Araştırma Makalesi

Fixed Point Results for a Class of Nonexpansive Type Mappings in Banach Spaces

Cilt: 5 Sayı: 3 30 Eylül 2021
PDF İndir
EN

Fixed Point Results for a Class of Nonexpansive Type Mappings in Banach Spaces

Öz

Abstract. In this paper, we present some new fixed point results for a well-known class of generalized nonexpansive type mappings and associated Krasnosel'ski type mappings in Banach spaces. Further, we consider Mann type iteration for finding a common fixed point of a nonexpansive type semigroup. We also present a couple of nontrivial examples to illustrate facts and show numerical convergence.

Anahtar Kelimeler

Kaynakça

  1. [1] K. Aoyama and F. Kohsaka, Fixed point theorem for α-nonexpansive mappings in Banach spaces, Nonlinear Anal. 74(2011), no. 13, 4387-4391.
  2. [2] F. E. Browder, Fixed-point theorems for noncompact mappings in Hilbert space, Proc. Nat. Acad. Sci. U.S.A. 53(1965), 1272-1276.
  3. [3] F. E. Browder and W. V. Petryshyn, The solution by iteration of nonlinear functional equations in Banach spaces, Bull. Amer. Math. Soc. 72(1966), 571-575.
  4. [4] F. E. Browder, Convergence theorems for sequences of nonlinear operators in Banach spaces, Math. Z. 100(1967), 201-225.
  5. [5] C. Chidume, Geometric properties of Banach spaces and nonlinear iterations, volume 1965 of Lecture Notes in Mathematics, Springer-Verlag London, Ltd., London, (2009).
  6. [6] J. García-Falset, E. Llorens-Fuster, and T. Suzuki, Fixed point theory for a class of generalized nonexpansive mappings, J. Math. Anal. Appl. 375(2011), 185-195.
  7. [7] K. Goebel and M. Japon-Pineda, A new type of nonexpansiveness, In Proceedings of 8-th international conference on ?xed point theory and applications, Chiang Mai, (2007).
  8. [8] K. Goebel and W. A. Kirk, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 35(1972), 171-174.

Ayrıntılar

Birincil Dil

İngilizce

Konular

Matematik

Bölüm

Araştırma Makalesi

Yazarlar

Prashant Patel Bu kişi benim
South Africa

Rahul Shukla Bu kişi benim
South Africa

Yayımlanma Tarihi

30 Eylül 2021

Gönderilme Tarihi

12 Şubat 2021

Kabul Tarihi

24 Mayıs 2021

Yayımlandığı Sayı

Yıl 2021 Cilt: 5 Sayı: 3

Kaynak Göster

APA
Pant, R., Patel, P., & Shukla, R. (2021). Fixed Point Results for a Class of Nonexpansive Type Mappings in Banach Spaces. Advances in the Theory of Nonlinear Analysis and its Application, 5(3), 368-381. https://doi.org/10.31197/atnaa.878951
AMA
1.Pant R, Patel P, Shukla R. Fixed Point Results for a Class of Nonexpansive Type Mappings in Banach Spaces. ATNAA. 2021;5(3):368-381. doi:10.31197/atnaa.878951
Chicago
Pant, Rajendra, Prashant Patel, ve Rahul Shukla. 2021. “Fixed Point Results for a Class of Nonexpansive Type Mappings in Banach Spaces”. Advances in the Theory of Nonlinear Analysis and its Application 5 (3): 368-81. https://doi.org/10.31197/atnaa.878951.
EndNote
Pant R, Patel P, Shukla R (01 Eylül 2021) Fixed Point Results for a Class of Nonexpansive Type Mappings in Banach Spaces. Advances in the Theory of Nonlinear Analysis and its Application 5 3 368–381.
IEEE
[1]R. Pant, P. Patel, ve R. Shukla, “Fixed Point Results for a Class of Nonexpansive Type Mappings in Banach Spaces”, ATNAA, c. 5, sy 3, ss. 368–381, Eyl. 2021, doi: 10.31197/atnaa.878951.
ISNAD
Pant, Rajendra - Patel, Prashant - Shukla, Rahul. “Fixed Point Results for a Class of Nonexpansive Type Mappings in Banach Spaces”. Advances in the Theory of Nonlinear Analysis and its Application 5/3 (01 Eylül 2021): 368-381. https://doi.org/10.31197/atnaa.878951.
JAMA
1.Pant R, Patel P, Shukla R. Fixed Point Results for a Class of Nonexpansive Type Mappings in Banach Spaces. ATNAA. 2021;5:368–381.
MLA
Pant, Rajendra, vd. “Fixed Point Results for a Class of Nonexpansive Type Mappings in Banach Spaces”. Advances in the Theory of Nonlinear Analysis and its Application, c. 5, sy 3, Eylül 2021, ss. 368-81, doi:10.31197/atnaa.878951.
Vancouver
1.Rajendra Pant, Prashant Patel, Rahul Shukla. Fixed Point Results for a Class of Nonexpansive Type Mappings in Banach Spaces. ATNAA. 01 Eylül 2021;5(3):368-81. doi:10.31197/atnaa.878951

Cited By