Caspian Journal of Mathematical Sciences
Volume:9 Issue: 2, Summer Autumn 2020

Let $A$ be a Banach algebra, $Omega(A)$ be the character space of $A$ and $alphainOmega(A)$. In this paper, we examine the characteristics of $alpha$-projective (injective) $A$-modules and demonstrate that these character-based $A$-modules also satisfy well-known classical homological properties on Banach $A$-modules.

It is pointed out that, one of the results in the recently published article, ’On the Iyengar-Madhava Rao-Nanjundiah inequality and it’s hyperbolic version’ [3] by J´ozsef S´andor is logically incorrect and new corrected result with it’s proof is presented.

‎Let $Omega_X$ be a bounded‎, ‎circular and strictly convex domain in a complex Banach space $X$‎, ‎and $mathcal{H}(Omega_X)$ be the space of all holomorphic functions from $Omega_X$ to $mathbb{C}$‎. ‎The growth space $mathcal{A}^nu(Omega_X)$ consists of all $finmathcal{H}(Omega_X)$‎ ‎such that $$|f(x)|leqslant C nu(r_{Omega_X}(x)),quad xin Omega_X,$$‎ ‎for some constant $C>0$‎, ‎whenever $r_{Omega_X}$ is the Minkowski‎ ‎functional on $Omega_X$ and $nu‎ :‎[0,1)rightarrow(0,infty)$‎ ‎is a nondecreasing‎, ‎continuous and unbounded function‎. ‎For complex Banach spaces $X$ and $Y$‎ ‎and a holomorphic map $varphi:Omega_XrightarrowOmega_Y$‎, ‎put‎ ‎$C_varphi( f)=fcirc varphi,finmathcal{H}(Omega_Y)$‎. ‎We characterize those $varphi$ for which the composition operator‎ ‎$ C_varphi:mathcal{A}^{omega}(Omega_Y)rightarrowmathcal{A}^{nu}(Omega_X)$ is a bounded or compact operator‎.

Lifting modules and their various generalizations as some main concepts in module theory have been studied and investigated extensively in recent decades. Some authors tried to present some homological aspects of lifting modules and -supplemented modules. In this work, we shall present a homological approach to -supplemented modules via fully invariant submodules. Lifting modules and H-supplemented modules with respect to images of a xed fully invariant submodule of a module where investigated in rst author's last works. We intend here to introduce and study a module M such that '(F) has a supplement as a direct summand for every endomorphism ' of M where F is a xed fully invariant submodule of M.

In this article, we introduce the multi-$m$-Jensen mappings and characterize them as a single equation. Using a fixed point theorem, we study the generalized Hyers-Ulam stability for such mappings. As a consequence, we show that every multi-$m$-Jensen mappings (under some conditions) is hyperstable.

In this paper, we define topological hyperrings and study their basic concepts which supported by illustrative examples. We show some differences between topological rings and topological hyperrings. Also, by the fundamental relation $Gamma^{*}$, we indicate the role of complete parts (saturated subsets) and complete hyperrings in topological hyperrings and specially we show that if every (closed) open subset is a complete part in a topological complete hyperring then its fundamental ring is a topological ring. Finally, we study the quotient topology induced by $Gamma^{*}$-relation on an associated Krasner hyperring obtained by a ring and show that it is isomorphic to a quotient space of the ring by its ideals.

In the present work, under some di¤erentiability conditions on the potential functions , we …rst reduce the inverse scattering problem (ISP) for the polynomial pencil of the Scroedinger equation to the corresponding ISP for the generalized matrix Scrödinger equation . Then ISP will be solved in analogy of the Marchenko method. We aim to establish an e¤ective algorithm for uniquely reconstructing of the potential functions of the equation in that case when there is no a discrete spectrum

In this paper, weight function and composition technique is utilized to speeds up the convergence order and increase the efficiency of an existing quadrature based iterative method. This results in the proposition of its improved form from a two-point quadrature based method of convergence order ρ = 3 with efficiency index EI = 1:3161 to a three-point method of convergence order ρ = 8 with EI = 1:5157 at the cost of one additional function evaluation. The method is used to approximate the solution of some nonlinear equations and the results generated are compared with that of some existing methods. Numerical results shows that method developed herein is very efficient in approximation of solution of nonlinear equations.

In this work we study numbers and polynomials generated by two type of composition of generating functions and get their explicit formulae. Furthermore we state an improvementof the composita formulae's given in [6] and [3], using the new composita formula's we construct a variety of combinatorics identities. This study go alone to dene new family of generalized Bernoulli polynomials which include Hermite-Bernoulli polynomials introduced by G. Dattoli and al [1].

In this paper, the Schwarz boundary value problem (BVP) for the inhomogeneous Cauchy-Riemann equation in a triangle is investigated explicitly. Firstly, by the technique of parquetingreflection and the Cauchy-Pompeiu representation formula a modified Cauchy-Schwarz representation formula is obtained. Then, the solution of the Schwarz BVP is explicitly solved. In particular, the boundary behaviors at the corner points are considered.

‎We consider the oscillator group equipped with‎ ‎a biinvariant Lorentzian metric‎. ‎Some geometrical properties of this space and the harmonicity properties of left-invariant vector fields on this space are determined‎. ‎In some cases‎, ‎all these vector fields are critical points for the energy functional‎ ‎restricted to vector fields‎. ‎Left-invariant vector fields defining harmonic maps are also classified‎, ‎and the energy of these vector‎ ‎fields is explicitly calculat‎e‎d.

This paper investigates the solvability, existence and uniqueness of solutions for a class of nonlinear fractional hybrid differential equations with Hilfer fractional derivative in a weighted normed space. The main result is proved by means of a fixed point theorem due to Dhage. An example to illustrate the results is included.

We consider the aff(1)-module structure on the spaces of bilinear differential operators acting on the spaces of weighted densities. We compute the first differential cohomology of the Lie superalgebra aff(1) with coefficients in space Dλ,ν;µ of bilinear differential operators acting on weighted densities. We study also the super analogue of this problem getting the same results.

In this article, we apply the operational matrix to find the numerical solution of two- dimensional nonlinear Volterra integro-differential equation (2DNVIDE). Form this prospect, two-dimensional shifted Legendre functions (2DSLFs) has been presented for integration, product as well as differentiation. This method converts 2DNVIDE to an algebraic system of equations, so the numerical solution of 2DNVIDE is computable. The effectiveness and accuracy of the method were examined with some examples as well. The results and comparison with other methods have shown a remarkable performance.

‎In this article‎, ‎the multi-step conformable fractional differential transform method (MSCDTM) is applied to give approximate solutions of the conformable fractional-order differential systems‎. ‎Moreover‎, ‎we check the stability of conformable fractional-order L"{u} system with the MSCDTM to demonstrate the efficiency and effectiveness of the proposed procedure.