CpG islands (CGIs) play a vital role in genome analysis as genomic markers. Identification of the CpG pair has contributed not only to the prediction of promoters but also to the understanding of the epigenetic causes of cancer. In the human genome [1] wherever the dinucleotides CG occurs the C nucleotide (cytosine) undergoes chemical modifications.There is a relatively high probability of this modification that mutates C into a T. For biologically important reasons the mutation modification process is suppressed in short stretches of the genome, such as 'start' regions. In these regions [2] predominant CpG dinucleotides are found than elsewhere. Such regions are called CpG islands. DNA methylation is an effective means by which gene expression is silenced. In normal cells, DNA methylation functions to prevent the expression of imprinted and inactive X chromosome genes. In cancerous cells, DNA methylation inactivates tumor-suppressor genes, as well as DNA repair genes, can disrupt cell-cycle regulation. The most current methods for identifying CGIs suffered from various limitations and involved a lot of human interventions. This paper gives an easy searching technique with data mining of Markov Chain in genes. Markov chain model has been applied to study the probability of occurrence of C-G pair in the given gene sequence. Maximum Likelihood estimators for the transition probabilities for each model and analgously for the model has been developed and log odds ratio that is calculated estimates the presence or absence of CpG is lands in the given gene which brings in many facts for the cancer detection in human genome.

Using direct method, we prove the generalized Hyers-Ulam stability of the cubic functional equation f (x+3y)−3f (x+2y)+4f (x+y)−4f (x)+3f (x−y)−f (x−2y) = 12f (y) in Felbin's type fuzzy normed spaces.

In this paper, we obtain the general solution and the generalized Ulam-Hyers stability of the 2-variable $k$-AC mixed type functional equation$$\begin{aligned}& f(x+k y, z+k w)+f(x-k y, z-k w) \\& \quad=k^2[f(x+y, z+w)+f(x-y, z-w)]+2\left(1-k^2\right) f(x, z) .\end{aligned}$$for any $k \in Z-\{0, \pm 1\}$ in $\alpha$-Šerstnev Menger Probabilistic normed spaces.