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In this paper, we are dealing with the ill-posed Cauchy problem for an elliptic operator. This is a follow-up to a previous paper on the same subject. Indeed, in an earlier publication, we introduced a regularization method, called the controllability method, which allowed us to propose, on the one hand, a characterization of the existence of a regular solution to the ill-posed Cauchy problem. On the other hand, we have also succeeded in proposing, via a strong singular optimality system, a characterization of the optimal solution to the considered control problem, and this, without resorting to the Slater-type assumption, an assumption to which many analyses had to resort. On occasion, we have dealt with the control problem, with state boundary observation, the problem initially analyzed by J. L. Lions. The proposed point of view, consisting of the interpretation of the Cauchy system as a system of two inverse problems, then called naturally for conjectures in favor of which the present manuscript wants to constitute an argument. Indeed, we conjectured, in view of the first results obtained, that the proposed method could be improved from the point of view of the initial interpretation that we had made of the problem. In this sense, we analyze here two other variants (observation of the flow, then distributed observation) of the problem, the results of which confirm the intuition announced in the previous publication mentioned above. Those results, it seems to us, are of significant relevance in the analysis of the controllability method previously introduced. [ABSTRACT FROM AUTHOR]

In this paper, under appropriate hypotheses, we have the existence of a solution semigroup of partial differential equations with delay operator. These equations are used to describe time–age-structured cell cycle model. We also prove that the solution semigroup is a frequently hypercyclic semigroup. [ABSTRACT FROM AUTHOR]

In this paper, we propose an eco-epidemiological mathematical model in order to describe the effect of migration on the dynamics of a prey–predator population. The functional response of the predator is governed by the Holling type II function. First, from the perspective of mathematical results, we develop results concerning the existence, uniqueness, positivity, boundedness, and dissipativity of solutions. Besides, many thresholds have been computed and used to investigate the local and global stability results by using the Routh–Hurwitz criterion and Lyapunov principle, respectively. We have also established the appearance of limit cycles resulting from the Hopf bifurcation. Numerical simulations are performed to explore the effect of migration on the dynamic of prey and predator populations. [ABSTRACT FROM AUTHOR]

This paper introduces a novel category of nonlinear mappings and provides several theorems on their existence and convergence in Banach spaces, subject to various assumptions. Moreover, we obtain convergence theorems concerning iterates of α -Krasnosel'skiĭ mapping associated with the newly defined class of mappings. Further, we present that α -Krasnosel'skiĭ mapping associated with b -enriched quasinonexpansive mapping is asymptotically regular. Furthermore, some new convergence theorems concerning b -enriched quasinonexpansive mappings have been proved. [ABSTRACT FROM AUTHOR]

We study in this paper a general shape of damped Euler–Bernoulli beams with variable coefficients. Our main goal is to generalize several works already done on damped Euler–Bernoulli beams. We start by studying the spectral properties of a particular case of the system, and then we determine asymptotic expressions that generalize those obtained by other authors. At last, by adopting well-known techniques, we establish the Riesz basis property of the system in the general case, and the exponential stability of the system is obtained under certain conditions relating to the feedback coefficients and the sign of the internal damping on the interval studied of length 1. [ABSTRACT FROM AUTHOR]

In this paper, we study the hyperstability problem for the well-known σ -Jensen's functional equation f x y + f x σ y = 2 f x for all x , y ∈ S , where S is a semigroup and σ is an involution of S. We present sufficient conditions on E ⊂ ℝ + S 2 so that the inhomogeneous form of σ -Jensen's functional equation f x y + f x σ y = 2 f x + φ x , y for all x , y ∈ S , where the inhomogeneity φ is given, can be E -hyperstable on S. [ABSTRACT FROM AUTHOR]

Nirenberg proposed a problem as to whether or not a continuous and expansive operator T : X ⟶ X (where X is a Hilbert space) is surjective if R T ∘ ≠ ∅. I shall give a positive answer for the problem provided that R T ∘ is unbounded. For contents related to this paper, the reader is referred to the remarks and the study of Asfaw (2021). The present paper gives a complete answer for the problem that has been open for about 47 years. [ABSTRACT FROM AUTHOR]

