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Some Fixed Point Results for A Multivalued Generalization of Generalized Hybrid Mappings in CAT(κ)-Spaces

Yıl 2018, Cilt: 6 Sayı: 1, 26 - 34, 15.04.2018

Öz

The studies about hybrid mappings are mainly focused on single-valued mappings. Now, we give definition of multivalued generalization of generalized hybrid mappings which is defined in CAT(0) spaces and also studied on CAT($\kappa$) spaces. This new definition s general than multivalued  nonexpansive mappings, multivalued  hybrid mappings and multivalued nonspreading mappings. Under suitable conditions, we prove some existence and stability results. We also study some convergence of multivalued proximal version of Thianwan iteration scheme for non-self multivalued generalized hybrid mappings  in CAT($\kappa $)-spaces

Kaynakça

  • [1] F. Kohsaka and W. Takahashi, Fixed point theorems for a class of nonlinear mappings related to maximal monotone operators in Banach spaces, Arch. Math. (Basel), 91(2008), 166-177.
  • [2] W. Takahashi, Fixed point theorems for new nonlinear mappings in a Hilbert space, J.Nonlinear Convex Anal., 11 (2010), 79-88.
  • [3] K. Aoyama, S. Iemoto, F. Kohsaka and W. Takahashi, Fixed point and ergodic theorems for l-hybrid mappings in Hilbert spaces, J. Nonlinear Convex Anal., 11 (2010), 335-343.
  • [4] K. Aoyama and F. Kohsaka, Fixed point theorem for a-nonexpansive mappings in Banach spaces, Nonlinear Anal., 74 (2011), 4387-4391.
  • [5] M. R. Bridson and A. Haefliger, Metric Spaces of Non-Positive Curvature, Springer-Verlag, BerlinU, Heidelberg, 1999.
  • [6] S. Ohta, Convexities of metric spaces, Geom. Dedic. 125 (2007), 225-250
  • [7] Panyanak, Bancha, Mann and Ishikawa iterative processes for multivalued mappings in Banach spaces, Computers & Mathematics with Applications 54.6 (2007), 872-877.
  • [8] Esp´ınola, Rafa, and Aurora Fern´andez-Le´on, CAT(k)-spaces, weak convergence and fixed point, Journal of Mathematical Analysis and Applications, 353.1 (2009), 410-427.
  • [9] F. Gursoy and V. Karakaya, A Picard-S hybrid type iteration method for solving a differential equation with retarded argument , ArXiv preprint, (2014), arXiv:1403.2546.
  • [10] F. Gursoy, A Picard-S Iterative Method for Approximating Fixed Point of Weak-Contraction Mappings, Filomat, 30 (2016), 2829-2845.
  • [11] S. Dhompongsa, B. Panyanak, On 4-convergence theorems in CAT(0) spaces, Comput. Math. Appl.56 (2008), 2572-2579.
  • [12] E. Hacioğlu and V. Karakaya, Existence and convergence for a new multivalued hybrid mapping in CAT(k) spaces, Carpathian Journal of Mathematics, 33(3) (2017), 319-326.
  • [13] R. A. Rashwan and S. M. Altwqi, On the convergence of SP-iterative scheme for three multivalued nonexpansive mappings in CAT(k) spaces, Palestine Journal of Mathematics, Vol. 4(1) (2015) , 73-83.
Yıl 2018, Cilt: 6 Sayı: 1, 26 - 34, 15.04.2018

