In this paper, we will be discussing fuzzy statistically convergent in 2-norm in a fuzzy 2-normed Riesz spaces. We also define the notion of a Fsc2 n- Cauchy in fuzzy 2-normed Riesz spaces and establish some basic facts.
It is well known, that if f be continuous functions define on [a, b], a, b ∈ R, there is interpolating polynomials Pn on {a_i}_{i=1}^{m} satisfy: ||f − P_n||_p ≤ (1/n^r) ω_t(f^(r), 1/n)_p. where ωt is the t – th usual modulus for the smoothness’ , and Pn (i) (ai) = f(i) (ai ), 1 ≤ i ≤ m, m < r, m, r ∈ N. In this paper we shall answer the following questions: Is the above result true for intertwining, one-sided, positive, co-positive approximation.
In this essay, address the recently found microbiological topological spaces, such as microbiological closed and open sets in bitopological spaces. Furthermore, make and justify a number from statements about these concepts. A micro bitopological space is one whose topology is determined via a group of bundles. In comparison, in a typical topological space, the topology is specified via a single set. The power of micro bitopological spaces lies in their ability to model a broad range of mathematical objects that can describe the topology of a manifold or a group. Micro bitopological spaces have numerous uses in mathematics, such as investigating the geometry of a space or the structure of a group. Microtopological spaces are also simple to manipulate and have numerous mathematical applications.
Differential equations play a role in Applied Physics; it’s not always feasible to find analytical solutions for nonlinear partial differential equations when dealing with certain phenomena. In this instance, we provide series solutions using a semi-analytical approach. These approaches’ solutions are looked for as series. The basic principle of semi-analytical approaches is to determine the series’ other terms from specified initial conditions. Some semi-analytic techniques can achieve extremely good convergence with only a few series terms, but other issues may require more terms to improve convergence to the analytical solution. This study uses the Variational Iteration Adomian Decomposition Method (VIADM) to investigate the convergence of approximate-analytical solutions of certain kinds of nonlinear differential equations.
This article introduces the complex - valued public metric spaces, with some examples, and study its properties as well as we have been proven an existence for the fixed points via weakly types compatible maps and also study (CLRg)) and (EA) properties.
In this paper, we study the approximate solutions of the second-order fractional Bratu-type equation. In order to find a solution, we examine by the homotopy perturbation transform method (HPTM) using the derivative of Caputo-Fabrizio (CFD). The fractional Bratu-type equation (FBTEs) arises in various fields such as chemical reaction theory, nanotechnology, and heat transfer. We are able to find a few new approximate solutions. To acquire comprehensive configurations, we plot two- and three-dimensional diagrams using Mathematica. This study demonstrates that the completely discriminative system technique is an easy and effective way to arrive at different kinds of approximate solutions. It also offers a more potent mathematical tool for solving a large number of additional fractional Bratutype equations using computers and symbolic computation.
In this work, we describe and investigate a novel class of analytic functions, including the new functions and the Bazilevič functions. Bazilevič functions are a crucial part of analytic functions and have many applications in pure and applied mathematics. We focus on constructing Toeplitz matrices, studying their structural properties, and assessing their eigenvalues and trends for this class of functions. The goal of this work is to calculate coefficient estimates for the functions in this family for the Toeplitz matrix’s first four determinants, symmetric T2 (2), T2 (3), T3 (1), and T3 (2).
The study evaluates how dissipation influences wave phenomena through a viscoporoelastic sandy layer and a visco-poroelastic semi-infinite half-space where initial stress exists. The model includes analysis of both poroelastic and viscoelastic characteristics together with detailed studies of solid-fluid phase connections in porous materials. The mathematical model relies on coupled equations that describe the mechanics of porous media, emphasizing the effects of viscosity and porosity on wave speed, attenuation, and dissipation. Influence of several parameters including initial stress, viscosity, porosity, and dissipative effects on wave propagation are demonstrated numerically. Applications in Material Science, seismic exploration, Geotechnical Engineering can benefit from the findings, which offer valuable insights on how waves behave in porous media.
This article introduces some concepts on the 𝑠𝑜𝑓𝑡 topological 𝑠𝑜𝑓𝑡 group (Stsg). We used a concept for the 𝑠𝑜𝑓𝑡 topological 𝑠𝑜𝑓𝑡 groups to construct the bτi-𝑠𝑜𝑓𝑡 topological 𝑠𝑜𝑓𝑡 groups, b-regular 𝑠𝑜𝑓𝑡 topology 𝑠𝑜𝑓𝑡 groups, as well as studied relationships between them.
An efficient approach is used in this article to solve and analyze the nonlinear autonomous equations. The Tanh method provides more general, precise traveling wave solutions with little additional work. The Tanh technique is demonstrated to be an effective mathematical tool for solving nonlinear autonomous equations and any model equation in mathematical physics. Additionally, the obtained solutions are physically represented and interpreted. Furthermore, the authors present the visual effects of the behavior of wave structures using various figures and contour plots, in the results to enhance our comprehensive understanding.
