Search

In this paper, we establish some new fixed point theorems for multivalued mappings in the context of metric spaces. Some special cases are also discussed to derive some well known results of the literature. Finally, one example is also presented to verify the effectiveness and applicability of our main results. [ABSTRACT FROM AUTHOR]

The aim of this paper is to define ... and establish some new fixed point theorems in the setting of left K-complete T1-quasi metric space. Our theorems generalize, extend, and unify several results of literature. [ABSTRACT FROM AUTHOR]

Jleli and Samet [J. Fixed Point Theory Appl. (2018) 20:128] introduced a new metric space named as F-metric space. They established a new version of the Banach contraction principle in the setting of this generalized metric spaces. The aim of this article is to define rational contraction and obtain some fixed point theorems in the context of F-metric spaces. Our results extend, generalize and unify several known results in the literature. [ABSTRACT FROM AUTHOR]

Based on the ethnomedicinal use of Isodon rugosus the current study was designed to evaluate its crude saponins (Ir.Sp), and subsequent fractions for anti-angiogenic and anti-tumor potentials. Chorioallantoic membrane (CAM) assay was used in anti-angiogenic potentials with Dexamethasone as positive control. The antitumor activity was evaluated with potato disk method using Vincristine sulfate as positive control. Moreover, antibacterial activity was also conducted against A. tumefaciens. The highest anti-angiogenic effect was observed with Ir.Sp, i.e., 79.00±0.58% at concentration of 1000 µg/ml which drop drown to 48.67±1.20% at lowest tested concentration of 31.25 µg/ml with IC50 of 41 µg/ml. Similarly, in the anti-tumor activity the Ir. Chf revealed excellent inhibition of tumor with IC50 value of 60 µg/ml. All the samples (excluding Ir. Sp and Ir. Cr) were inactive against A. tumefaciens, which demonstrates that the samples which did not show any antibacterial activity are rich in certain bioactive principles which may be responsible for the anti-tumor and anti-angiogenic potentials. Our results conclude that the Ir.Sp, Ir.Chfmay be good targets for isolation of bioactive compounds responsible for the inhibition of excessive proliferation of cells and angiogenesis. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce α-generalized multi-valued contractions in cone metric spaces over Banach Algebras with solid cones and show the existence of fixed points of these contractions in this context. Our results generalize and extend several known results in metric and cone metric spaces given by some authors. Also, we give one example to illustrate significance of the main result in this paper. [ABSTRACT FROM AUTHOR]

In the quest for bioactive natural products of fungal origin, Aspergillus flavus was isolated from rhizosphere of Mentha piperita using Potato Dextrose Agar (PDA) and Czapec Yeast Broth (CYB) nutrient media for metabolites production. In total, three different metabolites were purified using HPLC/LCMS and the structures were established using 500 Varian NMR experiments. Further the isolated metabolites in different concentrations (10, 100, 1000 μg/mL) were tested for herbicidal activity using Completely Randomized design (CRD) against the seeds of Silybum marianum and Avena fatua which are major threats to wheat crop in Pakistan. Among the isolated metabolites, one compound was found active against the test weed species whose activity is reported in the present work. The chemical name of the compound is 2-(1, 4-dihydroxybutan-2-yl)-1, 3-dihydroxy-6, 8-dimethoxyanthracene-9, 10(4aH, 9aH)-dione with mass of 388. Results showed that all seeds germinated in control treatment; however, with the metabolite treated, the growth was retarded to different levels in all parts of the weeds. At a dose of 1000 μg/mL of the pure compound, 100% seeds of S. marianum and 60% seeds of A. fatua were inhibited. Interestingly, the pure compound exhibited less inhibition of 10% towards the seeds of common wheat (Triticum aestivum). [ABSTRACT FROM AUTHOR]

Motivated by the recent work of Liu and Xu, we establish a generalized fixed point theorem for multivalued mapping in the setting of G-cone metric spaces over Banach algebra without assuming the normality of the underlying cone. Our results generalize and extend some known results of G-metric and G-cone metric spaces. An example and certain consequences are presented to illustrate significance of proved results. [ABSTRACT FROM AUTHOR]

The aim of this article is to study the cone b-metric spaces over Banach Algebra with solid cones and establish some fixed points of multivalued mappings in this setting. Our results generalize and extend several known results of metric, cone metric and cone b-metric spaces. An example and certain consequences are presented to illustrate significance of established results. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish some existence theorems for coupled fixed points ofϴ-type contractive operator in metric spaces endowed with a directed graph. Our results unify, generalize and extend various results related with G-contraction for a directed graph G. We also provide an application to some nonlinear integral system equations to support the results. [ABSTRACT FROM AUTHOR]

The purpose of this article is to establish the existence of common fixed points of multivalued-contraction mappings on a metric space endowed with a graph. Presented theorems are generalizations of recent fixed point theorems due to Hussain et al. [Fixed Point Theory and Applications (2015)2015:185]. An example is also given to support our generalized result. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce the notion of generalized Hausdorff distance function on Gb-cone metric spaces and exploit it to study some fixed point results in the setting of Gb-cone metric spaces without the assumption of normality. These results improve and generalize some important known results. Some illustrative examples are also furnished to highlight the realized improvements. [ABSTRACT FROM AUTHOR]

The aim of this paper is to define generalized (α-η)-Θ contraction and to extend the results of Jleli and Samet [M. Jleli, B. Samet, J. Inequal. Appl., 2014 (2014), 8 pages] by applying a simple condition on the function Θ. We also deduce certain fixed and periodic point results for orbitally continuous generalized Θ-contractions and certain fixed point results for integral inequalities are derived. Finally, we provide an example to show the significance of the investigation of this paper. [ABSTRACT FROM AUTHOR]

The aim of this article is to introduce new family of functions M(S; T) and N(S; T) and obtain some new common fixed point theorems in the context of multiplicative metric spaces. The established results carry some well known results from the literature to multiplicative metric space. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce cyclic compatible Θ-contraction and establish some common fixed point theorems in the setting of a generating space of a b-quasi-metric family. We also apply a simple condition on the function Θ to extend the result of Samet et al. (J. Inequal. Appl. 2014; 38(2014)). With this condition, we also prove a fixed point theorem for Suzuki type Θ-contractions which generalize various results of literature. [ABSTRACT FROM AUTHOR]

Plants are important sources of antimicrobial compounds which since centuries have contributed to control animal and human diseases. In the present study ethanol extracts and fractions of Nycthantis arbor-tristis is tested for its antifungal and antibacterial potential in a series of in vitro experiments. The plant extracts were tested against 5 pathogenic bacteria i.e. (Erwinia carotovora subspecies carotovora, Erwinia carotovora subspecies atroseptica, Clavibacter michiganensis subspecies michiganensis, Ralstonia solanocerum and Erwinia chrysenthemi) and 4 pathogenic fungal stains i.e. (Penicillium notatum, Aspergillus niger, Fusarium solani and Alterneria solani). From the dry leaves and bark different extracts were prepared in solvents of different polarities (ethyl acetate, chloroform, n-hexane and water). Results were recorded as percent growth inhibition, compared with positive control. The results exhibited that ethyl acetate, chloroform and hexane fractions show excellent antifungal activity against the test fungal stains. However, against phytopathogenic bacterial strains no or negligible activity was recorded for all fractions including the crude extract of leaves and bark. Among the extracts tested, crude extract of N. arbor-tristis showed minimum activity against both fungi and bacteria. These in vitro experiments exhibit that in comparison to bacterial pathogens the extract of N. arbor-tristis can be more effective against fungal pathogens. [ABSTRACT FROM AUTHOR]