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Year 2023, Volume: 11 Issue: 2, 184 - 194, 31.10.2023

Seyit Temir Zeynep Bayram

Abstract

Keywords

Suzuki’s generalized nonexpansive mappings α−nonexpansive mappings Opial property uniformly convex Banach space common fixed point convergence theorems.

References

  • [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, Publications de l’Institut Mathematique 110 (124) (2021), 121-129.
  • [16] S. Temir and O. Korkut, Approximating fixed points of generalized a􀀀nonexpansive mapping by the new iteration process, Journal of Mathematical Sciences and Modelling 5(1) (2022), 35-39.
  • [17] S. Temir and O. Korkut, Some Convergence Results Using A New Iteration Process for Generalized Nonexpansive Mappings in Banach Spaces, Asian-European Journal of Mathematics, 16(05) 2350077 (2023).
  • [18] S. Temir, Convergence theorems for a general class of nonexpansive mappings in Banach spaces, International Journal of Nonlinear Analysis and Applications (in press).
  • [19] B.S.Thakur, D.Thakur, M.Postolache, A new iterative scheme for numerical reckoning fixed points of Suzuki’s generalized nonexpansive mappings, Applied Mathematics and Computation, 275 (2016), 147-155.
  • [20] K.Ullah and M.Arshad, Numerical reckoning fixed points for Suzuki’s generalized nonexpansive mappings via new iteration process, Filomat 32(1) (2018), 187-196.
  • [21] H. K. Xu, Inequalities in Banach spaces with applications, Nonlinear Analysis 16 (1991), 1127-1138.
  • [22] I. Yildirim, On fixed point results for mixed nonexpansive mappings, Mathematical Methods for Engineering Applications, ICMASE 2021, Salamanca, Spain, July 1–2, 2022/4/16.
  • [23] I. Yildirim, N. Karaca, Generalized (a;b)􀀀nonexpansive multivalued mappings and their properties, 1st Int. Cong. Natural Sci., (2021), 672–679.

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

Year 2023, Volume: 11 Issue: 2, 184 - 194, 31.10.2023

Seyit Temir Zeynep Bayram

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.

Keywords

Suzuki’s generalized nonexpansive mappings α−nonexpansive mappings Opial property uniformly convex Banach space common fixed point convergence theorems.

References

  • [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, Publications de l’Institut Mathematique 110 (124) (2021), 121-129.
  • [16] S. Temir and O. Korkut, Approximating fixed points of generalized a􀀀nonexpansive mapping by the new iteration process, Journal of Mathematical Sciences and Modelling 5(1) (2022), 35-39.
  • [17] S. Temir and O. Korkut, Some Convergence Results Using A New Iteration Process for Generalized Nonexpansive Mappings in Banach Spaces, Asian-European Journal of Mathematics, 16(05) 2350077 (2023).
  • [18] S. Temir, Convergence theorems for a general class of nonexpansive mappings in Banach spaces, International Journal of Nonlinear Analysis and Applications (in press).
  • [19] B.S.Thakur, D.Thakur, M.Postolache, A new iterative scheme for numerical reckoning fixed points of Suzuki’s generalized nonexpansive mappings, Applied Mathematics and Computation, 275 (2016), 147-155.
  • [20] K.Ullah and M.Arshad, Numerical reckoning fixed points for Suzuki’s generalized nonexpansive mappings via new iteration process, Filomat 32(1) (2018), 187-196.
  • [21] H. K. Xu, Inequalities in Banach spaces with applications, Nonlinear Analysis 16 (1991), 1127-1138.
  • [22] I. Yildirim, On fixed point results for mixed nonexpansive mappings, Mathematical Methods for Engineering Applications, ICMASE 2021, Salamanca, Spain, July 1–2, 2022/4/16.
  • [23] I. Yildirim, N. Karaca, Generalized (a;b)􀀀nonexpansive multivalued mappings and their properties, 1st Int. Cong. Natural Sci., (2021), 672–679.
There are 23 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Seyit Temir

Zeynep Bayram This is me

Publication Date October 31, 2023
Submission Date January 3, 2023
Acceptance Date September 11, 2023
Published in Issue Year 2023 Volume: 11 Issue: 2

Cite

APA Temir, S., & Bayram, Z. (2023). Approximating Common Fixed Point of Three $C$-$\alpha$ Nonexpansive Mappings. Konuralp Journal of Mathematics, 11(2), 184-194.
AMA Temir S, Bayram Z. Approximating Common Fixed Point of Three $C$-$\alpha$ Nonexpansive Mappings. Konuralp J. Math. October 2023;11(2):184-194.
Chicago Temir, Seyit, and Zeynep Bayram. “Approximating Common Fixed Point of Three $C$-$\alpha$ Nonexpansive Mappings”. Konuralp Journal of Mathematics 11, no. 2 (October 2023): 184-94.
EndNote Temir S, Bayram Z (October 1, 2023) Approximating Common Fixed Point of Three $C$-$\alpha$ Nonexpansive Mappings. Konuralp Journal of Mathematics 11 2 184–194.
IEEE S. Temir and Z. Bayram, “Approximating Common Fixed Point of Three $C$-$\alpha$ Nonexpansive Mappings”, Konuralp J. Math., vol. 11, no. 2, pp. 184–194, 2023.
ISNAD Temir, Seyit - Bayram, Zeynep. “Approximating Common Fixed Point of Three $C$-$\alpha$ Nonexpansive Mappings”. Konuralp Journal of Mathematics 11/2 (October 2023), 184-194.
JAMA Temir S, Bayram Z. Approximating Common Fixed Point of Three $C$-$\alpha$ Nonexpansive Mappings. Konuralp J. Math. 2023;11:184–194.
MLA Temir, Seyit and Zeynep Bayram. “Approximating Common Fixed Point of Three $C$-$\alpha$ Nonexpansive Mappings”. Konuralp Journal of Mathematics, vol. 11, no. 2, 2023, pp. 184-9.
Vancouver Temir S, Bayram Z. Approximating Common Fixed Point of Three $C$-$\alpha$ Nonexpansive Mappings. Konuralp J. Math. 2023;11(2):184-9.
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