In order to solve delay differential equations (DDEs), this work proposes a novel hybrid methodology that combines the Emad-Falih transform (EF) and homotopy perturbation methods (HPM), which is named (HPEFM). A perturbation theory is combined with an unusual transform known as the EF transform. The few numerical cases are solved to illustrate this new methodology. The goal for this study is to make computational jobsrelated to traditional methods easier. The results show the extent of the valuation decrease and are comparable to those of earlier studies.
The sporadic Held group hides a concealed geometric superstructure within its algebraic essence. The model is realized as the uniform A4-graph, facilitating the assessment of a wide variety of molecular descriptor and the corresponding wiener distanceenumerating polynomial and topological generating polynomial. The overall consequence presents encapsulated formulations that analytically link the topological descriptors to two major elements: conjugacy class cardinalities and graph disc dynamics. This suggests that the intricate topology of the entire system is, in fact, a concealed expression of its fundamental algebraic base.
In this research, we introduce a recent type of open set, called a pre-feebly-open set, obtained by accrediting the feebly open set. We have defined and studied this type and specified several of its characteristics. We found some features and connections with other sets, obtained results that explain them, and symbolized them with the symbol pre-feeblyopen. Also, we introduced and defined the notions of pre-f-closure and pre-f-interior. As well as offer the properties, prove them, and others.
This research presents an effective approach for resolving nonlinear differential equations with mixed derivatives, focusing on the Ito problem. Unlike traditional methods that require decomposing or transforming the problem into a system of differential equations, our proposed approach directly tackles the problem’s complexity while ensuring computational efficiency and precision. The Ito equation, recognized for its importance in simulating many physical and stochastic phenomena, poses considerable challenges owing to its nonlinearity and mixed-derivative terms. Our methodology uses this technique, which decomposes the mixed derivative to derive partial solutions for the other derivative of the equation, then leads to partial solutions for the equation itself, ultimately representing the entire or approximate solution to the equation. This approach guarantees reliable, accurate solutions while preserving the structural integrity of the original equation.
An innovative collection of openR setsR, specifically αγos-openR setsR are offered by this paper authors and its rudimentary properties utilizing the respective τγos-interiorR and τγos- closureR operatorsR are premeditated in their previous papers. As well, it has been substantiated that the idea of γos-openR setsR besides αγos - openR setsR are autonomous and each γos-openR setR is an αos openR setR, but the contrary need not be exact. The perceptions of αγos Ti spacesR also their properties are familiarized and recognized the connection among these spacesR by establishing several Theorems, undistinguishable statements, consequences besides corollaries. Another new collection of openR setsR namely α(γos, γ¢os)-openR setsRwas introduced and their properties were presented with the corresponding interiorR and closureR operators. Further the idea of α(γos, γ¢os) Ti spacesR were adapted and documented the connection among these spaces by providing several theorems. The theory of α(γos, γ¢os) Ri spacesR have been familiarized and their descriptions have been premeditated by illustrating τα(γos, γ¢os) -kernel and several statements comprehend to that idea. Also the association amongst these α(γos, γ¢os) Ri spacesR have been formed and evaluated by means of several axioms and opposite affirmations.
In this article, we present a novel space, said complex valued public metric spaces, and show some of its properties. Examine the convergence of sequences in this space. We will also demonstrate the standard F.P theorems for mappings that are w-compatible.
In this operation, construct ZMA-transform (ZMAT) for solving initial-value problem (IVP) of linear first and second (1st and 2nd) order delay differential equation (DDEs), to realize this method produce provided theorem used it to solve applications to acquire the exact solution (EX).
This work satisfies cohomology theory within the framework of fuzzy bornological groups. The primary objective is to establish a robust formalization of cohomology for these fuzzy groups and to extend the fundamental properties of classical cohomology to the fuzzy group setting. To achieve this, we construct a cohomology theory for a fuzzy bornological group (G ̃, δ ̃) and a fuzzy bornological G ̃-modules (M ̃ ,δ ̃), by utilizing the concept of fuzzy bounded cochains.
In this paper, we establish a neuromorphic crisp triple tri topological group. The neuromorphic crisp triple, a topological space and continuous function, is defined and used in constructing the new concept. We study the basic properties of this new concept, including the fundamental system of NBHDS.
This research article investigates two subclasses of bi-univalent functions associated with (s, t)-Lucas polynomials in 𝔻. It intriguing since they are fundamental to geometric function theory. To understand the geometrical properties of these subclasses, the estimates of two initial Taylor-Maclaurin coefficients |a2| as well as |a3| are very essential. These playa vital role to explore a number of significant geometric features of subclasses. These initial coefficients provide significant information about the behavior of the function near the origin, revealing its functional characteristics, interaction with the boundary of the unit disk, and possible subclassifications. In particular, their distortion, growth behaviour, and mapping qualities. Additionally, we employ the Fekete-Szegö approximation, a technique frequently employed to derive precise constraints for these two subclasses, which traditionally gives upper bounds for |a3 – τa22|.