Hepatitis B is one of the leading causes of morbidity and mortality, affecting hundreds of millions of people worldwide. Thus, this paper focuses on three control measures as the best way to intervene against the hepatitis B viral infection. These measures are condom use, testing and treatment, and vaccination to stop the disease from spreading over a community. The model comprises seven (7) compartments that include susceptible individuals, latent individuals, acute-infected individuals, chronic-infected individuals, infected by carrier individuals, recovered individuals from the disease, and the vaccinated population. We mathematically established a nonlinear differential equation to study the dynamics of the model. The disease-free equilibrium (DFE) and endemic equilibrium (EE) are reached. The basic reproduction numbers, R 0 A , R 0 H , and R 0 C , determine the transmission of the disease and thus are gotten. We perform sensitivity analysis on the reproduction numbers to identify the factors that affect the reproduction numbers. The results of the sensitivity analysis paved a way for introducing a controlled system which was solved using Pontryagin's maximum principle (PMP) and the optimality system got. The optimality system was then solved numerically using the forward and backward sweep approach, and graphs were generated, establishing the conditions for local and global stability of the disease-free equilibrium using the Routh-Hurwitz criterion and Castillo-Chavez approach, respectively. We also used Pontryagin's maximum principle to determine the optimality system. The result of the analysis of the stability of the disease-free equilibrium states that hepatitis B virus can be completely wiped out if the rate of infection is kept at a number less than unity. A numerical simulation of the model was carried out and showed that hepatitis B virus transmission can best be controlled when condom use, testing and treatment, and vaccination are implemented. [ABSTRACT FROM AUTHOR]

In this paper, we consider an initial value problem for the 2-D compressible Navier-Stokes equations without heat conductivity. We prove the global existence of a strong solution when the initial perturbation is small in H 2 and its L 1 norm is bounded. Moreover, we derive some decay estimate for such a solution. [ABSTRACT FROM AUTHOR]

In this paper, we extend the results obtained by Ezearn on annihilated points for his higher-order nonexpansive mappings to the context of general higher-order nonexpansive mappings. Precisely in his thesis, Ezearn introduced the concept of annihilated points, which extends the notion of fixed points, and it is only meaningful in the context of higher-order nonexpansive mappings and gave some mild conditions when the annihilated points could exist in strictly convex Banach spaces. In the last direction, we also extend Ezearn's result on the approximate fixed point sequence for higher-order nonexpansive mappings to general higher-order nonexpansive mappings. [ABSTRACT FROM AUTHOR]

Throughout this paper, we will present a new extension of the Wright hypergeometric matrix function by employing the extended Pochhammer matrix symbol. First, we present the extended hypergeometric matrix function and express certain integral equations and differential formulae concerning it. We also present the Mellin matrix transform of the extended Wright hypergeometric matrix function. After that, we present some fractional calculus findings for these expanded Wright hypergeometric matrix functions. Lastly, we present several theorems of the extended Wright hypergeometric matrix function in fractional Kinetic equations. [ABSTRACT FROM AUTHOR]

The small Lipschitz is a generalization of the Lipschitz condition. The Lipschitz condition guarantees the uniqueness of the solution of the initial value problems. A special Lipschitz condition in the small is a contraction in the small. Based on the small Lipschitz in this paper, fixed-point theorems involving contraction in the small will be presented. The results will be applied to develop Picard's theorem. [ABSTRACT FROM AUTHOR]

In this paper, we explore a generalised solution of the Cauchy problems for the q -heat and q -wave equations which are generated by Jackson's and the q -Sturm-Liouville operators with respect to t and x , respectively. For this, we use a new method, where a crucial tool is used to represent functions in the Fourier series expansions in a Hilbert space on quantum calculus. We show that these solutions can be represented by explicit formulas generated by the q -Mittag-Leffler function. Moreover, we prove the unique existence and stability of the weak solutions. [ABSTRACT FROM AUTHOR]

