Convergence of Noor, and Abbas and Nazir iteration procedures for a class of three nonlinear quasi contractive maps in convex metric spaces

Gedala Satyanarayana; G. V. R. Babu

Araştırma Makalesi

Convergence of Noor, and Abbas and Nazir iteration procedures for a class of three nonlinear quasi contractive maps in convex metric spaces

Yıl 2020, Cilt: 2 Sayı: 1, 14 - 26, 30.04.2020

Gedala Satyanarayana G. V. R. Babu

Öz

We define Noor iteration procedure and, Abbas and Nazir iteration procedure associated

with three self maps in the setting of convex metric spaces . We prove that these

iterations converge strongly to a unique common fixed point of three nonlinear quasicontractive

self maps in convex metric spaces. One of our results (Theorem 2.2) extend

the results of Sastry, Babu and Srinivasa Rao [10].

Anahtar Kelimeler

Convex metric space, quasi-contraction map, Noor iteration, Abbas and Nazir iteration

Kaynakça

[1] M. Abbas and T. Nazir, A new faster iteration process applied to constrained minimization and feasibility problems, Mat. Vesnik., 66(2) (2014), 223-234.
[2] M. Bridson and A. Haefliger, Metric spaces of non-positive curvature, Springer-Verlag, Berlin, Heidelberg, New York, 1999.
[3] L. B. Ciric, A generalization of Banach’s contraction principle, Proc. Amer. Math. Soc., ´ 45(2) (1974), 267-273.
[4] L. B. Ciric, Convergence theorems for a sequence of Ishikawa iterations for nonlinear quasi- ´ contractive mappings, Indian J. Pure Appl. Math., 30(4) (1999), 425-433.
[5] X. P. Ding, Iteration processes for nonlinear mappings in convex metric spaces, J. Math. Anal. Appl., 132(1) (1988), 114-122.
[6] S. Ishikawa, Fixed points by a new iteration method, Proc. Amer. Math. Soc., 44(1) (1974), 147-150.
[7] M. Moosaei, Fixed point theorems in convex metric spaces, Fixed Point Theory and Appl., Vol. 2012(2012), Article 164, 6 pages.
[8] M. A. Noor, New approximation schemes for general variational inequalities. J. Math. Anal. Appl., 251(1) (2000), 217-229.
[9] K. P. R. Sastry, G. V. R. Babu and Ch. Srinivasa Rao, Convergence of an Ishikawa iteration scheme for nonlinear quasi-contractive mappings in convex metric spaces, Tamkang J. Math., 32(2) (2001), 117-126.
[10] K. P. R. Sastry, G. V. R. Babu and Ch. Srinivasa Rao, Convergence of an Ishikawa iteration scheme for a nonlinear quasi-contractive pair of selfmaps in convex metric spaces, Indian J. Pure Appl. Math., 33(2) (2002), 203-214.
[11] W. Takahashi, A convexity in metric space and nonexpansive mappings, I, Kodai Math. Sem. Rep., 22(2) (1970), 142-149.

