Coupled Coincidence Point and Coupled Fixed Point Theorems via Generalized Meir-Keeler Type Contractions

We prove coupled coincidence point and coupled fixed point results of ∶×→ and ∶→ involving Meir-Keeler type contractions on the class of partially ordered metric spaces. Our results generalize some recent results in the literature. Also, we give some illustrative examples and application

Geraghty type contraction mappings on Branciari b-metric spaces

In this paper fixed points of α-admissible contraction mappings of Geraghty type defined on Branciari bmetric spaces are studied. Existence and uniqueness theorems for these types of mappings of are proved. Some consequences of these theorems are given and specific examples are presented

ON A GENERALIZED alpha-ADMISSIBLE RATIONAL TYPE CONTRACTIVE MAPPING

Recently, many generalized contractive conditions which involve rational contractive inequalities have been introduced in the context of partially ordered metric spaces. In this paper, we aim to give a generalized rational contractive condition which involves some of these results without need of extra restrictions

A model for the computation of quantum billiards with arbitrary shapes

An expansion method for the stationary Schrodinger equation of a three-dimensional quantum billiard system whose boundary is defined by an arbitrary analytic function is introduced. The method is based on a coordinate transformation and an expansion in spherical harmonics. The effectiveness is verified and confirmed by a numerical example, which is a billiard system depending on a parameter

An Ulam stability result on quasi-b-metric-like spaces

In this paper a class of general type α-admissible contraction mappings on quasi-b-metric-like spaces are defined. Existence and uniqueness of fixed points for this class of mappings is discussed and the results are applied to Ulam stability problems. Various consequences of the main results are obtained and illustrative examples are presented

Critical-size alveolar defect treatment via TGF-ss 3 and BMP-2 releasing hybrid constructs

WOS: 000462355600005PubMed: 30688157In the present study a combination of Transforming Growth Factor Beta 3 (TGF-beta 3) and Bone Morphogenetic Protein-2 (BMP-2) loaded gelatin films sandwiched between poly (L-lactide) (PLLA)/poly (epsilon-caprolactone) (PCL) matrices were produced to enhance bone formation in alveolar bone defects. Osteogenic properties of tissue constructs were tested in alveolar bone defect model in rats. Bone healing was assessed by osteogenic gene expression levels of bone sialoprotein (BSP), alkaline phosphatase (ALP), osteonectin (ON, SPARC), osteocalcin (OC), runt-related transcription factor 2 (RUNX2), bone specific alkaline phosphatase (BALP) activity, histomorphometry and microtomography. Increase in osteogenic gene expression levels and BALP activity results showed that new bone formation was significantly accelerated in TGF-beta 3 + BMP-2 loaded scaffold group compared to growth factor free and only BMP-2 loaded groups. The micro-computed tomography (mu-CT) data from the 4(th) months revealed that (TGF-beta 3+ BMP-2) loaded scaffolds displayed increased bone formation and was able to fulfill 84% of the defect area (p < 0.05). Accelerated bone formation in the S-GF-B-T group compared to that of the S-GF group at the end of the 4th month was further verified via histomorphometric analysis (p = 0.008). Gene expression, BALP activity, microtomography and histomorphometry analysis indicated that (TGF-beta 3 + BMP-2) loaded PLLA/PCL scaffolds increased the new bone formation. BMP-2 loaded scaffolds were less effective than combination of TGF-beta 3 and BMP-2 loaded scaffolds. These findings demonstrated that focusing on the PLLA/PCL hybrid scaffolds combined with (TGF-beta 3 + BMP-2) may lay the groundwork for future therapy-oriented efforts to enhance bone formation in alveolar defects.Turkish Scientific and Technological Research Council (TUBITAK) [108S336, SBAG-4083]We thank Professor Hamdi H. Alkan, MD to provide using the mu-CT facility. This study was funded by the Turkish Scientific and Technological Research Council (TUBITAK) Project No: 108S336 (SBAG-4083). Erhan Piskin is a full member of Turkish Academy of Sciences