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In this paper we give a classification of endomorphisms and additive mappings of a prime ring satisfying certain algebraic identities. Moreover, we provide an example proving that the primeness hypothesis imposed in our theorems is not superfluous. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence and uniqueness of solutions for a tripled system of fractional differential equations with nonlocal integro multi point boundary conditions by using the p-Laplacian operator and the γ-Caputo derivatives. The presented results are obtained by the two fixed point theorems of Banach and Krasnoselskii. An illustrative example is presented at the end to show the applicability of the obtained results. To the best of our knowledge, this is the first time where such problem is considered. [ABSTRACT FROM AUTHOR]

There are situations when we have to resort to the approximate optimal solution of equations of the type g(t) = t when g is not a self-map, because exact solution of that equation does not exist. The existence of such optimal solutions are ensured by best proximity point theorems. In this paper, we define multivalued Geraghty contraction (MVGC) in a complete metric space and establish the corresponding best proximity point (BPP) result. Our result extends the famous result due to Geraghty on fixed points. [ABSTRACT FROM AUTHOR]

In this paper, we study a coupled system of nonlinear Liouville–Caputo fractional differential equations equipped with a new set of nonlocal boundary conditions involving an arbitrary strip together with two sets of nonlocal multi-points on either part of the strip on the given domain. We emphasize that the boundary conditions considered in this study are formulated with respect to the sum and difference of the unknown functions. We apply the well-known tools of the fixed point theory to derive the main results. Examples are presented for the illustration of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we prove the stability of Hadamard homomorphisms and Hadamard derivations in Banach algebras. This is applied to investigate Hadamard isomorphisms between Banach algebras. [ABSTRACT FROM AUTHOR]

In the present paper, we proposed a new sequence of summation-integral type operators involving Apostol-Genocchi polynomials. We study some approximation results of the proposed operators using first and second-order modulus of continuity, the global rate of convergence using Voronovskaja-type asymptotic theorem, Lipschitz-type space, and Ditzian-Totik modulus of smoothness. Lastly, we study the weighted approximation. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the ∗-identities with a pair of generalized derivations on ∗-ideals of prime rings with involution. In particular, we prove that if a noncommutative prime ∗-ring admit two generalized derivations F and G such that [F (x),G(x* )] = 0 for all x ∈ I, where I is a nonzero ∗-ideal of R, then there exists λ ∈ C such that F = λG. Finally, we provide an example which shows that the primeness of R is crucial in our results. [ABSTRACT FROM AUTHOR]

In this paper, we extend the result of Romaguera [21] with the aid of best proximity point theory on partial metric spaces by considering the approach of Haghi et al. [9], and so celebrated Boyd-Wong fixed point theorem [7]. We first introduce two concepts called generalized proximal BW-contraction and generalized best BW-contraction. Then, we obtain some best proximity point theorems for such mappings. To illustrate the effectiveness of our results, we provide some nontrivial and interesting examples. Finally, unlike homotopy applications existing in the literature, we present for the first time an application of the best proximity result to the homotopy theory. [ABSTRACT FROM AUTHOR]

In this paper, we mainly consider the oscillation of numerical solutions for a nonlinear delay differential equation which is generalized from a delay Lotka-Volterra type single species population growth model. By studying the corresponding difference scheme of the equation discretized by θ-method, forward Euler method and backward Euler method, some sufficient conditions under which the numerical solutions oscillate are obtained. Furthermore, we prove that the positive non-oscillatory numerical solutions tend to the equilibrium of the original differential equation. Finally, some numerical experiments are given to verify the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, a two dimensional discrete-time predator-prey system with weak Allee effect, affecting the prey population, is considered. The existence of the positive fixed points of the system and topological classification of coexistence positive fixed point are examined. By using the bifurcation theory, it is shown that the discrete-time predator-prey system with Allee effect undergoes flip and Neimark-Sacker bifurcations depending on the parameter a. The parametric conditions for existence and direction of bifurcations are investigated. Numerical simulations including bifurcation diagrams, phase portraits and maximum Lyapunov exponents of the system are performed to validate analytical results. The computation of the maximum Lyapunov exponents confirm the presence of chaotic behaviour in the considered system. Finally, the OGY feedback control method is implemented to stabilize chaos existing in the system. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of integration with respect to a given derivation on a lattice. More precisely, we give the definitions of integrable elements of a lattice and their integral sets. We investigate several characterizations and properties of integrations on a lattice. Also, we give a lattice structure to the family of integral sets with respect to a given integration. Further, we provide a representation theorem for the lattice of fixed points of an isotone derivation based on the family of integral sets. As an application of this notion of integration, we use the integrable elements of a Boolean lattice to determine the necessary and sufficient conditions under which a linear differential equation on this Boolean lattice has a solution. [ABSTRACT FROM AUTHOR]

In this paper, we use Schauder and Banach fixed point theorems to study the existence, uniqueness and stability of bounded nonhomogeneous iterative functional differential equations of the form x' (t) = λ1x(t) + λ2x[2](t)+...+λnx[n](t)+f(t). [ABSTRACT FROM AUTHOR]

In this paper, we consider a discrete population model and obtain a couple of criteria to guarantee our model being stable, including the global attractor, the extreme stability, and the periodicity. [ABSTRACT FROM AUTHOR]

In this paper we extend Darbo's fixed point theorem in Banach spaces and obtain a tripled fixed point theorem. The technique of measure of noncompactness is the main tool in carrying out our proof. Finally, as an application of our results, we analyze the existence of solutions for a system of neutral differential equations. [ABSTRACT FROM AUTHOR]

In this paper, we obtained some fixed point results for continuous mappings satisfying a generalized contractive condition in the setting of two metrics space endowed with a binary relation. Our theorems generalize and extend several known results in the literature. As application, we establish an existence theorem for the solution of a nonlinear first order differential equation. [ABSTRACT FROM AUTHOR]