Authors:
Işıl Açık Demırcı Department of Mathematics, Mehmet Akif Ersoy University, 15030, Burdur, Turkey

Search for other papers by Işıl Açık Demırcı in
Current site
Google Scholar
PubMed
Close
,
Ömer Kışı Department of Mathematics, Bartın University, 74100, Bartın, Turkey

Search for other papers by Ömer Kışı in
Current site
Google Scholar
PubMed
Close
, and
Mehmet Gürdal Department of Mathematics, Süleyman Demirel University, 32260, Isparta, Turkey

Search for other papers by Mehmet Gürdal in
Current site
Google Scholar
PubMed
Close
Open access

Fast [12] is credited with pioneering the field of statistical convergence. This topic has been researched in many spaces such as topological spaces, cone metric spaces, and so on (see, for example [19, 21]). A cone metric space was proposed by Huang and Zhang [17]. The primary distinction between a cone metric and a metric is that a cone metric is valued in an ordered Banach space. Li et al. [21] investigated the definitions of statistical convergence and statistical boundedness of a sequence in a cone metric space. Recently, Sakaoğlu and Yurdakadim [29] have introduced the concepts of quasi-statistical convergence. The notion of quasi I-statistical convergence for triple and multiple index sequences in cone metric spaces on topological vector spaces is introduced in this study, and we also examine certain theorems connected to quasi I-statistically convergent multiple sequences. Finally, we will provide some findings based on these theorems.

  • [1]

    ABBAS, M. AND RHOADES, B. E. Fixed and periodic point results in cone metric space. Appl. Math. Lett. 2 (2009), 511515.

  • [2]

    AÇIK DEMIRCI I. AND GÜRDAL, M. On generalized statistical convergence via ideal in cone metric space. ICRAPAM 2020 Conference Proceeding, September 25-28 (2020) Mugla, Turkey, 3641.

    • Search Google Scholar
    • Export Citation
  • [3]

    ALIPRANTICE, C. D., AND TOURKY, R. Cones and duality. Amer. Math. Soc. 30 (2007), 33573366.

  • [4]

    ALTINOK, H., ET, M., AND ALTIN, Y. Lacunary statistical boundedness of order β for sequences of fuzzy numbers. J. Intell. Fuzzy Syst. 35, 2 (2018), 23832390.

    • Search Google Scholar
    • Export Citation
  • [5]

    BRAHA, N. L., SRIVASTAVA, H. M., AND ET, M. Some weighted statistical convergence and associated Korovkin and Voronovskaya type theorems. J. Appl. Math. Comput. 65, 1 (2021), 429450.

    • Search Google Scholar
    • Export Citation
  • [6]

    BRAHA, N. L., LOKU, V., MANSOUR, T., AND MURSALEEN, M. A new weighted statistical conver-gence and some associated approximation theorems. Math. Methods Appl. Sci. 45, 10 (2021), 56825698

    • Search Google Scholar
    • Export Citation
  • [7]

    CHI, K. P., AN, T. V. Dugungji’s theorem for cone metric spaces. Appl. Math. Lett. 24 (2011), 387390.

  • [8]

    CONNOR, J. The statistical and strong p-Cesàro convergence of sequences. Analysis 8 (1988), 4763.

  • [9]

    CONNOR, J. On strong matrix summability with respect to a modulus and statistical convergence.Canad. Math. Bull. 32 (1989), 194198.

  • [10]

    DAS, P., KOSTYRKO, P., WILCZYNCKI, W., AND MALIK, P. I and I-convergence of double sequence. Math. Slovaca 58, 5 (2008), 605620.

  • [11]

    DAS, P., SAVAŞ, E., AND GHOSAL, S. On generalized ofcertain summability methods using ideals. Appl. Math. Lett. 26 (2011), 15091514.

    • Search Google Scholar
    • Export Citation
  • [12]

    FAST, H. Sur la convergence statistique. Colloq. Math. 2 (1951), 241244.

  • [13]

    FRIDY, J. A. On statistical convergence. Analysis (Munich), 5 (1985), 301313.