Yıl 2020, Cilt: 2 Sayı: 1, 14 - 26, 30.04.2020

Gedala Satyanarayana G. V. R. Babu

Öz

Kaynakça

[1] M. Abbas and T. Nazir, A new faster iteration process applied to constrained minimization and feasibility problems, Mat. Vesnik., 66(2) (2014), 223-234.
[2] M. Bridson and A. Haefliger, Metric spaces of non-positive curvature, Springer-Verlag, Berlin, Heidelberg, New York, 1999.
[3] L. B. Ciric, A generalization of Banach’s contraction principle, Proc. Amer. Math. Soc., ´ 45(2) (1974), 267-273.
[4] L. B. Ciric, Convergence theorems for a sequence of Ishikawa iterations for nonlinear quasi- ´ contractive mappings, Indian J. Pure Appl. Math., 30(4) (1999), 425-433.
[5] X. P. Ding, Iteration processes for nonlinear mappings in convex metric spaces, J. Math. Anal. Appl., 132(1) (1988), 114-122.
[6] S. Ishikawa, Fixed points by a new iteration method, Proc. Amer. Math. Soc., 44(1) (1974), 147-150.
[7] M. Moosaei, Fixed point theorems in convex metric spaces, Fixed Point Theory and Appl., Vol. 2012(2012), Article 164, 6 pages.
[8] M. A. Noor, New approximation schemes for general variational inequalities. J. Math. Anal. Appl., 251(1) (2000), 217-229.
[9] K. P. R. Sastry, G. V. R. Babu and Ch. Srinivasa Rao, Convergence of an Ishikawa iteration scheme for nonlinear quasi-contractive mappings in convex metric spaces, Tamkang J. Math., 32(2) (2001), 117-126.
[10] K. P. R. Sastry, G. V. R. Babu and Ch. Srinivasa Rao, Convergence of an Ishikawa iteration scheme for a nonlinear quasi-contractive pair of selfmaps in convex metric spaces, Indian J. Pure Appl. Math., 33(2) (2002), 203-214.
[11] W. Takahashi, A convexity in metric space and nonexpansive mappings, I, Kodai Math. Sem. Rep., 22(2) (1970), 142-149.

Toplam 11 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Konular	Matematik
Bölüm	Articles
Yazarlar	Gedala Satyanarayana G. V. R. Babu
Yayımlanma Tarihi	30 Nisan 2020
Kabul Tarihi	2 Nisan 2020
Yayımlandığı Sayı	Yıl 2020 Cilt: 2 Sayı: 1

Kaynak Göster

APA	Satyanarayana, G., & Babu, G. V. R. (2020). Convergence of Noor, and Abbas and Nazir iteration procedures for a class of three nonlinear quasi contractive maps in convex metric spaces. Maltepe Journal of Mathematics, 2(1), 14-26.
AMA	Satyanarayana G, Babu GVR. Convergence of Noor, and Abbas and Nazir iteration procedures for a class of three nonlinear quasi contractive maps in convex metric spaces. Maltepe Journal of Mathematics. Nisan 2020;2(1):14-26.
Chicago	Satyanarayana, Gedala, ve G. V. R. Babu. “Convergence of Noor, and Abbas and Nazir Iteration Procedures for a Class of Three Nonlinear Quasi Contractive Maps in Convex Metric Spaces”. Maltepe Journal of Mathematics 2, sy. 1 (Nisan 2020): 14-26.
EndNote	Satyanarayana G, Babu GVR (01 Nisan 2020) Convergence of Noor, and Abbas and Nazir iteration procedures for a class of three nonlinear quasi contractive maps in convex metric spaces. Maltepe Journal of Mathematics 2 1 14–26.
IEEE	G. Satyanarayana ve G. V. R. Babu, “Convergence of Noor, and Abbas and Nazir iteration procedures for a class of three nonlinear quasi contractive maps in convex metric spaces”, Maltepe Journal of Mathematics, c. 2, sy. 1, ss. 14–26, 2020.
ISNAD	Satyanarayana, Gedala - Babu, G. V. R. “Convergence of Noor, and Abbas and Nazir Iteration Procedures for a Class of Three Nonlinear Quasi Contractive Maps in Convex Metric Spaces”. Maltepe Journal of Mathematics 2/1 (Nisan 2020), 14-26.
JAMA	Satyanarayana G, Babu GVR. Convergence of Noor, and Abbas and Nazir iteration procedures for a class of three nonlinear quasi contractive maps in convex metric spaces. Maltepe Journal of Mathematics. 2020;2:14–26.
MLA	Satyanarayana, Gedala ve G. V. R. Babu. “Convergence of Noor, and Abbas and Nazir Iteration Procedures for a Class of Three Nonlinear Quasi Contractive Maps in Convex Metric Spaces”. Maltepe Journal of Mathematics, c. 2, sy. 1, 2020, ss. 14-26.
Vancouver	Satyanarayana G, Babu GVR. Convergence of Noor, and Abbas and Nazir iteration procedures for a class of three nonlinear quasi contractive maps in convex metric spaces. Maltepe Journal of Mathematics. 2020;2(1):14-26.