There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Fractional Differential Equations

There have been many attempts to generalize the definition of a metric space in order to obtain possibilities for more general fixed point results. In this paper, we give a survey of recent results on reducing fixed point theorems on generalized metric spaces to fixed point theorems on metric spaces and then investigate this fact in other generalized metric spaces. We show that many generalized metric spaces are topologically equivalent to certain metric spaces or to previously generalized metric spaces. Also, the fixed point theory in these generalized metric spaces may be a consequence of the fixed point theory in certain metric spaces or in previously generalized metric spaces.

Various generalizations of metric spaces and fixed point theorems

The work is giving estimations of the discrepancy between solutions of the initial and the homogenized problems for a one{dimensional second order elliptic operators with random coeecients satisfying strong or uniform mixing conditions. We obtain several sharp estimates in terms of the corresponding mixing coeecient. Abstract. In the theory of homogenisation it is of particular interest to determine the classes of problems which are stable on taking the homogenisation limits. A notable situation where the limit enlarges the class of original problems is known as memory (nonlocal) eeects. A number of results in that direction has been obtained for linear problems. Tartar (1990) innitiated the study of the eeective equation corresponding to nonlinear equation: @ t u n + a n u 2 n = f: Signiicant progress has been hampered by the complexity of required computations needed in order to obtain the terms in power{series expansion. We propose a method which overcomes that diiculty by introducing graphs representing the domain of integration of the integrals in each term. The graphs are relatively simple, it is easy to calculate with them and they give us a clear image of the form of each term. The method allows us to discuss the form of the eeective equation and the convergence of power{series expansions. The feasibility of our method for other types of nonlinearities will be discussed as well.

Applied Mathematics and Computation

Proceedings of the National Academy of Sciences

The study of asymmetric structures and their applications in mathematics is interesting. One of the types of asymmetric structures on a metric space has been initiated by Kada et al. (1996) and is known as a w-distance. That lack of symmetry attracts many researchers in fixed point theory. In this manuscript, we introduce a new type of contraction named generalized ( α , ψ , M Ω ) -contractive mappings via w-distances, and then we prove some new related fixed point results, generalizing and improving the recent results of Lakzian et al. (2016) and others. At the end, we give some examples. To illustrate the usability of the new theory, we apply our obtained results to resolve a nonlinear Fredholm-integral-type equation.

On Generalized (α, ψ, MΩ)-Contractions with w-Distances and an Application to Nonlinear Fredholm Integral Equations

the cited. In this manuscript, we establish some ﬁ xed point results for fuzzy mappings via ð α ∗ , F Þ -contractions. For validation of the proved results, some nontrivial examples are presented. Few interesting consequences are also stated which authenticate that our results generalize many existing ones in the literature.

Fuzzy Fixed Point Results of Fuzzy Mappings on b -Metric Spaces via ð α ∗ , F Þ -Contractions

The purpose of this paper is to present a new concept of a Banach algebra in a fuzzy metric space (FM-space). We define an open ball, an open set and prove that every open ball in an FM-space over a Banach algebra $ \mathcal{A} $ is an open set. We present some more topological properties and a Hausdorff metric on FM-spaces over $ \mathcal{A} $. Moreover, we state and prove a fuzzy Banach contraction theorem on FM-spaces over a Banach algebra $ \mathcal{A} $. Furthermore, we present an application of an integral equation and will prove a result dealing with the integral operators in FM-spaces over a Banach algebra.

An approach of Banach algebra in fuzzy metric spaces with an application

/pdf/fixed-discs-in-quasi-metric-spaces-3m5w128668.pdf

Fixed discs in quasi-metric spaces


 The objective of this research is to establish new results for set-valued dominated mappings that meet the criteria of advanced locally contractions in a complete extended b-metric space. Additionally, we intend to establish new fixed point outcomes for a couple of dominated multi-functions on a closed ball that satisfy generalized local contractions. In this study, we present novel findings for dominated maps in an ordered complete extended b-metric space. Additionally, we introduce a new concept of multi-graph dominated mappings on a closed ball within these spaces and demonstrate some original results for graphic contractions equipped with a graphic structure. To demonstrate the uniqueness of our new discoveries, we verify their applicability in obtaining a joint solution of integral and functional equations. Our findings have also led to modifications of numerous classical and contemporary results in existing research literature.


On dominated multivalued operators involving nonlinear contractions and applications

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

Hassen Aydi

Author Tools

Chat about Author