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Characterization of Absolute and Uniform Continuity

İsmail ASLAN [1] , Oktay DUMAN [2]

In the present paper, by considering nonlinear integral operators and using their approximations via regular summability methods, we obtain characterizations for some function spaces including the space of absolutely continuous functions, the space of uniformly continuous functions, and their other variants. We observe that Bell-type summability methods are quite effective to generalize and improve some related results in the literature. At the end of the paper, we discuss some special cases and applications.
Summability process, absolute continuity, uniform continuity, nonlinear integral operators, bounded variation
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Primary Language en Mathematics Mathematics Orcid: 0000-0001-9753-6757Author: İsmail ASLAN (Primary Author)Institution: Hacettepe UniversityCountry: Turkey Orcid: 0000-0001-7779-6877Author: Oktay DUMAN Institution: TOBB UNIVERSITY OF ECONOMICS AND TECHNOLOGYCountry: Turkey Publication Date : October 6, 2020
 Bibtex @research article { hujms585581, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2020}, volume = {49}, pages = {1550 - 1565}, doi = {10.15672/hujms.585581}, title = {Characterization of Absolute and Uniform Continuity}, key = {cite}, author = {Aslan, İsmail and Duman, Oktay} } APA Aslan, İ , Duman, O . (2020). Characterization of Absolute and Uniform Continuity . Hacettepe Journal of Mathematics and Statistics , 49 (5) , 1550-1565 . DOI: 10.15672/hujms.585581 MLA Aslan, İ , Duman, O . "Characterization of Absolute and Uniform Continuity" . Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1550-1565 Chicago Aslan, İ , Duman, O . "Characterization of Absolute and Uniform Continuity". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1550-1565 RIS TY - JOUR T1 - Characterization of Absolute and Uniform Continuity AU - İsmail Aslan , Oktay Duman Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.585581 DO - 10.15672/hujms.585581 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1550 EP - 1565 VL - 49 IS - 5 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.585581 UR - https://doi.org/10.15672/hujms.585581 Y2 - 2019 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics Characterization of Absolute and Uniform Continuity %A İsmail Aslan , Oktay Duman %T Characterization of Absolute and Uniform Continuity %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 5 %R doi: 10.15672/hujms.585581 %U 10.15672/hujms.585581 ISNAD Aslan, İsmail , Duman, Oktay . "Characterization of Absolute and Uniform Continuity". Hacettepe Journal of Mathematics and Statistics 49 / 5 (October 2020): 1550-1565 . https://doi.org/10.15672/hujms.585581 AMA Aslan İ , Duman O . Characterization of Absolute and Uniform Continuity. Hacettepe Journal of Mathematics and Statistics. 2020; 49(5): 1550-1565. Vancouver Aslan İ , Duman O . Characterization of Absolute and Uniform Continuity. Hacettepe Journal of Mathematics and Statistics. 2020; 49(5): 1550-1565.

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