This project was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah under Grant No. 2Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India. Both authors read and approved the final manuscript.ġ Department of Mathematics, King Abdulaziz University, P.O. Authors' contributionsīoth authors contributed equally and significantly in writing this paper. The authors declare that they have no competing interests. Now, taking the limit as n - to, we get S^(A(u)) c S0(A(u)). Then the asymptotic density of K denoted by S(K) is defined as S(K)=lim„i |, we have Let K be a subset of the set of natural numbers N. We find some relations with sets of sequences which are related to the notion of strong convergence. In this paper we define the notion of X-statistical convergence as a matrix domain of a difference operator, which is obtained by replacing the sequence x by uAx, where Ax = (xk -xk+1)f=1 and u = (ukis another sequence with uk =0 for all k. For example, lacunary statistical convergence, A-statistical convergence, statistical summability (C,1), statistical X-summability, statistical a-convergence, statistical A-summability, X-statistical convergence with order a, lacunary and X-statistical convergence in a solid Riesz space, lacunary statistical convergence and ideal convergence in random 2-normed spaces, generalized weighted statistical convergence etc. The notion of statistical convergence (see Fast ) has been studied in various setups, and its various generalizations, extensions and variants have been studied by various authors so far. Keywords: statistical convergence X-statistical convergence difference sequences In this paper we define the X(u)-statistical convergence that generalizes, in a certain sense, the notion of X-statistical convergence. Read our Privacy Notice if you are concerned with your privacy and how we handle personal information.Generalized statistical convergence of difference sequencesĪbdullah Alotaibi1 and Mohammad Mursaleen2*Ĭorrespondence: 2Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, Indiaįull list ofauthor information is available at the end ofthe article If you plan to use these services during a course please contact us. If you have any feedback or encountered any issues please let us know via EMBL-EBI Support. Please read the provided Help & Documentation and FAQs before seeking help from our support staff. The tools described on this page are provided using Search and sequence analysis tools services from EMBL-EBI in 2022 These specialist programs allow searches of databases using sequence fragments as the query. This can be useful when you want to match all of a short query sequence to part of a larger database sequence. GLSEARCH performs an optimal sequence search using alignments that are global in the query but local in the database sequence.
GGSEARCH performs optimal global-global alignment searches using the Needleman-Wunsch algorithm. PSI-Search2 combines the sensitivity of the Smith-Waterman search algorithm (SSEARCH) with the PSI-BLAST profile construction strategy to find distantly related protein sequences. PSI-Search combines the sensitivity of the Smith-Waterman search algorithm (SSEARCH) with the PSI-BLAST profile construction strategy to find distantly related protein sequences. Optimal searches guarantee you find the best alignment score for your given parameters. SSEARCH is an optimal (as opposed to heuristics-based) local alignment search tool using the Smith-Waterman algorithm. Protein Nucleotide Genomes Whole Genome Shotgun PHI-BLAST functionality is also available to restrict results using patterns.įASTA is another commonly used sequence similarity search tool which uses heuristics for fast local alignment searching.
PSI-BLAST allows users to construct and perform a BLAST search with a custom, position-specific, scoring matrix which can help find distant evolutionary relationships.
It uses heuristics to perform fast local alignment searches. NCBI BLAST is the most commonly used sequence similarity search tool. The tools can be launched with different form pre-sets using the links - these can be changed on the tool page as well. By statistically assessing how well database and query sequences match one can infer homology and transfer information to the query sequence. Sequence Similarity Searching is a method of searching sequence databases by using alignment to a query sequence.
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