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

Research Article

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

Year 2020, Volume: 2 Issue: 1, 14 - 26, 30.04.2020

Gedala Satyanarayana G. V. R. Babu

Abstract

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].

Keywords

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

References

[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.

Year 2020, Volume: 2 Issue: 1, 14 - 26, 30.04.2020

Gedala Satyanarayana G. V. R. Babu

Abstract

References

[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.

There are 11 citations in total.

Details

Primary Language	English
Subjects	Mathematical Sciences
Journal Section	Articles
Authors	Gedala Satyanarayana G. V. R. Babu
Publication Date	April 30, 2020
Acceptance Date	April 2, 2020
Published in Issue	Year 2020 Volume: 2 Issue: 1

Cite

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. April 2020;2(1):14-26.
Chicago	Satyanarayana, Gedala, and 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, no. 1 (April 2020): 14-26.
EndNote	Satyanarayana G, Babu GVR (April 1, 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 and 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, vol. 2, no. 1, pp. 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 (April 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 and 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, vol. 2, no. 1, 2020, pp. 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.