In this work, we define the notion of an algebraic distance in algebraic cone metric spaces defined by Niknam et al. [A. Niknam, S. Shamsi Gamchi and M. Janfada, Some results on TVS-cone normed spaces and algebraic cone metric spaces, Iranian J. Math. Sci. Infor. 9 (1) (2014), 71--80] and introduce some its elementary properties. Then we prove the existence and uniqueness of fixed point for a B...

For any semifinite von Neumann algebra ${\mathcal M}$ and $1\leq p<\infty$, we introduce a natutal $S^1$-valued noncommutative $L^p$-space $L^p({\mathcal M};S^1)$. We say that bounded map $T\colon L^p({\mathcal M})\to N})$ is $S^1$-bounded (resp. $S^1$-contractive) if $T\otimes I_{S^1}$ extends to contractive) $T\overline{\otimes} from $ M};S^1)$ into N};S^1)$. show completely positive $S^1$-bo...

In this paper, we establish some existence of fixed-point results for asymptotically regular multivalued mappings satisfying Kannan-type contractive condition without assuming compactness the underlying metric space or continuity mapping.

Definition 1.1 (see [1]). A triple (X ,M,∗), where X is an arbitrary set, ∗ is a continuous t-norm, andM is a fuzzy set on X2× (0,∞), is said to be a fuzzy metric space (in the sense of George and Veeramani) if the following conditions are satisfied for all x, y ∈ X and s, t > 0: (GV-1) M(x, y, t) > 0; (GV-2) M(x, y, t)= 1 if and only if x = y; (GV-3) M(x, y, t)=M(y,x, t); (GV-4) M(x, y,·) is c...

In this paper, first we prove fixed point theorems for different variant of compatible maps, satisfying a contractive condition of integral type in fuzzy metric spaces, which improve the results of Branciari [2], Rhoades [33], Kumar et al. [23], Subramanyam [35] and results of various authors cited in the literature of ”Fixed Point Theory and Applications”. Secondly, we introduce the notion of ...

Let X be a reflexive Banach space which has a weakly sequentially continuous duality mapping. In this paper, we consider the following viscosity approximation sequence x n λ n fx n 1−λ n T n x n , where λ n ∈ 0, 1, {T n } is a uniformly asymptotically regular sequence, and f is a weakly contractive mapping. Strong convergence of the sequence {x n } is proved.

The purpose of this paper is to study the convergence problem of Mann and Ishikawa type iterative schemes of weakly contractive mapping in a complete convex metric space. We establish the results on invariant approximation for the mapping defined on a class of nonconvex sets in a convex metric space. Finally, we obtain the existence of common fixed points of two asymptotically nonexpansive mapp...

Keywords-Fuzzy reasoning, Fuzzy system, Variable weighted synthesis inference method, CRI method, Fuzzy control. 1. I N T R O D U C T I O N It is well known that fuzzy inference is a theoretical foundation of fuzzy control systems and fuzzy expert systems. At present, general fuzzy inference methods include the CRI (compositional rules of inference) method, (+,-)-centroid method, simple inferen...