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Common Fixed Point Theorems For F-Contractions In $G$-Metric Spaces Using Compatible Mappings

Yıl 2018, Cilt: 6 Sayı: 1, 92 - 97, 15.04.2018

Cafer Aydın Seher Sultan Sepet

Öz

Using a mapping $F:\mathbb{R_{+}}\rightarrow \mathbb{R}$, Wardowski [1] introduce a new type of contraction called $F$-contraction and prove a new fixed point theorem concerning $F$-contraction. In the present article, we prove some fixed point theorems with helping compatible maps for type $1$ and type $2$ $F$-contraction in complete $G$-metric spaces.

Anahtar Kelimeler

Fixed point $G$-metric space $F$-contraction Compatible mapping

Kaynakça

  • [1] D. Wardowski, Fixed Point of a new type of contactive mappings in complete metric spaces, Fixed Point Theory and Applications, 94, 6 pp., (2012), DOI:10.1186/1687-1812-2012-94.
  • [2] S. Banach, Surles operations dansles ensembles abstracits et leur application aux equations integrales, Fund Math., 3, (1922), 133-181.
  • [3] Z. Mustafa and B. Sims, A new approach to a generalized metric spaces, J. Nonlinear Convex Anal., 7, (2), (2006), 289-297.
  • [4] M. Abbas, A. R. Khan and T. Nazir, Coupled common fixed point results in two generalized metric spaces, Applied Mathematics and Computation, Vol:217 No.13 pp. (2011), 6328-6336.
  • [5] M. Abbas, T. Nazir and D. Doric, Common fixed point of mappings satisfying (E.A) property in generalized metric spaces, Applied Mathematics and Computation, Vol:218, No.14 pp., (2012), 7665-7670.
  • [6] Z. Mustafa, W. Shatanawi and M. Bataineh, Existence of fixed point results in G-metric spaces, Int. J. Math. and Math. Sci., page 10, (2009), DOI:10.1155/2009/283028.
  • [7] H.S. Ding and E. Karapınar, A note on some coupled fixed point theorems on G-metric space, Journal of Inequalities and Applications, Vol:2012, article 170, (2012), DOI: 10.1186/1029-242X-2012-170.
  • [8] G. Jungck, Commuting mappings and fixed point, Amer. Math. Monthly, Vol:83, No.4 (1976), 261-263.
  • [9] G. Jungck, Compatible mappings and common fixed points, Int. J. Math. Math. Sci., 9, (1986), 771-779.
  • [10] M. Kumar, Compatible Maps in G-Metric spaces, Int. Journal of Math. Anaysis, Vol:6, No.29 (2012), 1415-1421.
  • [11] M. Cosentino, and P. Vetro, Fixed point results for F-contractive mappings of Hardy-Rogers-type, Filomat Vol:28, No.4 pp., (2014), 715-722.
  • [12] J. Ahmad, A. Rawashdeh and A. Azam, New fixed point theorems for generalized F-contractions in complete metric space, Fixed Point Theory and Applications, 80, (2015), DOI: 10.1186/s13663-015-0333-2.
  • [13] R. Batra and S. Vashistha, Fixed points of an F-contraction on metric spaces with a graph, Int. J. Comput. Math., Vol:91, (12), (2014), 2483-2490.
  • [14] S. Chong, J. K. Kim, L. Wong, and J. Tang, Existence of fixed points for generalized F-contractions and generalized F-suzuki contractions in metric spaces, Global Journal of pure and applied Mathematics, ISSN 0973-1768, Vol:12, No.6 (2016), pp. 4867-4882.
  • [15] G. Mınak, A. Helvacı, and I. Altun, C´ iric´ type generalized F-contractions on complete metric spaces and fixed point results, Filomat, 28, (6), (2014), 1143-1151.
  • [16] H. Piri and P. Kumam, Some fixed point theorems concerning F-contraction in complete metric spaces, Fixed Point Theory Appl., 210, (2014), DOI:10.1186/1687-1812-2014,210.
  • [17] D. Wardowski and N. Van Dung, Fixed points of F -weak contractions on complete metric spaces, Demonstr. Math., Vol:XLVII No.1, (2014), 146-155.
  • [18] R. Batra, S. Vashistha and R. Kumar, A coincidence point theorem for F-contractions on metric spaces equipped with an altered distance, J. Math.Comput. Sci., 4, (5), (2014), 826-833.