By combining the notions of G -metric space and b -metric space, in this paper, we present coincidence fixed-point theorems for p -hybrid mappings in G b -metric spaces. An example is given to demonstrate the novelty of our main results. Henceforth, the illustrative applications are given by using nonlinear fractional differential equations. [ABSTRACT FROM AUTHOR]

The paper deals with a coupling algorithm using shape and topological derivatives of a given cost functional and a problem governed by nonstationary Maxwell's equations in 3D. To establish the shape and topological derivatives, an adjoint method is used. For the topological asymptotic expansion, two examples of cost functionals are considered with the perturbation of the electric permittivity and magnetic permeability. We combine the shape derivative and topological one to propose an algorithm. The proposed algorithm allows to insert a small inhomogeneity (electric or magnetic) in a given shape. [ABSTRACT FROM AUTHOR]

This paper introduces novel concepts of joint Y , Z cyclic G ‐ Ω S , T , a b e f -weak contraction and joint Y , Z cyclic G ‐ Ω S , T , a b e f -weak nonexpansive mappings and then proves the existence of a unique common fixed point of such mappings in case of complete and compact metric spaces, respectively, in particular, it proves the existence of a unique fixed point for both cyclic G ‐ Ω S , a b e f -weak contraction and cyclic G ‐ Ω S , a b e f -weak nonexpansive mappings, and hence, it also proves the existence of a unique fixed point for both cyclic Ω S , a b e f -weak contraction and cyclic Ω S , a b e f -weak nonexpansive mappings. The results of this research paper extend and generalize some fixed point theorems previously proved via the attached references. [ABSTRACT FROM AUTHOR]

This paper introduces novel concepts of joint Y , Z cyclic G ‐ Ω S , T , a b e f -weak contraction and joint Y , Z cyclic G ‐ Ω S , T , a b e f -weak nonexpansive mappings and then proves the existence of a unique common fixed point of such mappings in case of complete and compact metric spaces, respectively, in particular, it proves the existence of a unique fixed point for both cyclic G ‐ Ω S , a b e f -weak contraction and cyclic G ‐ Ω S , a b e f -weak nonexpansive mappings, and hence, it also proves the existence of a unique fixed point for both cyclic Ω S , a b e f -weak contraction and cyclic Ω S , a b e f -weak nonexpansive mappings. The results of this research paper extend and generalize some fixed point theorems previously proved via the attached references. [ABSTRACT FROM AUTHOR]

This paper is aimed at proving a common fixed point theorem for F -Kannan mappings in metric spaces with an application to integral equations. The main result of the paper will extend and generalise the recent existing fixed point results in the literature. We also provided illustrative examples and some applications to integral equation, nonlinear fractional differential equation, and ordinary differential equation for damped forced oscillations to support the results. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some stability results of fixed point sets for a sequence of enriched contraction mappings in the setting of convex metric spaces. In particular, two types of convergence of mappings, namely, G -convergence and H -convergence are considered. We also illustrate our results by an application to an initial value problem for an ordinary differential equation. [ABSTRACT FROM AUTHOR]

In this paper, by using properties of attractive points, we study an iteration scheme combining simplified Baillon type and Mann type to find a common fixed point of commutative two nonlinear mappings in Hilbert spaces. Then, we apply the obtained results to prove a new weak convergence theorem. [ABSTRACT FROM AUTHOR]

In this paper, common best proximity point theorems for weakly contractive mapping in b-metric spaces in the cases of nonself-mappings are proved; we introduced the notion of generalized proximal weakly contractive mappings in b-metric spaces and proved the existence and uniqueness of common best proximity point for these mappings in complete b-metric spaces. We also included some supporting examples that our finding is more generalized with the references we used. [ABSTRACT FROM AUTHOR]

Based on the concept of pseudocomplement, we introduce a new representation of preopenness of L -fuzzy sets in R L -fuzzy bitopological spaces. The concepts of pairwise R L -fuzzy precontinuous and pairwise R L -fuzzy preirresolute functions are extended and discussed based on the i , j - R L -preopen gradation. Further, we follow up with a study of pairwise R L -fuzzy precompactness in R L -fuzzy bitopological spaces of an L -fuzzy set. We find that our paper offers more general results since R L -fuzzy bitopology is a generalization of L -bitopology, R L -bitopology, and L -fuzzy topology. [ABSTRACT FROM AUTHOR]

