Ahmed Al-Rawashdeh

Common fıxed points of almost generalized (ψ, ϕ)-contractive mappings in ordered metric spaces

In this article, we introduce the notion of almost generalized (ψ, ϕ)-contractive mappings in ordered metric spaces and we establish some fixed and common fixed point results in ordered complete metric spaces. Our results generalize several well-known comparable results in the literature. Finally, an example and an application are given in order to support the useability of our results.Mathematics Subject Classifications 2000: 54H25; 47H10; 54E50

Transcriptome Analysis Reveals Genes Commonly Induced by Botrytis cinerea Infection, Cold, Drought and Oxidative Stresses in Arabidopsis

Signaling pathways controlling biotic and abiotic stress responses may interact synergistically or antagonistically. To identify the similarities and differences among responses to diverse stresses, we analyzed previously published microarray data on the transcriptomic responses of Arabidopsis to infection with Botrytis cinerea (a biotic stress), and to cold, drought, and oxidative stresses (abiotic stresses). Our analyses showed that at early stages after B. cinerea inoculation, 1498 genes were up-regulated (B. cinerea up-regulated genes; BUGs) and 1138 genes were down-regulated (B. cinerea down-regulated genes; BDGs). We showed a unique program of gene expression was activated in response each biotic and abiotic stress, but that some genes were similarly induced or repressed by all of the tested stresses. Of the identified BUGs, 25%, 6% and 12% were also induced by cold, drought and oxidative stress, respectively; whereas 33%, 7% and 5.5% of the BDGs were also down-regulated by the same abiotic stresses. Coexpression and protein-protein interaction network analyses revealed a dynamic range in the expression levels of genes encoding regulatory proteins. Analysis of gene expression in response to electrophilic oxylipins suggested that these compounds are involved in mediating responses to B. cinerea infection and abiotic stress through TGA transcription factors. Our results suggest an overlap among genes involved in the responses to biotic and abiotic stresses in Arabidopsis. Changes in the transcript levels of genes encoding components of the cyclopentenone signaling pathway in response to biotic and abiotic stresses suggest that the oxylipin signal transduction pathway plays a role in plant defense. Identifying genes that are commonly expressed in response to environmental stresses, and further analyzing the functions of their encoded products, will increase our understanding of the plant stress response. This information could identify targets for genetic modification to improve plant resistance to multiple stresses.

Mizoguchi-Takahashi-type theorems in tvs-cone metric spaces

In this paper, the concepts of a set-valued contraction of Mizoguchi-Takahashi type in the context of topological vector space (tvs)-cone metric spaces are introduced and a fixed point theorem in the context of tvs-cone metric spaces with respect to a solid cone is proved. We obtained results which extend and generalize the main results of S. H. Cho with J. S. Bae, Mizoguchi with Takahashi and S. B. Nadler Jr. Two examples are given to illustrate the usability of our results.2010 MSC: 47H10, 54H25.

On a Fixed Point for Generalized Contractions in Generalized Metric Spaces

Lakzian and Samet (2010) studied some fixed-point results in generalized metric spaces in the sense of Branciari. In this paper, we study the existence of fixed-point results of mappings satisfying generalized weak contractive conditions in the framework of a generalized metric space in sense of Branciari. Our results modify and generalize the results of Laksian and Samet, as well as, our results generalize several well-known comparable results in the literature.

Fixed point results for { α , ξ } -expansive locally contractive mappings

We recall the concepts of {α,ξ}-contractive and α-admissible mappings on complete metric spaces to state related fixed point theorems. In this paper, we obtain some fixed point results for {α,ξ}-expansive locally contractive mappings in complete metric spaces. The contractiveness of the mapping is only on a closed ball instead of the whole space. Our results unify, generalize, and complement various well-known comparable results in the literature.MSC:46S40, 47H10, 54H25.

New fixed point theorems for generalized F-contractions in complete metric spaces

In this paper, owing to the concept of F-contraction, we define two new classes of functions M(S,T)

Generalized Common Fixed Point Results via Greatest Lower Bound Property

M(S,T)

Normed Ordered and -Metric Spaces

and N(S,T)

Fixed Point Results for a Class of Monotone Nonexpansive Type Mappings in Hyperbolic Spaces

N(S,T)

New Types of Almost Countable Dense Homogeneous Space

, and we prove some new fixed point results for single-valued and multivalued mappings in complete metric spaces. Our results extend, generalize and unify several known results in the literature. We include an example to show that the generalization is proper.