Yıl 2018, Cilt: 6 Sayı: 1, 92 - 97, 15.04.2018

Cafer Aydın Seher Sultan Sepet

Öz

Kaynakça

  • [1] D. Wardowski, Fixed Point of a new type of contactive mappings in complete metric spaces, Fixed Point Theory and Applications, 94, 6 pp., (2012), DOI:10.1186/1687-1812-2012-94.
  • [2] S. Banach, Surles operations dansles ensembles abstracits et leur application aux equations integrales, Fund Math., 3, (1922), 133-181.
  • [3] Z. Mustafa and B. Sims, A new approach to a generalized metric spaces, J. Nonlinear Convex Anal., 7, (2), (2006), 289-297.
  • [4] M. Abbas, A. R. Khan and T. Nazir, Coupled common fixed point results in two generalized metric spaces, Applied Mathematics and Computation, Vol:217 No.13 pp. (2011), 6328-6336.
  • [5] M. Abbas, T. Nazir and D. Doric, Common fixed point of mappings satisfying (E.A) property in generalized metric spaces, Applied Mathematics and Computation, Vol:218, No.14 pp., (2012), 7665-7670.
  • [6] Z. Mustafa, W. Shatanawi and M. Bataineh, Existence of fixed point results in G-metric spaces, Int. J. Math. and Math. Sci., page 10, (2009), DOI:10.1155/2009/283028.
  • [7] H.S. Ding and E. Karapınar, A note on some coupled fixed point theorems on G-metric space, Journal of Inequalities and Applications, Vol:2012, article 170, (2012), DOI: 10.1186/1029-242X-2012-170.
  • [8] G. Jungck, Commuting mappings and fixed point, Amer. Math. Monthly, Vol:83, No.4 (1976), 261-263.
  • [9] G. Jungck, Compatible mappings and common fixed points, Int. J. Math. Math. Sci., 9, (1986), 771-779.
  • [10] M. Kumar, Compatible Maps in G-Metric spaces, Int. Journal of Math. Anaysis, Vol:6, No.29 (2012), 1415-1421.
  • [11] M. Cosentino, and P. Vetro, Fixed point results for F-contractive mappings of Hardy-Rogers-type, Filomat Vol:28, No.4 pp., (2014), 715-722.
  • [12] J. Ahmad, A. Rawashdeh and A. Azam, New fixed point theorems for generalized F-contractions in complete metric space, Fixed Point Theory and Applications, 80, (2015), DOI: 10.1186/s13663-015-0333-2.
  • [13] R. Batra and S. Vashistha, Fixed points of an F-contraction on metric spaces with a graph, Int. J. Comput. Math., Vol:91, (12), (2014), 2483-2490.
  • [14] S. Chong, J. K. Kim, L. Wong, and J. Tang, Existence of fixed points for generalized F-contractions and generalized F-suzuki contractions in metric spaces, Global Journal of pure and applied Mathematics, ISSN 0973-1768, Vol:12, No.6 (2016), pp. 4867-4882.
  • [15] G. Mınak, A. Helvacı, and I. Altun, C´ iric´ type generalized F-contractions on complete metric spaces and fixed point results, Filomat, 28, (6), (2014), 1143-1151.
  • [16] H. Piri and P. Kumam, Some fixed point theorems concerning F-contraction in complete metric spaces, Fixed Point Theory Appl., 210, (2014), DOI:10.1186/1687-1812-2014,210.
  • [17] D. Wardowski and N. Van Dung, Fixed points of F -weak contractions on complete metric spaces, Demonstr. Math., Vol:XLVII No.1, (2014), 146-155.
  • [18] R. Batra, S. Vashistha and R. Kumar, A coincidence point theorem for F-contractions on metric spaces equipped with an altered distance, J. Math.Comput. Sci., 4, (5), (2014), 826-833.
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

Cafer Aydın

Seher Sultan Sepet Bu kişi benim

Yayımlanma Tarihi 15 Nisan 2018
Gönderilme Tarihi 22 Eylül 2017
Kabul Tarihi 28 Aralık 2017
Yayımlandığı Sayı Yıl 2018 Cilt: 6 Sayı: 1

Kaynak Göster

APA Aydın, C., & Sepet, S. S. (2018). Common Fixed Point Theorems For F-Contractions In $G$-Metric Spaces Using Compatible Mappings. Konuralp Journal of Mathematics, 6(1), 92-97.
AMA Aydın C, Sepet SS. Common Fixed Point Theorems For F-Contractions In $G$-Metric Spaces Using Compatible Mappings. Konuralp J. Math. Nisan 2018;6(1):92-97.
Chicago Aydın, Cafer, ve Seher Sultan Sepet. “Common Fixed Point Theorems For F-Contractions In $G$-Metric Spaces Using Compatible Mappings”. Konuralp Journal of Mathematics 6, sy. 1 (Nisan 2018): 92-97.
EndNote Aydın C, Sepet SS (01 Nisan 2018) Common Fixed Point Theorems For F-Contractions In $G$-Metric Spaces Using Compatible Mappings. Konuralp Journal of Mathematics 6 1 92–97.
IEEE C. Aydın ve S. S. Sepet, “Common Fixed Point Theorems For F-Contractions In $G$-Metric Spaces Using Compatible Mappings”, Konuralp J. Math., c. 6, sy. 1, ss. 92–97, 2018.
ISNAD Aydın, Cafer - Sepet, Seher Sultan. “Common Fixed Point Theorems For F-Contractions In $G$-Metric Spaces Using Compatible Mappings”. Konuralp Journal of Mathematics 6/1 (Nisan 2018), 92-97.
JAMA Aydın C, Sepet SS. Common Fixed Point Theorems For F-Contractions In $G$-Metric Spaces Using Compatible Mappings. Konuralp J. Math. 2018;6:92–97.
MLA Aydın, Cafer ve Seher Sultan Sepet. “Common Fixed Point Theorems For F-Contractions In $G$-Metric Spaces Using Compatible Mappings”. Konuralp Journal of Mathematics, c. 6, sy. 1, 2018, ss. 92-97.
Vancouver Aydın C, Sepet SS. Common Fixed Point Theorems For F-Contractions In $G$-Metric Spaces Using Compatible Mappings. Konuralp J. Math. 2018;6(1):92-7.
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