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Some coincidence best proximity point results in S-metric spaces

Yıl 2021, Cilt: 3 Sayı: 2, 75 - 87, 30.12.2021

Aynur Şahin Kadir Şamdanlı

https://doi.org/10.47086/pims.1035385
Cited By: 1

Öz

In this paper, we introduce the notions of S-proximal Berinde g-cyclic contraction of two nonself mappings and S-proximal Berinde g-contractions of the first kind and second kind in an S-metric space and prove some coincidence best proximity point theorems for these types of nonself mappings in this space. Also, we give two examples to analyze and support our main results. The results presented here generalize some results in the existing literature.

Anahtar Kelimeler

S-metric space Best proximity point Coincidence best proximity point S-proximal Berinde g-cyclic contraction

Kaynakça

  • Banach, S: Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fund. Math., 3, 133--181 (1922)
  • Çevik, C, Altun, I, Şahin, H, Özeken, ÇC, Some fixed point theorems for contractive mapping in ordered vector metric spaces. J. Nonlinear Sci. Appl. 10(4), 1424-1432 (2017)
  • Şahin, A: Some new results of M-iteration process in hyperbolic spaces. Carpathian J. Math. 35(2), 221-232 (2019)
  • Kalkan, Z, Şahin, A: Some new results in partial cone b-metric space. Commun. Adv. Math. Sci. 3(2), 67-73 (2020)
  • Özeken, ÇC, Çevik, C: Unbounded vectorial Cauchy completion of vector metric spaces. Gazi Uni. J. Sci. 33(3), 761-765 (2020)
  • Özeken, ÇC, Çevik, C: Ordered vectorial quasi and almost contractions on ordered vector metric spaces. Mathematics, 9(19), 2443 (2021)
  • Şahin, A, Başarır, M: Some Convergence Results of the K^{∗}-Iteration Process in CAT(0) Spaces. In: Cho Y.J., Jleli M., Mursaleen M., Samet B., Vetro C. (eds) Advances in Metric Fixed Point Theory and Applications, Springer, Singapore, 2021.
  • Abbas, M, Hussain, A, Kumam, P: A coincidence best proximity point problem in G-metric spaces. Abst. Appl. Anal. 2015, Article ID 243753, 12 pages (2015)
  • Saleem, N, Vujakovic, J, Baloch, WU, Radenovic, S: Coincidence point results for multivalued Suzuki type mappings using θ-contraction in b-metric spaces. Mathematics, 7, 1017 (2019)
  • Altun, I, Aslantaş, M, Sahin, H: KW-type nonlinear contractions and their best proximity points. Num. Func. Anal. Opt. 42(8), 935-954 (2021)
  • Aslantaş, M: Some best proximity point results via a new family of F-contraction and an application to homotopy theory. J. Fixed Point Theory Appl. 23(54), 1-20 (2021)
  • Aslantaş, M: Best proximity point theorems for proximal b-cyclic contractions on b-metric spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 70(1), 483-496 (2021)
  • Basha, SS: Best proximity point theorems generalizing the contraction principle. Nonlinear Anal. 74, 5844-5850 (2011)
  • Klanarong, C, Chaiya, I: Coincidence best proximity point theorems for proximal Berinde g-cyclic contractions in metric spaces. J. Inequal. Appl. 2021, Article ID 21, 16 pages (2021)
  • Sedghi, S, Shobe, N, Aliouche, A: A generalization of fixed point theorems in S-metric spaces. Mat. Vesnik 64(3), 258-266 (2012)
  • Nantadilok, J: Best proximity point results in S-metric spaces. Int. J. Math. Anal. 10(27), 1333-1346 (2016)
  • Ansari, AH, Nantadilok, J: Best proximity points for proximal contractive type mappings with C-class functions in S-metric spaces. Fiaed Point Theory Appl. 2017, Article ID:12, 17 pages (2017)
  • Khanpanuk, T: Coincidence best proximity points for generalized MT-proximal cyclic contractive mappings in S-metric space, Thai J. Math. 18(4), 1787-1799 (2020)
  • Sedghi, S, Dung, NV: Fixed point theorems on S-metric spaces. Mat. Vesnik 66(1), 113-124 (2014)
  • Özgür, NY, Taş, N: Some fixed point theorems on S-metric spaces. Mat Vesnik, 69(1), 39--52 (2017)
  • Özgür, NY, Taş, N: The Picard theorem on S-metric spaces. Acta Math. Sci., 38B(4), 1245-1258 (2018)
  • Hieu, NT, Thanh Ly, NT, Dung, NV: A generalization of Ćirić quasi-contractions for maps on S-metric spaces. Thai J. Math. 13(2), 369-380 (2015)
  • Özgür, NY, Taş, N: Some new contractive mappings on S-metric spaces and their relationships with the mapping (S25), Math. Sci. 11, 7-16 (2017)
  • Gupta, A: Cyclic contraction on S-metric space, Int. J. Anal. Appl. 3(2), 119-130 (2013)

