Yıl 2018, Cilt 22, Sayı 6, Sayfalar 1893 - 1900 2018-12-01

Some Remarks on Completeness and Compactness in G-Metric Spaces

Merve İlkhan [1] , Emrah Evren Kara [2]

20 81

Complete metric spaces have great importance in functional analysis and its applications. The purpose of this paper is to introduce and study on some types of completeness in generalized metric spaces by the aid of Bourbaki Cauchy and cofinally Bourbaki-Cauchy sequences which are belonging to the class bigger than the class of Cauchy sequences. Moreover, by transporting some topological concepts to generalized metric spaces, the relations between these concepts and these new types of completeness properties are given.

generalized metric spaces, compactness, completeness
  • [1] M. Abbas, T. Nazir and D. Doric, Common fixed point of mappings satisfying (E.A) propertyin generalized metric spaces, Appl. Math. Comput. 218 (2012), 7665-7670.[2] M. Abbas, T. Nazir and P. Vetro, Common fixed point results for three maps in G-metricspaces, Filomat 25(4) (2011), 1-17.[3] M. Abbas and B. E. Rhoades, Common fixed point results for noncommuting mappingswithout continuity in generalized metric spaces, Appl. Math. Comput. 215 (2009), 262-269.[4] T. V. An, N. V. Dung and V. T. L. Hang, A new approach to fixed point theorems on G-metricspaces, Topology Appl. 160(12) (2013), 1486-1493.[5] G. Beer, Between compactness and completeness, Topology Appl. 155(6) (2008), 503-514.[6] B. S. Choudhury, and P. Maity, Coupled fixed point results in generalized metric spaces,Math. Comput. Model. 54 (2011), 73-79.[7] M. I. Garrido, and A. S. Mero˜no, New types of completeness in metric spaces, Ann. Acad.Sci. Fenn. Math. 39 (2014), 733–758.[8] M. ˙Ilkhan and E.E. Kara Uniform continuity and Cauchy continuity in G-metric spaces, J.Inequal. Spec. Funct. 8(3) (2017), 59-68.[9] A. Kaewcharoen, Common fixed point theorems for contractive mappings satisfying Φ-mapsin G-metric spaces, Banach J. Math. Anal. 6(1) (2012), 101-111.[10] S. A. Mohiuddine and A. Alotaibi, Some results on a triplet fixed point for nonlinear contractionsin partially ordered G-metric spaces, Fixed Point Theory Appl. 2012(179) (2012),12 pages.[11] F. Moradlou, P. Salimi, and P. Vetro, Some new extensions of Edelstein-Suzuki-type fixed point theorem to G-metric and G-cone metric spaces, Acta Math. Sci. 33(4) (2013), 1049-1058.[12] Z. Mustafa, F. Awawdeh, and W. Shatanawi, Fixed Point Theorem for Expansive Mappingsin G-Metric Spaces, Int. J. Contemp. Math. Sciences 5(50) (2010), 2463-2472.[13] Z. Mustafa, H. Aydi and E. Karapınar, On common fixed points in G-metric spaces using(E.A) property, Comput. Math. Appl. 64 (2012), 1944-1956.[14] Z. Mustafa, M. Khandagji, and W. Shatanawi, Fixed point results on complete G-metricspaces, Studia Sci. Math. Hungar. 48(3) (2011), 304-319.[15] Z. Mustafa, and B. Sims, A new approach to generalized metric spaces, J. Nonlinear ConvexAnal. 7(2) (2006), 289-297.[16] M. Ozt¨urk and M. Ba¸sarır, ¨ On some common fixed point theorems with φ-maps on G-conemetric spaces, Bull. Math. Anal. Appl. 3(1) (2011), 121-133.
Birincil Dil en
Konular Matematik
Yayımlanma Tarihi December 2018
Dergi Bölümü Araştırma Makalesi
Yazarlar

Orcid: 0000-0002-0831-1474
Yazar: Merve İlkhan (Sorumlu Yazar)
Kurum: DÜZCE ÜNİVERSİTESİ
Ülke: Turkey


Orcid: 0000-0002-6398-4065
Yazar: Emrah Evren Kara
Kurum: DÜZCE ÜNİVERSİTESİ
Ülke: Turkey


Bibtex @araştırma makalesi { saufenbilder453343, journal = {Sakarya University Journal of Science}, issn = {1301-4048}, eissn = {2147-835X}, address = {Sakarya Üniversitesi}, year = {2018}, volume = {22}, pages = {1893 - 1900}, doi = {10.16984/saufenbilder.453343}, title = {Some Remarks on Completeness and Compactness in G-Metric Spaces}, key = {cite}, author = {İlkhan, Merve and Kara, Emrah Evren} }
APA İlkhan, M , Kara, E . (2018). Some Remarks on Completeness and Compactness in G-Metric Spaces. Sakarya University Journal of Science, 22 (6), 1893-1900. DOI: 10.16984/saufenbilder.453343
MLA İlkhan, M , Kara, E . "Some Remarks on Completeness and Compactness in G-Metric Spaces". Sakarya University Journal of Science 22 (2018): 1893-1900 <http://www.saujs.sakarya.edu.tr/issue/31266/453343>
Chicago İlkhan, M , Kara, E . "Some Remarks on Completeness and Compactness in G-Metric Spaces". Sakarya University Journal of Science 22 (2018): 1893-1900
RIS TY - JOUR T1 - Some Remarks on Completeness and Compactness in G-Metric Spaces AU - Merve İlkhan , Emrah Evren Kara Y1 - 2018 PY - 2018 N1 - doi: 10.16984/saufenbilder.453343 DO - 10.16984/saufenbilder.453343 T2 - Sakarya University Journal of Science JF - Journal JO - JOR SP - 1893 EP - 1900 VL - 22 IS - 6 SN - 1301-4048-2147-835X M3 - doi: 10.16984/saufenbilder.453343 UR - http://dx.doi.org/10.16984/saufenbilder.453343 Y2 - 2018 ER -
EndNote %0 Sakarya University Journal of Science Some Remarks on Completeness and Compactness in G-Metric Spaces %A Merve İlkhan , Emrah Evren Kara %T Some Remarks on Completeness and Compactness in G-Metric Spaces %D 2018 %J Sakarya University Journal of Science %P 1301-4048-2147-835X %V 22 %N 6 %R doi: 10.16984/saufenbilder.453343 %U 10.16984/saufenbilder.453343
ISNAD İlkhan, Merve , Kara, Emrah Evren . "Some Remarks on Completeness and Compactness in G-Metric Spaces". Sakarya University Journal of Science 22 / 6 (Aralık 2018): 1893-1900. http://dx.doi.org/10.16984/saufenbilder.453343