Journal of Mathematical Extension
Volume:16 Issue: 7, Jul 2022

In this manuscript, we investigate and study some coho- mological properties of Banach algebras. Let A be a Banach alge- bra with a bounded left approximate identity, and let B be a Banach A − bimodule. We show that if AB∗∗ and B∗∗A are subset of B, then H1(A, B(2n+1)) = 0 for all n ≥ 0, whenever H1(A, B∗) = 0

Fuzzy Integral equations is a mathematical tool for mod- eling the uncertain control system and economic. In this paper, we present numerical solution of nonlinear fuzzy Volterra integral equa- tions(NFVIEs) using successive approximations scheme and block-pulse functions. Additionally, the convergence analysis of the presented ap- proach is investigated involving Lipschitz and several conditions and error bound between the approximate and the exact solution is pro- vided. Finally, to approve the outcomes concerned with the theory a numerical experiment is considered.

Classification, boundedness, and existence of solutions of a second order nonlinear difference equation are investigated. First, it is proved that all solutions are eventually monotone. Then, the necessary and sufficient conditions for the boundedness of all solutions are estab- lished. Finally, the existence of different types of monotonic solutions are presented. The obtained results have extended and improved some existing ones.

In this paper, we use the concept of a generalized - Geraghty contraction type mapping to introduce the new notion of - Geraghty type F-contraction multivalued mapping and prove some new common Öxed point results for such contraction in b-metric-like spaces. Also, we give some examples to illustrate our main results, we also dis- cuss existence a solution for a system of non-linear integral equation.

In this paper, we consider the problem of estimating stress- strength reliability R = Pr(X > Y ) for Gompertz lifetime models hav- ing the same shape parameters but different location parameters under a set of upper record values. We obtain the maximum likelihood es- timator (MLE), the approximate Bayes estimator and the exact confi- dence intervals of stress-strength reliability when the shape parameter is known. Also, when the shape parameter is unknown, the MLE, the asymptotic confidence interval and some bootstrap confidence intervals of stress-strength reliability are studied. Furthermore, a Bayesian ap- proach is proposed for estimating the parameters and then the corre- sponding credible interval are achieved using Gibbs sampling technique via OpenBUGS software. Monte Carlo simulations are performed to compare the performance of different proposed estimation methods. Fi- nally, analysis of a real dataset is performed

In the present world, there are many two-stage systems which provide information of inputs, outputs and intermediate measures which are imprecise, such as, (stochastic, fuzzy, interval etc). In these conditions, a two-stage data envelopment analysis or a (two-stage DEA method) cannot evaluate the efficiencies of these systems. In several two-stage systems, the simultaneous presence of stages is necessary for the final product. Hence, in this paper, we shall propose the stochas- tic multiplicative model and the deterministic equivalent, to measure the efficiencies of these systems, primarily, in the presence of stochastic data, under the constant returns to scale (CRS) assumption, by using the non-compensatory property of the multiplication operator.Then, we will use the reparative property of the additive operation to propose the additive models as well as the deterministic equivalents, to calculate the efficiencies of two-stage systems, in presence of stochastic data, under the constant returns to scale (CRS) and variable returns to scale (VRS) assumptions. This is to illustrate that a simultaneous presence of the stages is not necessary for the final product and one stage compen- sates the shortcomings of another stage. Likewise, we shall convert each of these deterministic equivalents to quadratic programming prob- lems. Based on the proposed stochastic models, the whole system is efficient if and only if, the first and the second stages are efficient. Ul- timately, in the proposed multiplicative model, we will illustrate the proposed multiplicative model, by employing the data of the Taiwanese non-life insurance companies, which has been extracted from the extant literature.

n this article, we introduce generalized cyclic contractions in the context of metric-like spaces and prove some new fixed point results concerning these contractions. Our results, extend and unify several results in existing literature. We present suitable examples to make our findings worth mentioning.

In this paper, we discuss the existence, uniqueness and sta- bility of mild solutions of time-dependent impulsive neutral stochastic partial integrodifferential equations with fractional Brownian motion and Poisson jumps. The existence of mild solutions for the equations are discussed by means of semigroup theory and theory of resolvent op- erator. Next, certain sufficient conditions and results are obtained by using the method of successive approximation and Bihari’s inequality. Finally, an example is provided to illustrate our results.

Let σ be a linear ∗-endomorphism on a C∗-algebra A so that σ(A) acts on a Hilbert space H which including K(H) and let {αt}t∈R be a σ-C∗-dynamical system on A with the generator δ. In this paper, we demonstrate some conditions under which {αt}t∈R is implemented by a C0-groups of unitaries on H. In particular, we prove that for a rank- one projection p ∈ A, which is invariant under αt, there is a C0-group {ut}t∈R of unitaries in B(H) such that αt(a) = utσ(a)u∗ t . Furthermore, introducing the concepts of σ-inner endomorphism and σ-bijective map, we prove that each σ-bijective linear endomorphism on A is a σ-inner endomorphism, where σ ia idempotent. Finally, as an application, we characterize each so-called σ-C∗-dynamical system on the concrete C∗- algebra A := B(H) × B(H), where H is a separable Hilbert space and σ is the linear ∗-endomorphism σ(S, T ) = (0, T ) on A.

We present some new numerical radius inequalities of Hilbert space operators. We improve and generalize some inequalities with re- spect to Specht’s ratio. Let A and B be two positive invertible operators on a Hilbert space H and let X be a bounded operator on H. Then ω((A♮B)X) ≤ 1 2S(√h) ∥X∗BX + A∥, (h > 0, h ̸ = 1) where ∥ · ∥, ω(·), S(·), and ♮ denote the usual operator norm, numeri- cal radius, the Specht’s ratio, and the operator geometric mean, respec- tively.