  • [14]

    GANGULY, D. K. AND DAFADAR, A. On quasi statistical convergence of double sequences. Gen. Math. Notes 32, 2 (2016), 4253.

  • [15]

    GANICHEV, M. AND KADETS, V. Filter convergence in Banach spaces and generalized bases. In: General topology in Banach spaces. Huntington, NY: Nova Science Publishers (2001), 6169.

    • Search Google Scholar
    • Export Citation
  • [16]

    GÜRDAL, M. AND ŞAHINER, A. Extremal I-limit points of double sequences. Appl. Math. E-Notes 8 (2008), 131137.

  • [17]

    HUANG, L. G.AND ZHANG, X. Cone metric spaces and fixed point theorems of contractive mappings. J. Math. Anal. Appl. 332 (2007), 14671475.

    • Search Google Scholar
    • Export Citation
  • [18]

    KADELBURG, Z., RADENOVIC, S., AND RAKOCEVIC, V. A note on the equivalence of some metric and cone metric fixed point results. Appl. Math. Lett. 24 (2011), 370374.

    • Search Google Scholar
    • Export Citation
  • [19]

    KOSTYRKO, P., ŠALÁT, T., AND WILCZYNSKI, W. I-convergence. Real Anal. Exch. 26 (2000), 669686.

  • [20]

    LAHIRI, B. K., AND DAS, P. I and I∗-convergence in topological spaces. Math. Bohemica 130, 2 (2005) 153160.

  • [21]

    LI, K., LIN, S., AND GE, Y. On statistical convergence in cone metric space. Topol. Appl. 196 (2015), 641651.

  • [22]

    LONG-GUANG, H., AND XIAN, Z. Cone metric spaces and fixed point theorems of contractive mappings. J. Math. Anal. Appl. 332 (2007), 14681476.

    • Search Google Scholar
    • Export Citation
  • [23]

    MAMUZIC, Z. P. Introduction to general topology. P. Noordhoff, Ltd., The Netherlands (1963).

  • [24]

    MORICZ, F. Statistical convergence of multiple sequences. Arc. Math. 81 (2003), 8289.

  • [25]

    MURSALEEN, M.AND EDELY, O. H. H. Statistical convergence of double sequences. J. Math. Anal. Appl. 288 (2003), 223231.

  • [26]

    MURSALEEN, M., MOHIUDDINE, S. A., AND EDELY, O. H. H. On ideal convergence of double sequences in intuitionistic fuzzy normed spaces. Comput. Math. Appl. 59 (2010), 603611.

    • Search Google Scholar
    • Export Citation
  • [27]

    NABIEV, A., PEHLIVAN, S., AND GÜRDAL, M. On I-Cauchy sequences. Taiwanese J. Math. 12 (2007), 569576.

  • [28]

    PAL, S. K., SAVAŞ, E., AND ÇAKALLI, H. I-convergence on cone metric spaces. Sarajevo J. Math. 9, 21 (2013), 8593.

  • [29]

    SAKAOČLU ÖZGÜÇ, I., AND YURDAKADIM, T. On quasi-statistical convergence. Commun. Fac. Sci. Univ. Ank. Series A1 61, 1 (2012), 1117.

    • Search Google Scholar
    • Export Citation
  • [30]

    ŠALÁT, T. On statistically convergent sequences of real numbers. Math. Slovaca 30 (1980), 139150.

  • [31]

    ŞAHINER, A., GÜRDAL, M., AND DÜDEN, F. K. Triple sequences and their statistical convergence. Selçuk J. Appl. Math. 8, 2 (2007), 4955.

    • Search Google Scholar
    • Export Citation
  • [32]

    ŞAHINER, A.AND TRIPATHY, B. C. Some I-related properties of triple sequences. Selçuk J. Appl. Math. 9, 2 (2008), 918.

  • [33]

    ŞAHINER, A. AND YILMAZ, N. Multiple sequences in cone metric spaces. TWMS J. App. Eng. Math. 4, 2 (2014), 226233.

  • [34]

    ŞAHINER, A., YIČIT, T., AND YILMAZ, N. I-convergence of multiple sequences in cone metric spaces. Contemporary Analy. Appl. Math. 2, 1 (2014), 116126.

