksi yang lebih kecil sebesar 6,43% untuk defleksi akibat gempa arah x dan 7,25% untuk defleksi akibat gempa arah y.

Elegant Iterative Methods for Solving a Nonlinear Matrix Equation X-A* eX A=I

The nonlinear matrix equation was solved by Gao (2016) via standard fixed point method. In this paper, three more elegant iterative methods are proposed to find the approximate solution of the nonlinear matrix equation namely: Newton’s method; modified fixed point method and a combination of Newton’s method and fixed point method. The convergence of Newton’s method and modified fixed point method are derived. Comparative numerical experimental results indicate that the new developed algorithms have both less computational time and good convergence properties when compared to their respective standard algorithms. Keywords: Hermitian positive definite solution; nonlinear matrix equation; modified fixed point method; iterative method

On Stability of a General Bilinear Functional Equation

We prove the Hyers–Ulam stability of the functional equation $$\begin{aligned}&f(a_1x_1+a_2x_2,b_1y_1+b_2y_2)=C_{1}f(x_1,y_1)\nonumber \\ \nonumber \\&\quad +C_{2}f(x_1,y_2)+C_{3}f(x_2,y_1)+C_{4}f(x_2,y_2) \end{aligned}$$ f ( a 1 x 1 + a 2 x 2 , b 1 y 1 + b 2 y 2 ) = C 1 f ( x 1 , y 1 ) + C 2 f ( x 1 , y 2 ) + C 3 f ( x 2 , y 1 ) + C 4 f ( x 2 , y 2 ) in the class of functions from a real or complex linear space into a Banach space over the same field. We also study, using the fixed point method, the generalized stability of $$(*)$$ ( ∗ ) in the same class of functions. Our results generalize some known outcomes.