Soft matrices on soft multisets in an optimal decision process

Coskun, Arzu; Aras, Çiğdem Gündüz; Cakalli, Huseyin; Sönmez, Ahmet

doi:10.1063/1.4959713

Cited by 22 publications

(8 citation statements)

References 13 publications

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“…For a further study, we suggest to investigate statistically p-quasi-Cauchy sequences of soft points and statistically p-quasi-Cauchy sequences of fuzzy points. However due to the change in settings, the definitions and methods of proofs will not always be analogous to those of the present work (for example see [1], [30], [41], and [47]). We also suggest to investigate statistically p-quasi-Cauchy double sequences of points in R (see [54], [53], [40], and [35] for the related definitions in the double case).…”

Section: Resultsmentioning

confidence: 99%

Variations on statistical quasi Cauchy sequences

Cakalli

2019

B Soc Paran Mat

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In this paper, we introduce a concept of statistically $p$-quasi-Cauchyness of a real sequence in the sense that a sequence $(\alpha_{k})$ is statistically $p$-quasi-Cauchy if $\lim_{n\rightarrow\infty}\frac{1}{n}|\{k\leq n: |\alpha_{k+p}-\alpha_{k}|\geq{\varepsilon}\}|=0$ for each $\varepsilon>0$. A function $f$ is called statistically $p$-ward continuous on a subset $A$ of the set of real umbers $\mathbb{R}$ if it preserves statistically $p$-quasi-Cauchy sequences, i.e. the sequence $f(\textbf{x})=(f(\alpha_{n}))$ is statistically $p$-quasi-Cauchy whenever $\boldsymbol\alpha=(\alpha_{n})$ is a statistically $p$-quasi-Cauchy sequence of points in $A$. It turns out that a real valued function $f$ is uniformly continuous on a bounded subset $A$ of $\mathbb{R}$ if there exists a positive integer $p$ such that $f$ preserves statistically $p$-quasi-Cauchy sequences of points in $A$.

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Section: Resultsmentioning

confidence: 99%

Variations on statistical quasi Cauchy sequences

Cakalli

2019

B Soc Paran Mat

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“…One may expect this investigation to be a useful tool in the field of analysis in modeling various problems occurring in many areas of science, dynamical systems, computer science, information theory, and biological science. On the other hand, we suggest to investigate the concept of fuzzy Abel statistical quasi Cauchy sequences of fuzzy points or soft points (see [15] for the definitions and related concepts in fuzzy setting, and see [25] related concepts in soft setting). However due to the change in settings, the definitions and methods of proofs will not always be the same.…”

Section: Resultsmentioning

confidence: 99%

Abel statistical quasi Cauchy sequences

Cakalli

2019

Filomat

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In this paper, we investigate the concept of Abel statistical quasi Cauchy sequences. A real function f is called Abel statistically ward continuous if it preserves Abel statistical quasi Cauchy sequences, where a sequence (α k) of point in R is called Abel statistically quasi Cauchy if lim x→1 − (1 − x) k:|∆α k | ε x k = 0 for every ε > 0, where ∆α k = α k+1 − α k for every k ∈ N. Some other types of continuities are also studied and interesting results are obtained. It turns out that the set of Abel statistical ward continuous functions is a closed subset of the space of continuous functions.

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“…As the set of downward half 6 HUSEYIN CAKALLI, MALTEPE UNIVERSITY, ISTANBUL-TURKEY Cauchy sequences is different from the set of asymptotically non-decreasing sequences, a further new research would be carried out if one allows to find new results. We suggest to investigate downward half Cauchy sequences of fuzzy points in asymmetric fuzzy spaces (see [34], [1], [45] , [39] for the definitions and related concepts in fuzzy setting and soft setting). We also suggest to investigate downward half Cauchy double sequences (see for example [33], [52], [53], [38] and [54] for the definitions and related concepts in the double sequences case).…”

Section: Resultsmentioning

confidence: 99%