KaydedilenlerDerginizi ekleyin

Dergiler / Konuralp Journal of Mathematics / 2023 / Cilt: 11 Sayı: 2

Approximating Common Fixed Point of Three $C$-$\alpha$ Nonexpansive Mappings

Seyit TEMİR
Zeynep BAYRAM
Sayfa
184–194
Yayın Tarihi
2023-10-31
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

We also numerically illustrate the common fixed point approximations of the presented iteration for the three $C$-$\alpha$ nonexpansive mappings.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, we consider a new class of nonlinear mappings presented in \cite{Shukla} that generalizes two well-known classes of nonexpansive type mappings and extends some other classes of mappings.
📊
Temel Bulgular & Veri:We introduce approximating common fixed point of three C-$\alpha$ nonexpansive mappings through weak and strong convergence of an iterative sequence in a uniformly convex Banach space.
💡
Sonuç & Katkı:We also numerically illustrate the common fixed point approximations of the presented iteration for the three $C$-$\alpha$ nonexpansive mappings.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Suzuki’s generalized nonexpansive mappings · α−nonexpansive mappings · Opial property

Abstract

In this paper, we consider a new class of nonlinear mappings presented in \cite{Shukla} that generalizes two well-known classes of nonexpansive type mappings and extends some other classes of mappings. We introduce approximating common fixed point of three C-$\alpha$ nonexpansive mappings through weak and strong convergence of an iterative sequence in a uniformly convex Banach space. We also numerically illustrate the common fixed point approximations of the presented iteration for the three $C$-$\alpha$ nonexpansive mappings.

🔖

Bu Makaleye Atıf Yap

TEMİR, S., BAYRAM, Z. (2023). Approximating Common Fixed Point of Three $C$-$\alpha$ Nonexpansive Mappings. Konuralp Journal of Mathematics, Cilt: 11 Sayı: 2, 184–194. https://ajindex.com/articles/1015617

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (15)

  1. J.Ali, F. Ali, F. P.Kumar, Approximation of Fixed Points for Suzuki’s Generalized Non-Expansive Mappings, Mathematics 7(6), 522 (2019), 1-11
  2. D. Ariza-Ruiz, C. Hernandez Linares, E. Llorens-Fuster and E. Moreno-Galvez, On a􀀀nonexpansive mappings in Banach spaces, Carpathian J. Math. 32 (2016), 13-28
  3. K. Aoyama and F. Kohsaka, Fixed point theorem for a􀀀nonexpansive mappings in Banach spaces, Nonlinear Analy. 74 (13) (2011), 4378-4391
  4. A. Ekinci and S. Temir, Convergence theorems for Suzuki generalized nonexpansive mapping in Banach spaces, Tamkang Journal of Mathematics 54 (1) (2023), 57-67
  5. J. Garcia-Falset, E. Llorens-Fuster, T. Suzuki, Fixed Point Theory for A Class of Generalized Nonexpansive Mappings, Journal of Mathematical Analysis and Applications 375(1), (2011), 185-195
  6. G. Maniu, On a three-step iteration process for Suzuki mappings with qualitative study, Numerical Functional Analysis and Optimization, 41:8 (2020), 929-949
  7. E. Naraghirad, N.-C. Wong and J.-C. Yao, Approximating fixed points of a􀀀nonexpansive mappings in uniformly convex Banach spaces and CAT(0) spaces, Fixed Point Theory and Applications 2013/1/57, (2013), 20 pages
  8. M.A. Noor, New approximation schemes for general variational inequalities, Journal of Mathematical Analysis and Applications, 251 (2000), 217-229
  9. Z. Opial, Weak convergence of successive approximations for nonexpansive mappings, Bull. Ame. Math.Soc. 73 (1967), 591-597
  10. R. Pandey, R. Pant, W. Rakocevic, R. Shukla, Approximating Fixed Points of A General Class of Nonexpansive Mappings in Banach Spaces with Applications, Results in Mathematics, 74(7) (2019), 24 pages
  11. R. Pant and R. Shukla, Approximating fixed points of generalized a-nonexpansive mappings in Banach spaces, Numer. Funct. Anal. Optim. 38(2) (2017), 248-266
  12. R. Pant and R. Shukla, Fixed point theorems for a new class of nonexpansive mappings, Appl. Gen. Topol. 23(2) (2022), 377-390
  13. H. Piri, B. Daraby, S. Rahrovi, M. Ghasemi, Approximating fixed points of generalized ?-nonexpansive mappings in Banach spaces by new faster iteration process, Numerical Algorithms 81 (2019),1129–1148, DOI:10.1007/s11075-018-0588-x
  14. T. Suzuki, Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, Journal of Mathematical Analysis and Applications, 340(2) (2008), 1088-1095
  15. S. Temir, Weak and strong convergence theorems for three Suzuki’s generalized nonexpansive mappings, Public