Öz

Kaynakça

  • [1] F. Kohsaka and W. Takahashi, Fixed point theorems for a class of nonlinear mappings related to maximal monotone operators in Banach spaces, Arch. Math. (Basel), 91(2008), 166-177.
  • [2] W. Takahashi, Fixed point theorems for new nonlinear mappings in a Hilbert space, J.Nonlinear Convex Anal., 11 (2010), 79-88.
  • [3] K. Aoyama, S. Iemoto, F. Kohsaka and W. Takahashi, Fixed point and ergodic theorems for l-hybrid mappings in Hilbert spaces, J. Nonlinear Convex Anal., 11 (2010), 335-343.
  • [4] K. Aoyama and F. Kohsaka, Fixed point theorem for a-nonexpansive mappings in Banach spaces, Nonlinear Anal., 74 (2011), 4387-4391.
  • [5] M. R. Bridson and A. Haefliger, Metric Spaces of Non-Positive Curvature, Springer-Verlag, BerlinU, Heidelberg, 1999.
  • [6] S. Ohta, Convexities of metric spaces, Geom. Dedic. 125 (2007), 225-250
  • [7] Panyanak, Bancha, Mann and Ishikawa iterative processes for multivalued mappings in Banach spaces, Computers & Mathematics with Applications 54.6 (2007), 872-877.
  • [8] Esp´ınola, Rafa, and Aurora Fern´andez-Le´on, CAT(k)-spaces, weak convergence and fixed point, Journal of Mathematical Analysis and Applications, 353.1 (2009), 410-427.
  • [9] F. Gursoy and V. Karakaya, A Picard-S hybrid type iteration method for solving a differential equation with retarded argument , ArXiv preprint, (2014), arXiv:1403.2546.
  • [10] F. Gursoy, A Picard-S Iterative Method for Approximating Fixed Point of Weak-Contraction Mappings, Filomat, 30 (2016), 2829-2845.
  • [11] S. Dhompongsa, B. Panyanak, On 4-convergence theorems in CAT(0) spaces, Comput. Math. Appl.56 (2008), 2572-2579.
  • [12] E. Hacioğlu and V. Karakaya, Existence and convergence for a new multivalued hybrid mapping in CAT(k) spaces, Carpathian Journal of Mathematics, 33(3) (2017), 319-326.
  • [13] R. A. Rashwan and S. M. Altwqi, On the convergence of SP-iterative scheme for three multivalued nonexpansive mappings in CAT(k) spaces, Palestine Journal of Mathematics, Vol. 4(1) (2015) , 73-83.
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

Emirhan Hacıoğlu

Vatan Karakaya Bu kişi benim

Yayımlanma Tarihi 15 Nisan 2018
Gönderilme Tarihi 19 Ocak 2018
Kabul Tarihi 10 Nisan 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 6 Sayı: 1

Kaynak Göster

APA Hacıoğlu, E., & Karakaya, V. (2018). Some Fixed Point Results for A Multivalued Generalization of Generalized Hybrid Mappings in CAT(κ)-Spaces. Konuralp Journal of Mathematics, 6(1), 26-34.
AMA Hacıoğlu E, Karakaya V. Some Fixed Point Results for A Multivalued Generalization of Generalized Hybrid Mappings in CAT(κ)-Spaces. Konuralp J. Math. Nisan 2018;6(1):26-34.
Chicago Hacıoğlu, Emirhan, ve Vatan Karakaya. “Some Fixed Point Results for A Multivalued Generalization of Generalized Hybrid Mappings in CAT(κ)-Spaces”. Konuralp Journal of Mathematics 6, sy. 1 (Nisan 2018): 26-34.
EndNote Hacıoğlu E, Karakaya V (01 Nisan 2018) Some Fixed Point Results for A Multivalued Generalization of Generalized Hybrid Mappings in CAT(κ)-Spaces. Konuralp Journal of Mathematics 6 1 26–34.
IEEE E. Hacıoğlu ve V. Karakaya, “Some Fixed Point Results for A Multivalued Generalization of Generalized Hybrid Mappings in CAT(κ)-Spaces”, Konuralp J. Math., c. 6, sy. 1, ss. 26–34, 2018.
ISNAD Hacıoğlu, Emirhan - Karakaya, Vatan. “Some Fixed Point Results for A Multivalued Generalization of Generalized Hybrid Mappings in CAT(κ)-Spaces”. Konuralp Journal of Mathematics 6/1 (Nisan 2018), 26-34.
JAMA Hacıoğlu E, Karakaya V. Some Fixed Point Results for A Multivalued Generalization of Generalized Hybrid Mappings in CAT(κ)-Spaces. Konuralp J. Math. 2018;6:26–34.
MLA Hacıoğlu, Emirhan ve Vatan Karakaya. “Some Fixed Point Results for A Multivalued Generalization of Generalized Hybrid Mappings in CAT(κ)-Spaces”. Konuralp Journal of Mathematics, c. 6, sy. 1, 2018, ss. 26-34.
Vancouver Hacıoğlu E, Karakaya V. Some Fixed Point Results for A Multivalued Generalization of Generalized Hybrid Mappings in CAT(κ)-Spaces. Konuralp J. Math. 2018;6(1):26-34.
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