A Common Fixed Point Theorem in Fuzzy Metric Spaces with Nonlinear Contractive Type Condition Defined Using Φ-Function

This paper is to present a common fixed point theorem for two R-weakly commuting self-mappings satisfying nonlinear contractive type condition defined using a Φ-function, defined on fuzzy metric spaces. Some comments on previously published results and some examples are given

A fixed point theorem in strictly convex b-fuzzy metric spaces

The main motivation for this paper is to investigate the fixed point property for non-expansive mappings defined on $b$-fuzzy metric spaces. First, following the idea of S. Ješić's result from 2009, we introduce convex, strictly convex and normal structures for sets in $b$-fuzzy metric spaces. By using topological methods and these notions, we prove the existence of fixed points for self-mappings defined on $b$-fuzzy metric spaces satisfying a nonlinear type condition. This result generalizes and improves many previously known results, such as W. Takahashi's result on metric spaces from 1970. A representative example illustrating the main result is provided

Integrated model of the vertebrate augmin complex

Accurate segregation of chromosomes is required to maintain genome integrity during cell division. This feat is accomplished by the microtubule-based spindle. To build a spindle rapidly and with high fidelity, cells take advantage of branching microtubule nucleation, which rapidly amplifies microtubules during cell division. Branching microtubule nucleation relies on the hetero-octameric augmin complex, but lack of structure information about augmin has hindered understanding how it promotes branching. In this work, we combine cryo-electron microscopy, protein structural prediction, and visualization of fused bulky tags via negative stain electron microscopy to identify the location and orientation of each subunit within the augmin structure. Evolutionary analysis shows that augmin\u27s structure is highly conserved across eukaryotes, and that augmin contains a previously unidentified microtubule binding site. Thus, our findings provide insight into the mechanism of branching microtubule nucleation

A Common Fixed Point Theorem in Fuzzy Metric Spaces with Nonlinear Contractive Type Condition Defined Using Φ-Function

This paper is to present a common fixed point theorem for two R-weakly commuting self-mappings satisfying nonlinear contractive type condition defined using a Φ-function, defined on fuzzy metric spaces. Some comments on previously published results and some examples are given

Common Fixed Points Theorems for Self-Mappings in Menger PM-Spaces

The purpose of this paper is to prove that orbital continuity for a pair of self-mappings is a necessary and sufficient condition for the existence and uniqueness of a common fixed point for these mappings defined on Menger PM-spaces with a nonlinear contractive condition. The main results are obtained using the notion of R-weakly commutativity of type Af (or type Ag). These results generalize some known results

Common Fixed Points Theorems for Self-Mappings in Menger PM-Spaces

The purpose of this paper is to prove that orbital continuity for a pair of self-mappings is a necessary and sufficient condition for the existence and uniqueness of a common fixed point for these mappings defined on Menger PM-spaces with a nonlinear contractive condition. The main results are obtained using the notion of R-weakly commutativity of type Af (or type Ag). These results generalize some known results