Recent content by ozkan12

  1. O

    MHB How does ${X}_{w}\subset {X^*}_{w}$ occur in modular metric space?

    No paper '''arXiv:1112.5561v1.pdf...''' this link, there is something related to modular metric space...And in page 6 you will see definition 2.2...Please can you explain that how happened ${X}_{w}\subset {X^*}_{w}$ ? Thank you for your attention...Best wishes...
  2. O

    MHB How does ${X}_{w}\subset {X^*}_{w}$ occur in modular metric space?

    $X\subseteq R$ and ${d}_{w}$ is wrong, I wrote wrong it, it must be ${d}_{\lambda}$
  3. O

    MHB How does ${X}_{w}\subset {X^*}_{w}$ occur in modular metric space?

    Dear Siron, First of all, thank you for your attention...But I couldn't prove this...Best wishes..
  4. O

    MHB How does ${X}_{w}\subset {X^*}_{w}$ occur in modular metric space?

    Let $d$ be a metric on $X$. Fix ${x}_{0}\in X$. Let ${d}_{\lambda}\left(x,y\right)=\frac{1}\lambda{}\left| x-y \right|$ and The two sets ${X}_{w}={X}_{w}\left({x}_{0}\right)=\left\{x\in X:{d}_{\lambda}\left(x,{x}_{0}\right)\to0\left( as \lambda\to\infty\right) \right \}$ and...
  5. O

    MHB Metric spaces and normed spaces

    Dear Ackbach, I know this...But what is the nonlinearity ? I have troubles related to this term...?
  6. O

    MHB Metric spaces and normed spaces

    What is the relation between metric spaces and normed spaces... What is the meaning of " metric spaces are seen as a nonlinear version of vector spaces endowed with a norm" ? Thank you for your attention...Best wishes...:)
  7. O

    MHB How Do Different Metrics Affect Convergence and Divergence of Sequences?

    Dear Euge Thank you for your attention...Best wishes...:) Have you any information related to modular metric spaces ?
  8. O

    MHB How Do Different Metrics Affect Convergence and Divergence of Sequences?

    Dear Euge, Yes, it suffices to work with metric ${d}_{2}$...I found somethings, I sent these things...Please can you check it ? Firstly, we will use metric ${d}_{2}$ and discuss on sequence ${x}_{n}=\frac{1}{n}$. Let $\varepsilon>0$ and ${n}_{0}>\frac{1}{\varepsilon}$ (i.e the smallest...
  9. O

    MHB How Do Different Metrics Affect Convergence and Divergence of Sequences?

    Let $X=R$ and ${d}_{1}\left(x,y\right)=\frac{1}{\eta}\left| x-y \right|$ $\eta\in \left(0,\infty\right)$ and ${d}_{2}\left(x,y\right)=\left| x-y \right|$..By using ${d}_{1}$ and ${d}_{2}$ please show that ${x}_{n}=\left(-1\right)^n$ is divergent and ${x}_{n}=\frac{1}{n}$ is convergent...
  10. O

    MHB Can we take limits to infinity in finite sets of $\Bbb{N}$?

    Dear ZaidAlyafey, Thank you for your attention...For second question odd numbers can be an example...İs there any examples anything else 2N and 2N+1
  11. O

    MHB Can we take limits to infinity in finite sets of $\Bbb{N}$?

    İn a finite set, can we take limit to $\infty$ ? Also, can you give an example related to infinite subset of $\Bbb{N}$ ?
  12. O

    MHB Limit of Absolute Values and Metric Spaces

    Yes, $d$ correspond to metric on $(X,d)$ metric space.
  13. O

    MHB Limit of Absolute Values and Metric Spaces

    Let $\lim_{{k}\to{\infty}}d\left({x}_{m\left(k\right)},{x}_{m\left(k\right)-1}\right)=\varepsilon$ and $\lim_{{k}\to{\infty}}d\left({x}_{n\left(k\right)},{x}_{m\left(k\right)}\right)=\varepsilon$...Can we say that...
  14. O

    MHB Is Every Sequence with a Cauchy Subsequence Also Cauchy?

    Sudharaka, I learned this information, Thank you for your attention, best wishes...:)
  15. O

    MHB Is Every Sequence with a Cauchy Subsequence Also Cauchy?

    Hi Sudharaka, İn some fixed point theorem, to prove that $\left\{{x}_{n}\right\}$ is cauchy sequence, author show that $\left\{{x}_{2n}\right\}$ is cauchy sequence...And in fixed point theorems, we use iteration sequence such that ${x}_{n}=f{x}_{n-1}$...İf we construct $\left\{{x}_{n}\right\}$...