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In the present paper, we introduce g-open soft mapping, g-closed soft mapping, g-pseudo-open soft mapping, g-quotient soft mapping on soft generalized topological spaces. Furthermore, we discuss some characterizations and some applications of them. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce the notion of ψF operator induced by a given filter F and a generalized topology μ, and to investigate some properties of this operator. We shall further discuss some characterizations of this operator with the help of F-codeness and F-compatibility. [ABSTRACT FROM AUTHOR]

The main result in this note slightly generalizes Theorem 3.4 in [Şt. Măruster and I. A. Rus, Kannan contractions and strongly demicontractive mappings, Creat. Math. Inform., 24 (2015), No. 3, 171-180]. We also significantly improve its proof. Both results in the paper are based on the concepts of demicontractivity and quasi-expansivity and involve relatively weak conditions that guarantee the convergence of Krasnoselskij method (the same conditions are not sufficient for the convergence of Picard iteration). Thus, our note is a satisfactory answer to the following question: if for a given mapping some specific conditions for the convergence of Picard iteration are not satisfied (and presumptively the Picard iteration fails to converge), what are the conditions which still ensure the convergence of the Mann iteration? [ABSTRACT FROM AUTHOR]

The aim of this paper is to prove some convergence theorems for a general Krasnoselskij type fixed point iterative method defined by means of the concept of admissible perturbation of a demicontractive operator in Hilbert spaces. [ABSTRACT FROM AUTHOR]

In the present paper, we adopt the concept of expansive mapping in the context of Gp-metric spaces in a similar manner expansive mapping in metric spaces. Furthermore, we obtain some results on fixed points of expansive type mappings. Also, we prove some common fixed point results for expansive mappings by using the notion of weak compatibility in Gp-metric space. Our results generalize some comparable results in metric spaces and partial metric spaces to Gp-metric spaces. Moreover, some examples are introduced in order to support our new results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of a monotone (α, β)-nonexpansive mapping in an ordered Banach space E with the partial order ≤ and prove some existence theorems of fixed points of a monotone (α, β)-nonexpansive mapping in a uniformly convex ordered Banach space. Also, we prove some weak and strong convergence theorems of Ishikawa type iteration under the control condition ... Finally, we give an numerical example to illustrate the main result in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we establish some strong and ▵ -convergence theorems of an iteration process for approximating a common fixed point of three nonexpansive mappings in a uniformly convex hyperbolic space. The results presented here extend and improve various results in the existing literature. [ABSTRACT FROM AUTHOR]

For q>1q>1 and p>1, let E be a 2-uniformly convex and q-uniformly smooth or p- uniformly convex and 2-uniformly smooth real Banach space and F:E→E*, K:E* → E be bounded and strongly monotone maps with D(K)=R(F)=E*. We construct a coupled iterative process and prove its strong convergence to a solution of the Hammerstein equation u+KFu=0. Futhermore, our technique of proof is of independent of interest. [ABSTRACT FROM AUTHOR]

Let X be a real Banach space, K be a nonempty closed convex subset of X, T:K→ be a nearly uniformly L-Lipschitzian mapping with sequence {an}. Let kn⊂[1,∞) and εn be sequences with limn→∞kn=1, limn→∞ 0 and F(T)={ρ∈K:Tρ=ρ}≠∅. Let {αn}n≥0 be real sequence in [0,1][0,1] satisfying the following conditions: (i)Σn≥0αn=∞ (ii) limn→∞αn=0 . For arbitrary x0∈K, let {xn}n≥0 be iteratively defined by xn+1=(1-αn)xn+αnTnxn,n≥0. If there exists a strictly increasing function Φ:[0,∞)→[0,∞)Φ:[0,∞)→[0,∞) with Φ(0)=0Φ(0)=0 such thatnx-Tnρ,j(x-ρ)>≤kn∥x-ρ∥²-Φ (∥x-ρ∥)+εn for all x∈Kx∈K, then, {xn}n≥0{xn}n≥0 converges strongly to ρ∈F(T)ρ∈F(T). It is also proved that the sequence of iteration {xn}{xn} defined by xn+1=(1-bn-dn)xn+bnTnxn+dnwn,n≥0, where {wn}n≥0 is a bounded sequence in K and {bn}n≥0,{dn}n≥0 are sequences in [0,1] satisfying appropriate conditions, converges strongly to a fixed point of T. [ABSTRACT FROM AUTHOR]

Inclusion relations between strongly demicontractive mappings, quasi (L,m)-contractions, and Kannan contractions are established. As corollaries, T-stability and strong convergence of Picard and Mann iterations for strongly demicontractive mappings are obtained. [ABSTRACT FROM AUTHOR]