In this paper, we combine the Elzaki transform method (ETM) with the new homotopy perturbation method (NHPM) for the first time. This hybrid approach can solve initial value problems numerically and analytically, such as nonlinear fractional differential equations of various normal orders. The Elzaki transform method (ETM) is used to solve nonlinear fractional differential equations, and then the homotopy is applied to the transformed equation, which includes the beginning conditions. To obtain the solution to an equation, we use the inverse transforms of the Elzaki transform method (ETM). The initial conditions have a big impact on the equation's result. We give three beginning value issues that were solved as precise or approximation solutions with high rigor to demonstrate the method's power and correctness. It is clear that solving nonlinear partial differential equations with the crossbred approach is the best alternative. [ABSTRACT FROM AUTHOR]

In this paper, we establish a generalization of the Galewski-Rădulescu nonsmooth global implicit function theorem to locally Lipschitz functions defined from infinite dimensional Banach spaces into Euclidean spaces. Moreover, we derive, under suitable conditions, a series of results on the existence, uniqueness, and possible continuity of global implicit functions that parametrize the set of zeros of locally Lipschitz functions. Our methods rely on a nonsmooth critical point theory based on a generalization of the Ekeland variational principle. [ABSTRACT FROM AUTHOR]

In this paper, we introduce original definitions of Smarandache ruled surfaces according to Frenet-Serret frame of a curve in E 3. It concerns TN-Smarandache ruled surface, TB-Smarandache ruled surface, and NB-Smarandache ruled surface. We investigate theorems that give necessary and sufficient conditions for those special ruled surfaces to be developable and minimal. Furthermore, we present examples with illustrations. [ABSTRACT FROM AUTHOR]

In this paper, we study initial boundary value problems that involve functional (nonlocal) partial differential equations with variable coefficients. These problems arise in cell growth models with symmetric and asymmetric modes of division. We determine the general solution to the symmetric cell division problem for a certain class of coefficients and establish the convergence of solutions to a large time asymptotic solution. The existence of a steady size distribution (SSD) solution for an asymmetric cell division problem is established and is shown to be the large time-attracting solution for a certain class of coefficients. The rate of convergence of solutions towards the SSD solution is affected by the choice of coefficients and remains unaffected by the asymmetry in cell division. The uniqueness of solutions to the initial boundary value problem is also established. [ABSTRACT FROM AUTHOR]

In this paper, I consider the Cauchy problem for the incompressible Navier-Stokes equations in ℝ + n for n ≥ 3 with bounded initial data and derive a priori estimates of the maximum norm of all derivatives of the solution in terms of the maximum norm of the initial data. This paper is a continuation of my work in my previous papers, where the initial data are considered in T n and ℝ n respectively. In this paper, because of the nonempty boundary in our domain of interest, the details in obtaining the desired result are significantly different and more challenging than the work of my previous papers. This challenges arise due to the possible noncommutativity nature of the Leray projector with the derivatives in the direction of normal to the boundary of the domain of interest. Therefore, we only consider one derivative of the velocity field in that direction. [ABSTRACT FROM AUTHOR]

In this paper, we develop an a posteriori error analysis for the stationary Stokes-Darcy coupled problem approximated by conforming the finite element method on isotropic meshes in ℝ d , d ∈ 2 , 3 . The approach utilizes a new robust stabilized fully mixed discretization. The a posteriori error estimate is based on a suitable evaluation on the residual of the finite element solution plus the stabilization terms. It is proven that the a posteriori error estimate provided in this paper is both reliable and efficient. [ABSTRACT FROM AUTHOR]

Several fixed point results for the existence of common fixed points of multivalued contractive mappings have been established in complex-valued metric space. In this paper, we study the existence of common fixed points for a pair of multivalued contractive mappings satisfying some rational inequalities in the framework of complex-valued b -metric spaces. The contractive condition used in this paper generalizes many contractive conditions used by other authors in the literature. Employing our results, we check the existence solution to the Riemann-Liouville equation. [ABSTRACT FROM AUTHOR]

