Asymptotically lacunary µ-statistical equivalence of generalized difference sequences in probabilistic normed spaces
Resumen
The current article introduces the notion of asymptotically lacunary $(\Delta^n,\mu)$-statistical equivalent sequence in the settings of a probabilistic norm $N$. Furthermore, the article presents the concepts of asymptotically $(\Delta^n,\mu)$-strongly Ces\'{a}ro equivalent sequences and asymptotically $(\Delta^n,\mu)$-strongly Ces\'{a}ro Orlicz equivalent sequences in the theory of probabilistic normed spaces and also investigates their various properties including some inclusion relations as well as some equivalent conditions in this new settings.
Descargas
Citas
Alsina, C., Schweizer, B., Sklar, A., On the definition of a probabilistic normed space, Aequationes Math., 46, 91-98, (1993). https://doi.org/10.1007/BF01834000
Altin, Y., Et, M., Colak, R., Lacunary statistical and lacunary strongly convergence of generalized difference sequences in fuzzy numbers, Comput. Math. Appl., 52, 1011-1020, (2016). https://doi.org/10.1016/j.camwa.2006.03.025
Braha, N. L., On asymptotically ∆m lacunary statistical equivalent sequences, Appl. Math. Comput., 219, 280-288, (2012). https://doi.org/10.1016/j.amc.2012.06.016
Connor, J., The statistical and strong p-Ces'aro convergence of sequences, Analysis, 8, 47-63, (1988). https://doi.org/10.1524/anly.1988.8.12.47
Connor, J., Two valued measure and summability, Analysis, 10, 373-385, (1990). https://doi.org/10.1524/anly.1990.10.4.373
Esi, A., Ozdemir, M. K., Generalized ∆m-statistical convergence in probabilistic normed space, J. Comput. Appl. Math., 13(5), 923-932, (2011).
Esi, A., On asymptotically lacunay statistical equivalent sequences in probabilistic normed space, J. Math. Stat., 9(2), 144-148, (2013). https://doi.org/10.3844/jmssp.2013.144.148
Et, M., Colak, R., On some generalized difference sequence spaces, Soochow J. Math., 21(4), 377-386, (1995).
Fast, H., Sur la convergence statistique, Colloq. Math., 2, 241-244, (1951). https://doi.org/10.4064/cm-2-3-4-241-244
Frechet, M., Sur quelques points du calcul functionnel, Rend. Circ. Mat. Palermo, 22, 1-74, (1906). https://doi.org/10.1007/BF03018603
Freedman, A. R., Sember, J. J., Raphael, M. Some Cesa'ro-type summability spaces, Proc. Lond. Math. Soc., 37(3), 508-520, (1978). https://doi.org/10.1112/plms/s3-37.3.508
Fridy, J. A., Orhan, C., Lacunary statistical convergence, Pacific J. Math., 160, 43-51, (1993). https://doi.org/10.2140/pjm.1993.160.43
Fridy, J. A., Orhan, C., Statistical limit superior and inferior, Proc. Amer. Math. Soc., 125, 3625-3631, (1997). https://doi.org/10.1090/S0002-9939-97-04000-8
Guillen, B. L., Lallena, J. A., Sempi, C., Some classes of probabilistic normed spaces, Rend. Math., 17(7), 237-252, (1997).
Kizmaz, H., On certain sequence spaces, Canad. Math. Bull., 24(2), 169-176, (1981). https://doi.org/10.4153/CMB-1981-027-5
Marouf, M., Asymptotic equivalence and summability, Int. J. Math. Sci., 16(4), 755-762, (1993). https://doi.org/10.1155/S0161171293000948
Menger, K., Statistical metrices, Proc. Nat. Acad. Sci. USA., 28, 535-537, (1942). https://doi.org/10.1073/pnas.28.12.535
Patterson, R. F., On asymptotically statistically equivalent sequences, Demonstr. Math., 36(1), 149-153, (2003). https://doi.org/10.1515/dema-2003-0116
Patterson, R. F., Savas, E., On asymptotically lacunary statistical equivalent sequences, Thai J. Math., 4(2), 267-272, (2006).
Salat, T., On statistically convergent sequences of real numbers, Math. Slovaca, 30, 139-150, (1980).
Schweizer, B., Sklar, A., Probabilistic Metric Spaces, Elsevier, New York, (1983).
Sen, M., Et, M. Lacunary statistical and lacunary strongly convergence of generalized difference sequences in intuitionistic fuzzy normed linear spaces, Bol. Soc. Paran. Mat., 38(1), 117-129, (2020). https://doi.org/10.5269/bspm.v38i1.34814
Sen, M., Nath, S., Tripathy, B. C., Best approximation in quotient probabilistic normed space, J. Appl. Anal., 23(1), 53-57, (2017). https://doi.org/10.1515/jaa-2017-0008
Serstnev, A. N., Random normed spaces, questions of completeness, Kazan Gos. Univ. Uchen. Zap, 122(4), 3-20, (1962).
Steinhaus, H., Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math., 2, 73-74, (1951).
Tripathy, B. C., Baruah, A., Lacunary statistically convergent and lacunary strongly convergent generalized difference sequences of fuzzy real numbers, Kyungpook Math. J., 50(4), 565-574, (2010). https://doi.org/10.5666/KMJ.2010.50.4.565
Tripathy, B. C., Dutta, H., On some lacunary difference sequence spaces defined by a sequence of Orlicz functions and q-lacunary ∆nm-statistical convergence, An. S¸tiint¸. Univ. "Ovidius" Constant¸a Ser. Mat, 20(1), 417-430, (2012). https://doi.org/10.2478/v10309-012-0028-1
Tripathy, B. C., Goswami, R., On triple difference sequences of real numbers in probabilistic normed spaces, Proyecciones, 33(2), 157-174, (2014). https://doi.org/10.4067/S0716-09172014000200003
Tripathy, B. C., Goswami, R., Multiple sequences in probabilistic normed spaces, Afr. Mat., 26(5-6), 753-760, (2015). https://doi.org/10.1007/s13370-014-0243-1
Tripathy, B. C., Goswami, R., Fuzzy real valued p-absolutely summable multiple sequences in probabilistic normed spaces, Afr. Mat., 26(7-8), 1281-1289, (2015). https://doi.org/10.1007/s13370-014-0280-9
Tripathy, B. C., Goswami, R., Statistically convergent multiple sequences in probabilistic normed spaces, U.P.B. Sci. Bull., Ser. A, 78(4), 83-94, (2016).
Tripathy, B. C., Hazarika, B., Choudhary, B., Lacunary I-convergent sequences, Kyungpook Math. J., 52(4), 473-482, (2012). https://doi.org/10.5666/KMJ.2012.52.4.473
Derechos de autor 2022 Boletim da Sociedade Paranaense de Matemática
Esta obra está bajo licencia internacional Creative Commons Reconocimiento 4.0.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