Yıl 2021, Cilt: 3 Sayı: 2, 75 - 87, 30.12.2021

Aynur Şahin Kadir Şamdanlı

https://doi.org/10.47086/pims.1035385
Cited By: 1

Öz

Kaynakça

  • Banach, S: Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fund. Math., 3, 133--181 (1922)
  • Çevik, C, Altun, I, Şahin, H, Özeken, ÇC, Some fixed point theorems for contractive mapping in ordered vector metric spaces. J. Nonlinear Sci. Appl. 10(4), 1424-1432 (2017)
  • Şahin, A: Some new results of M-iteration process in hyperbolic spaces. Carpathian J. Math. 35(2), 221-232 (2019)
  • Kalkan, Z, Şahin, A: Some new results in partial cone b-metric space. Commun. Adv. Math. Sci. 3(2), 67-73 (2020)
  • Özeken, ÇC, Çevik, C: Unbounded vectorial Cauchy completion of vector metric spaces. Gazi Uni. J. Sci. 33(3), 761-765 (2020)
  • Özeken, ÇC, Çevik, C: Ordered vectorial quasi and almost contractions on ordered vector metric spaces. Mathematics, 9(19), 2443 (2021)
  • Şahin, A, Başarır, M: Some Convergence Results of the K^{∗}-Iteration Process in CAT(0) Spaces. In: Cho Y.J., Jleli M., Mursaleen M., Samet B., Vetro C. (eds) Advances in Metric Fixed Point Theory and Applications, Springer, Singapore, 2021.
  • Abbas, M, Hussain, A, Kumam, P: A coincidence best proximity point problem in G-metric spaces. Abst. Appl. Anal. 2015, Article ID 243753, 12 pages (2015)
  • Saleem, N, Vujakovic, J, Baloch, WU, Radenovic, S: Coincidence point results for multivalued Suzuki type mappings using θ-contraction in b-metric spaces. Mathematics, 7, 1017 (2019)
  • Altun, I, Aslantaş, M, Sahin, H: KW-type nonlinear contractions and their best proximity points. Num. Func. Anal. Opt. 42(8), 935-954 (2021)
  • Aslantaş, M: Some best proximity point results via a new family of F-contraction and an application to homotopy theory. J. Fixed Point Theory Appl. 23(54), 1-20 (2021)
  • Aslantaş, M: Best proximity point theorems for proximal b-cyclic contractions on b-metric spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 70(1), 483-496 (2021)
  • Basha, SS: Best proximity point theorems generalizing the contraction principle. Nonlinear Anal. 74, 5844-5850 (2011)
  • Klanarong, C, Chaiya, I: Coincidence best proximity point theorems for proximal Berinde g-cyclic contractions in metric spaces. J. Inequal. Appl. 2021, Article ID 21, 16 pages (2021)
  • Sedghi, S, Shobe, N, Aliouche, A: A generalization of fixed point theorems in S-metric spaces. Mat. Vesnik 64(3), 258-266 (2012)
  • Nantadilok, J: Best proximity point results in S-metric spaces. Int. J. Math. Anal. 10(27), 1333-1346 (2016)
  • Ansari, AH, Nantadilok, J: Best proximity points for proximal contractive type mappings with C-class functions in S-metric spaces. Fiaed Point Theory Appl. 2017, Article ID:12, 17 pages (2017)
  • Khanpanuk, T: Coincidence best proximity points for generalized MT-proximal cyclic contractive mappings in S-metric space, Thai J. Math. 18(4), 1787-1799 (2020)
  • Sedghi, S, Dung, NV: Fixed point theorems on S-metric spaces. Mat. Vesnik 66(1), 113-124 (2014)
  • Özgür, NY, Taş, N: Some fixed point theorems on S-metric spaces. Mat Vesnik, 69(1), 39--52 (2017)
  • Özgür, NY, Taş, N: The Picard theorem on S-metric spaces. Acta Math. Sci., 38B(4), 1245-1258 (2018)
  • Hieu, NT, Thanh Ly, NT, Dung, NV: A generalization of Ćirić quasi-contractions for maps on S-metric spaces. Thai J. Math. 13(2), 369-380 (2015)
  • Özgür, NY, Taş, N: Some new contractive mappings on S-metric spaces and their relationships with the mapping (S25), Math. Sci. 11, 7-16 (2017)
  • Gupta, A: Cyclic contraction on S-metric space, Int. J. Anal. Appl. 3(2), 119-130 (2013)
Toplam 24 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Yazılım Mühendisliği (Diğer)
Bölüm Articles
Yazarlar

Aynur Şahin 0000-0001-6114-9966

Kadir Şamdanlı Bu kişi benim 0000-0001-5941-8274

Erken Görünüm Tarihi 27 Eylül 2021
Yayımlanma Tarihi 30 Aralık 2021
Kabul Tarihi 4 Ocak 2022
Yayımlandığı Sayı Yıl 2021 Cilt: 3 Sayı: 2

Kaynak Göster

Cited By

Fixed point results for nonlinear contractions of Perov type in abstract metric spaces with applications
AIMS Mathematics
https://doi.org/10.3934/math.2022817
 Kapak Resmi İndir
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