In this paper, a discretization of a three-dimensional fractional-order prey-predator model has been investigated with Holling type III functional response. All its fixed points are determined; also, their local stability is investigated. We extend the discretized system to an optimal control problem to get the optimal harvesting amount. For this, the discrete-time Pontryagin's maximum principle is used. Finally, numerical simulation results are given to confirm the theoretical outputs as well as to solve the optimality problem. [ABSTRACT FROM AUTHOR]

It is known that injective (complex or real) W ∗ -algebras with particular factors have been studied well enough. In the arbitrary cases, i.e., in noninjective case, to investigate (up to isomorphism) W ∗ -algebras is hard enough, in particular, there exist continuum pairwise nonisomorphic noninjective factors of type II. Therefore, it seems interesting to study maximal injective W ∗ -subalgebras and subfactors. On the other hand, the study of maximal injective W ∗ -subalgebras and subfactors is also related to the well-known von Neumann's bicommutant theorem. In the complex case, such subalgebras were investigated by S. Popa, L. Ge, R. Kadison, J. Fang, and J. Shen. In recent years, studies have also begun in the real case. Let us briefly recall the relevance of considering the real case. It is known that in the works of D. Topping and E. Stormer, it was shown that the study of JW-algebras (nonassociative real analogues of von Neumann algebras) of types II and III is essentially reduced to the study of real W ∗ -algebras of the corresponding type. It turned out that the structure of real W ∗ -algebras, generally speaking, differs essentially in the complex case. For example, in the finite-dimensional case, in addition to complex and real matrix algebras, quaternions also arise, i.e., matrix algebras over quaternions. In the infinite-dimensional case, it is proved that there exist, up to isomorphism, two real injective factors of type III λ (0 < λ < 1), and a countable number of pairwise nonisomorphic real injective factors of type III 0 , whose enveloping (complex) W ∗ -factors are isomorphic, is constructed. It follows from the above that the study of the real analogue of problems in the theory of operator algebras is topical. Moreover, the real analogue is a generalization of the complex case, since the class of real linear operators is much wider than the class of complex linear operators. In this paper, the maximal injective real W ∗ -subalgebras of real W ∗ -algebras or real factors are investigated. For real factors Q ⊂ R , it is proven that if Q + i Q is a maximal injective W ∗ -subalgebra in R + i R , then Q also is a maximal injective real W ∗ -subalgebra in R. The converse is proved in the case " II 1 "-factors, that is, it is shown that if R is a real factor of type II 1 , then the maximal injectivity of Q implies the maximal injectivity of Q + i Q. Moreover, it is proven that a maximal injective real subfactor Q of a real factor R is a maximal injective real W ∗ -subalgebra in R if and only if Q is irreducible in R , i.e., Q ′ ∩ R = ℝ I where I is the unit. The "splitting theorem" of Ge-Kadison in the real case is also proven, namely, if R 1 is a finite real factor, R 2 is a finite real W ∗ -algebra, and R is a real W ∗ -subalgebra of R 1 ⊗ ¯ R 2 containing R 1 ⊗ ¯ ℝ I , then there is some real W ∗ -subalgebra Q 2 ⊂ R 2 such that R = R 1 ⊗ ¯ Q 2 . Moreover, it is given some affirmative answers to the question of S. Popa for the real case. [ABSTRACT FROM AUTHOR]

This paper presents a new technique for solving linear Volterra integro-differential equations with boundary conditions. The method is based on the blending of the Chebyshev spectral methods. The application of the proposed method leads the Volterra integro-differential equation to a system of algebraic equations that are easy to solve. Some examples are introduced and the obtained results are compared with exact solution as well as the methods that reported in the literature to illustrate the effectiveness and accuracy of the method. The results demonstrate that there is congruence between the numerical and the exact results to a high order of accuracy. Tables were generated to verify the accuracy convergence of the method and error. Figures are presented to show the excellent agreement between the results of this study and the results from literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce generalized α , ψ -contraction mappings in the setting of rectangular b -metric spaces and established existence and uniqueness of fixed points for the mappings introduced. Our results extend and generalize related fixed point results in the existing literature. We derive some consequences and corollaries from our obtained results. Also, we provide examples in support of our main findings. Furthermore, we determined a solution to an integral equation by applying our obtained results. [ABSTRACT FROM AUTHOR]