    • Search Google Scholar
    • Export Citation
  • [35]

    TEMIZSU, F.AND ET, M. Some results on generalizations of statistical boundedness. Math. Methods Appl. Sci. 44, 9 (2021), 74717478.

  • [36]

    TURAN, N., KARA, E. E., AND İLKHAN, M. Quasi statistical convergence in cone metric spaces. Facta Univ. Ser. Math. Inform. 33, 4 (2018), 613626.

    • Search Google Scholar
    • Export Citation
  • [37]

    TURKOGLU, D.AND ABULOHA, M. Cone metric spaces and fixed point theorems in diametrically contractive mappings. Acta Math. Sin. Engl. Ser. Mar. 26, 3 (2010), 489496.

    • Search Google Scholar
    • Export Citation
  • Collapse
  • Expand
The Instruction for Authors is available in PDF format. Please, download the file from HERE.
Please, download the LaTeX template from HERE.

Editor in Chief: László TÓTH (University of Pécs)

Honorary Editors in Chief:

  • † István GYŐRI (University of Pannonia, Veszprém, Hungary)
  • János PINTZ (Rényi Institute of Mathematics, Budapest, Hungary)
  • Ferenc SCHIPP (Eötvös Loránd University, Budapest, Hungary and University of Pécs, Pécs, Hungary)
  • Sándor SZABÓ (University of Pécs, Pécs, Hungary)
     

Deputy Editors in Chief:

  • Erhard AICHINGER (JKU Linz, Linz, Austria)
  • Ferenc HARTUNG (University of Pannonia, Veszprém, Hungary)
  • Ferenc WEISZ (Eötvös Loránd University, Budapest, Hungary)

Editorial Board

  • Attila BÉRCZES (University of Debrecen, Debrecen, Hungary)
  • István BERKES (Rényi Institute of Mathematics, Budapest, Hungary)
  • Károly BEZDEK (University of Calgary, Calgary, Canada)
  • György DÓSA (University of Pannonia, Veszprém, Hungary)
  • Balázs KIRÁLY – Managing Editor (University of Pécs, Pécs, Hungary)
  • Vedran KRCADINAC (University of Zagreb, Zagreb, Croatia) 
  • Željka MILIN ŠIPUŠ (University of Zagreb, Zagreb, Croatia)
  • Gábor NYUL (University of Debrecen, Debrecen, Hungary)
  • Margit PAP (University of Pécs, Pécs, Hungary)
  • István PINK (University of Debrecen, Debrecen, Hungary)
  • Mihály PITUK (University of Pannonia, Veszprém, Hungary)
  • Lukas SPIEGELHOFER (Montanuniversität Leoben, Leoben, Austria)
  • Andrea ŠVOB (University of Rijeka, Rijeka, Croatia)
  • Csaba SZÁNTÓ (Babeş-Bolyai University, Cluj-Napoca, Romania)
  • Jörg THUSWALDNER (Montanuniversität Leoben, Leoben, Austria)
  • Zsolt TUZA (University of Pannonia, Veszprém, Hungary)

Advisory Board

  • Szilárd RÉVÉSZ (Rényi Institute of Mathematics, Budapest, Hungary)  - Chair
  • Gabriella BÖHM
  • György GÁT (University of Debrecen, Debrecen, Hungary)

University of Pécs,
Faculty of Sciences,
Institute of Mathematics and Informatics
Department of Mathematics
7624 Pécs, Ifjúság útja 6., HUNGARY
(36) 72-503-600 / 4179
ltoth@gamma.ttk.pte.hu

  • Mathematical Reviews
  • Zentralblatt
  • DOAJ

Publication Model Gold Open Access
Submission Fee none
Article Processing Charge 0 EUR/article (temporarily)
Subscription Information Gold Open Access

Mathematica Pannonica
Language English
Size A4
Year of
Foundation
1990
Volumes
per Year
1
Issues
per Year
2
Founder Akadémiai Kiadó
Founder's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Publisher Akadémiai Kiadó
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 2786-0752 (Online)
ISSN 0865-2090 (Print)