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The paper is devoted to prove the existence of solutions for an infinite system of non- linear integral equations. This system is investigated in the WC-Banach algebra C(I; c0), the space of all continuous functions acting from an interval I into the sequence space c0. Making use of the measure of weak noncompactness and the weak topology, we establish some fixed point theorems for the sum and the product of nonlinear weakly sequentially continuous operat- ors acting onWC-Banach algebra involving w-contractive operators. [ABSTRACT FROM AUTHOR]

In this paper, we suggest some new and efficient iterative methods for solving nonlinear equations f (x) = 0. These methods are free from derivatives having high order of convergence. We also give some examples to illustrate the efficiency of these methods. Finally, numerical tests confirm the theoretical results and allow us to compare these variants with the classical Steffensen's method. These new methods can be considered as alternative of existing derivative-free methods. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of a pair (f, h) called upper class of type II and αβ-contractive mappings. We obtain that all the corresponding established results of Hussain et al. [7] are immediately consequences of our main result. Our main result generalizes and modifies several existing results in literature. Also, an example is given to support the main result. [ABSTRACT FROM AUTHOR]

In this paper we introduce a class of quasipolar rings which is a generalization of J -quasipolar rings. Let R be a ring with identity. An element a ϵ 2 R is called 1-quasipolar if there exists p2 = p ϵ comm2(a) such that a + p is contained in δ(R), and the ring R is called δ-quasipolar if every element of R is δ-quasipolar. We use 1-quasipolar rings to extend some results of J-quasipolar rings. Then some of the main results of J-quasipolar rings are special cases of our results for this general setting. We give many characterizations and investigate general properties of 1-quasipolar rings. [ABSTRACT FROM AUTHOR]

In this paper, our approach allows to refine the results announced by Ebadian et al. [Results Math., 36 (2013), 409-423]. Namely, we reduce the distance between approximate and exact double derivations on Banach algebras and Lie C*-algebras up to 1/2n-1 and 1/2n-2 for n⩾2. Indeed, we give a correct utilization of fixed point theory in the sense of Diaz and Margolis [Bull. Amer. Math. Soc., 74 (1968), 305-309] concerning the stability of double derivations. [ABSTRACT FROM AUTHOR]

In this paper we investigate the generalized Hyers-Ulam stability of mappings of m-semigroups m ∊ N; m ≥ 2 into Banach spaces. For m = 3 the results can be found in Amyari and Moslehian [Approximate homomorphisms of ternary semigroups, Lett. Math. Phys. 77 (2006), 1-9] with the mention that they are true in the class of normal m-semigroups which is larger than the class of commutative m-semigroups. For m = 2 we find certain results of Hyers [On the stability of the linear functional equation, Proc. Nat. Acad. Sci. USA, 27 (1941), 222-224], Aoki [On the stability of the linear transformation in Banach spaces,J. Math. Soc. Japan, 2 (1950), 64-66], Rassias, Th. M. [On the stability of the linear mapping in Banach space, Proc. Amer. Math, Soc. 72 (1978), 297-300 ] and Rassias, J. M. [Solution of a Problem of Ulam, J. Approx. Theory Math. 57 (1989), 268-273]. In addition, we establish the superstability of m-ary homomorphims into Banach algebras endowed with multiplicative norms, generalizing the results of Szekelyhidi [On a theorem of Baker, Lawrence and Zorzitto, Proc. Amer. Math. Soc., 84 (1982), 95-96] and Amyari and Moslehian (2006). [ABSTRACT FROM AUTHOR]