This paper proves a common fixed point theorem for single-valued and multivalued mappings by using ternary relation in G -metric spaces. Henceforth, results obtained will be verified with the help of illustrative examples. Also, we demonstrate the results with an application. [ABSTRACT FROM AUTHOR]

In this paper, we present a mathematical model that describes agree-disagree opinions during polls. We first present the different compartments of the model. Then, using the next-generation matrix method, we derive thresholds of the stability of equilibria. We consider two sets of data from the Reuters polling system regarding the approval rating of the U.S presidential in two terms. These two weekly polls data track the percentage of Americans who approve and disapprove of the way the President manages his work. To validate the reality of the underlying model, we use nonlinear least-squares regression to fit the model to actual data. In the first poll, we consider only 31 weeks to estimate the parameters of the model, and then, we compare the rest of the data with the outcome of the model over the remaining 21 weeks. We show that our model fits correctly the real data. The second poll data is collected for 115 weeks. We estimate again the parameters of the model, and we show that our model can predict the poll outcome in the next weeks, thus, whether the need for some control strategies or not. Finally, we also perform several computational and statistical experiments to validate the proposed model in this paper. To study the influence of various parameters on these thresholds and to identify the most influential parameters, sensitivity analysis is carried out to investigate the effect of the small perturbation near a parameter value on the value of the threshold. An uncertainty analysis is performed to evaluate the forecast inaccuracy in the outcome variable due to uncertainty in the estimation of the parameters. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a proximal point algorithm for approximating a common solution of finite family of convex minimization problems and fixed point problems for k -demicontractive mappings in complete CAT(0) spaces. We prove a strong convergence result and obtain other consequence results which generalize and extend some recent results in the literature. We further provide a numerical example to illustrate the convergence behaviour of the sequence generated by our algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we consider a JS metric space endowed with convexity structure, which will allow us to examine and study convergence of Mann iteration and Ishikawa iteration for Banach type and Chatterjea type contractions defined on JS metric space. [ABSTRACT FROM AUTHOR]

Based on the concept of pseudocomplement, we introduce a new representation of preopenness of L -fuzzy sets in R L -fuzzy bitopological spaces. The concepts of pairwise R L -fuzzy precontinuous and pairwise R L -fuzzy preirresolute functions are extended and discussed based on the i , j - R L -preopen gradation. Further, we follow up with a study of pairwise R L -fuzzy precompactness in R L -fuzzy bitopological spaces of an L -fuzzy set. We find that our paper offers more general results since R L -fuzzy bitopology is a generalization of L -bitopology, R L -bitopology, and L -fuzzy topology. [ABSTRACT FROM AUTHOR]

The Bishop frame or rotation minimizing frame (RMF) is an alternative approach to define a moving frame that is well defined even when the curve has vanished second derivative, and it has been widely used in the areas of computer graphics, engineering, and biology. The main aim of this paper is using the RMF for classification of singularity type of timelike sweeping surface and Bishop spherical Darboux image which is mightily concerning a unit speed spacelike curve with timelike binormal vector in E 1 3 . [ABSTRACT FROM AUTHOR]

In this paper, we first introduce two new notions of uniform convexity on a geodesic space, and we prove their properties. Moreover, we reintroduce a concept of the set-convergence in complete geodesic spaces, and we prove a relation between the metric projections and the convergence of a sequence of sets. [ABSTRACT FROM AUTHOR]

In this paper, weighted norm inequalities for multilinear Fourier multipliers satisfying Sobolev regularity with mixed norm are discussed. Our result can be understood as a generalization of the result by Fujita and Tomita by using the L r -based Sobolev space, 1 < r ≤ 2 with mixed norm. [ABSTRACT FROM AUTHOR]

