In this work, some fixed point and common fixed point theorems are investigated in b-metric-like spaces. Some of our results generalize related results in the literature. Also, some examples and an application to integral equation are given to support our main results. MSC: 47H10; 54H25

No abstract

In this paper, we introduce the concept of -contraction and investigate some fixed point theorems for such contraction in b-metric-like spaces. Moreover, an example is given to support one of our results, and an application is proposed.

LncRNA TUG1 has been rarely studied in ovarian cancer (OC), our objective was to explore the role of TUG1 in the regulation of malignant phenotypes of OC. Vectors of sh-TUG1, miR-186-5p and pcDNA-ZEB1 were, respectively, constructed and used to infect OC cells. MTT and transwell assays were applied for representing cell proliferation and invasion, respectively. Sphere formation experiment was used to detect the stemness of OC cells. Western blotting and qRT-PCR were employed for detecting the expression of multiple biomarkers on protein and RNA levels, respectively. The luciferase assay was performed to reveal the interactions between miR-186-5p and TUG1 or ZEB1. The silencing of TUG1 and upregulation of miR-186-5p both suppressed the cell proliferation, invasion and cancer stem cell (CSC) properties. Additionally, luciferase assay verified that miR-186-5p directly binds TUG1 and ZEB1. Moreover, overexpression of ZEB1 rescued the impact on the proliferation, invasion and stemness of TUG1 silencing in OC. TUG1 sponges miR-186-5p to release ZEB1 and promotes the proliferation, invasion and stemness of OC cells, suggesting that TUG1 could be a potential therapeutic target for OC therapy. Significance of the study: LncRNA TUG1 could promote proliferation, invasion and stemness of ovarian cancer cells. Our study first discovered that TUG1 play a tumourigenic role in ovarian cancer by regulating stemness of cancer cells. Mechanism research exhibited the regulation role of TUG1 in ovarian cancer cells was miR-186-5p/ZEB1 axis depended. These results provided a new perspective to understand the pathogenesis and development of ovarian cancer; it will offer new evidence for better diagnosis and treatment therapy of ovarian cancer.

Single-valued neutrosophic cubic set is a good tool to solve the vague and uncertain problems because it contains more information. The article first gives the correlation coefficient of single-valued neutrosophic cubic sets. Then, a decision method is proposed, and an application in pattern recognition is considered. Finally, examples are given to explain the feasibility of this method. At the same time, the comparative analysis shows the superiority of this method.