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The aim of this paper is to present new results obtained in the study of spaces with a Δ-symmetric Banach Algebra, we defined the δ-characters functional and discuss the space of measurable function(Lo(µ)) is Δ- symmetric and is Banach algebra. Also, we define sℂ(Lo(µ)) by depended on Lo(µ) and proved the spaces is satisfies new properties in symmetric Banach algebra and prove any function in sℂ(Lo(µ)) satisfies all conditions of state functional and found corresponding between the space sℂ(Lo(µ)) and the space of all o- characters functional δch(Lo(µ)) on Lo(µ) as well as well defined. Also, we proved the functional ψ from Æ into sℂ(Lo(µ)) is continuous and state functional if every non-zero element has an inverse. We proved the quotient sℂ(Lo(µ))/Ι is also symmetric Δ –Banach algebra. [ABSTRACT FROM AUTHOR]

In this paper, we give a generalization of absolutely almost convergence, and prove interesting results. [ABSTRACT FROM AUTHOR]

In this paper, we shall establish the existence and uniqueness of fixed point of a Chatterjea - type contraction in Cone rectangular metric spaces over Banach algebras. We shall further give an example to illustrate our main results. Our results extend and generalize some results in the literature. [ABSTRACT FROM AUTHOR]

Some results concerning the Yosida approximation are given in this paper in the framework of the algebra Bp(X) which is more general than the standard Banach algebra of operators. As Yosida approximation is useful for demonstrating generation theorem for semigroups, this more general setting allows for working with universally bounded linear operators defined on locally convex spaces. [ABSTRACT FROM AUTHOR]

In this paper, we prove some fixed point theorems for generalized expansive mapping in a cone metric space over Banach algebras without the assumption of normality of cone. Moreover, we give an example to elucidate our result. Our results are significant extension and generalizations of recent result of B. Jiang et al., (J. Comput. Anal. Appl. 21(6):1103 - 1114, 2016) and many well-known results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, a nonlinear mi×ed integral equation (NMIE) with continuous kernels in the space L2 [0,1] × C[0,T], T < 1, under certain conditions is considered. The e×istence of a unique solution, using Banach Fi×ed Point theorem, is considered. Then, a quadratic numerical method is used to obtain a system of Fredholm integral equations (NSFIEs), we assume a quadratic method and Simpson rule to obtain, in each method, a nonlinear algebraic system (NAS). The e×istence of a unique solution of each nonlinear system, is considered. Numerical results are calculated and the error estimate, in each case, is computed. [ABSTRACT FROM AUTHOR]