In this paper, the dynamical behavior of a three-dimensional fractional-order prey-predator model is investigated with Holling type III functional response and constant rate harvesting. It is assumed that the middle predator species consumes only the prey species, and the top predator species consumes only the middle predator species. We also prove the boundedness, the non-negativity, the uniqueness, and the existence of the solutions of the proposed model. Then, all possible equilibria are determined, and the dynamical behaviors of the proposed model around the equilibrium points are investigated. Finally, numerical simulations results are presented to confirm the theoretical results and to give a better understanding of the dynamics of our proposed model. [ABSTRACT FROM AUTHOR]

In this paper, the notion of set-valued L -contractions is introduced, and a new fixed point theorem for such contractions is established. An example to illustrate main theorem is given. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an almost generalized α -admissible Z -contraction with the help of a simulation function and study fixed point results in the setting of partially ordered b-metric spaces. The presented results generalize and unify several related fixed point results in the existing literature. Finally, we verify our results by using two examples. Moreover, one of our fixed point results is applied to guarantee the existence of a solution of an integral equation. [ABSTRACT FROM AUTHOR]

Chaundy and Jolliffe proved that if a n is a nonnegative, nonincreasing real sequence, then series ∑ a n sin n x converges uniformly if and only if n a n ⟶ 0. The purpose of this paper is to show that if n a n is nonincreasing and n a n ⟶ 0 , then the series f x = ∑ a n sin n x can be differentiated term-by-term on c , d for c , d > 0. However, f ′ 0 may not exist. [ABSTRACT FROM AUTHOR]

In this paper, a singularly perturbed second-order ordinary differential equation with discontinuous source term subject to mixed-type boundary conditions is considered. A fitted nonpolynomial spline method is suggested. The stability and parameter uniform convergence of the proposed method are proved. To validate the applicability of the scheme, two model problems are considered for numerical experimentation and solved for different values of the perturbation parameter, ε , and mesh size, h. The numerical results are tabulated in terms of maximum absolute errors and rate of convergence, and it is observed that the present method is more accurate and ε -uniformly convergent for h ≥ ε where the classical numerical methods fail to give good result and it also improves the results of the methods existing in the literature. [ABSTRACT FROM AUTHOR]

This paper proposes a new fitted operator strategy for solving singularly perturbed parabolic partial differential equation with delay on the spatial variable. We decomposed the problem into three piecewise equations. The delay term in the equation is expanded by Taylor series, the time variable is discretized by implicit Euler method, and the space variable is discretized by central difference methods. After developing the fitting operator method, we accelerate the order of convergence of the time direction using Richardson extrapolation scheme and obtained O h 2 + k 2 uniform order of convergence. Finally, three examples are given to illustrate the effectiveness of the method. The result shows the proposed method is more accurate than some of the methods that exist in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce original definitions of Partner ruled surfaces according to the Darboux frame of a curve lying on an arbitrary regular surface in E 3 . It concerns T g Partner ruled surfaces, T n Partner ruled surfaces, and g n Partner ruled surfaces. We aim to study the simultaneous developability conditions of each couple of two Partner ruled surfaces. Finally, we give an illustrative example for our study. [ABSTRACT FROM AUTHOR]

In this paper, we consider a source problem for a time harmonic acoustic wave in two-dimensional space. Based on the boundary integral equation method, a Dirichlet-to-Neumann map in terms of boundary integral operators on the boundary of the source is constructed to transform this problem into two boundary value problems for the Helmholtz equation. [ABSTRACT FROM AUTHOR]

In the present paper, we establish some composition formulas for Marichev-Saigo-Maeda (MSM) fractional calculus operators with V -function as the kernel. In addition, on account of V -function, a variety of known results associated with special functions such as the Mittag-Leffler function, exponential function, Struve's function, Lommel's function, the Bessel function, Wright's generalized Bessel function, and the generalized hypergeometric function have been discovered by defining suitable values for the parameters. [ABSTRACT FROM AUTHOR]