A CONVERGENCE THEOREM IN GENERALIZED CONVEX

Birol Gündüz

Year 2018, Volume: 67 Issue: 2, 147 - 155, 01.08.2018

Birol Gündüz

Abstract

References

Takahashi, W., A convexity in metric space and nonexpansive mappings, Kodai. Math. Sem. Rep. 22 (1970), 142-149.
Huang, L. G. and Zhang, X., Cone metric spaces and …xed point theorems of contractive mappings, J. Math. Anal. Appl. 322 (2007), 1468-1476.
Vandergraft, J., Newton method for convex operators in partially ordered spaces, SIAM J. Numer. Anal. 4 (1967), 406-432.
Lee, B. S., Approximating common …xed points of two sequences of uniformly quasi- Lipschitzian mappings in convex cone metric spaces, Univ. J. Appl. Math. (2013), 1(3), 166-171.
Lee, B. S., Strong convergence in noor-type iterative schemes in convex cone metric spaces, J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math. (2015), 22(2) , 185-197.
Gunduz, B., Fixed points of a …nite family of I-asymptotically quasi-nonexpansive mappings in a convex metric space, Filomat (2017), 31(7), 2175-2182.
Gunduz, B., Convergence of a new multistep iteration in convex cone metric spaces, Commun. Korean Math. Soc. (2017), 32 (1), 39-46.
Gunduz B. and Akbulut, S., Strong convergence of an explicit iteration process for a …- nite family of asymptotically quasi-nonexpansive mappings in convex metric spaces, Miskolc Mathematical Notes (2013), 14 (3), 915-925.
Temir, S., On the convergence theorems of implicit iteration process for a …nite family of I-asymptotically nonexpansive mappings, J. Comput. Appl. Math. 225 (2009), 398-405.
Qihou, L., Iterative sequence for asymptotically quasi-nonexpansive mappings with errors
member, J. Math. Anal. Appl. 259 (2001), 18-24.
Current address : Birol GUNDUZ: Department of Mathematics, Faculty of Science and Art,
Erzincan University, Erzincan, 24000, Turkey. E-mail address : birolgndz@gmail.com ORCID: http://orcid.org/0000-0002-2322-8329

A CONVERGENCE THEOREM IN GENERALIZED CONVEX

Year 2018, Volume: 67 Issue: 2, 147 - 155, 01.08.2018

Birol Gündüz

Abstract

The aim of this work is to establish convergence theorem of a new
iteration process for a finite family of I-asymptotically quasi-nonexpansive
mappings and a finite family of asymptotically quasi-nonexpansive mappings
in generalized convex cone metric spaces. Our result is valid in the whole space,
whereas the results given in [4, 5] are valid in a nonempty convex subset of a
convex cone metric space. Our convergence results generalize and refine not
only result of Gunduz [6] but also results of Lee [4, 5] and Temir [9].

References

Takahashi, W., A convexity in metric space and nonexpansive mappings, Kodai. Math. Sem. Rep. 22 (1970), 142-149.
Huang, L. G. and Zhang, X., Cone metric spaces and …xed point theorems of contractive mappings, J. Math. Anal. Appl. 322 (2007), 1468-1476.
Vandergraft, J., Newton method for convex operators in partially ordered spaces, SIAM J. Numer. Anal. 4 (1967), 406-432.
Lee, B. S., Approximating common …xed points of two sequences of uniformly quasi- Lipschitzian mappings in convex cone metric spaces, Univ. J. Appl. Math. (2013), 1(3), 166-171.
Lee, B. S., Strong convergence in noor-type iterative schemes in convex cone metric spaces, J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math. (2015), 22(2) , 185-197.
Gunduz, B., Fixed points of a …nite family of I-asymptotically quasi-nonexpansive mappings in a convex metric space, Filomat (2017), 31(7), 2175-2182.
Gunduz, B., Convergence of a new multistep iteration in convex cone metric spaces, Commun. Korean Math. Soc. (2017), 32 (1), 39-46.
Gunduz B. and Akbulut, S., Strong convergence of an explicit iteration process for a …- nite family of asymptotically quasi-nonexpansive mappings in convex metric spaces, Miskolc Mathematical Notes (2013), 14 (3), 915-925.
Temir, S., On the convergence theorems of implicit iteration process for a …nite family of I-asymptotically nonexpansive mappings, J. Comput. Appl. Math. 225 (2009), 398-405.
Qihou, L., Iterative sequence for asymptotically quasi-nonexpansive mappings with errors
member, J. Math. Anal. Appl. 259 (2001), 18-24.
Current address : Birol GUNDUZ: Department of Mathematics, Faculty of Science and Art,
Erzincan University, Erzincan, 24000, Turkey. E-mail address : birolgndz@gmail.com ORCID: http://orcid.org/0000-0002-2322-8329

There are 13 citations in total.

Details

Other ID	JA85ZK36MD
Journal Section	Research Article
Authors	Birol Gündüz This is me
Publication Date	August 1, 2018
Submission Date	August 1, 2018
Published in Issue	Year 2018 Volume: 67 Issue: 2

Cite

APA	Gündüz, B. (2018). A CONVERGENCE THEOREM IN GENERALIZED CONVEX. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 67(2), 147-155.
AMA	Gündüz B. A CONVERGENCE THEOREM IN GENERALIZED CONVEX. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2018;67(2):147-155.
Chicago	Gündüz, Birol. “A CONVERGENCE THEOREM IN GENERALIZED CONVEX”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 67, no. 2 (August 2018): 147-55.
EndNote	Gündüz B (August 1, 2018) A CONVERGENCE THEOREM IN GENERALIZED CONVEX. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 67 2 147–155.
IEEE	B. Gündüz, “A CONVERGENCE THEOREM IN GENERALIZED CONVEX”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 67, no. 2, pp. 147–155, 2018.
ISNAD	Gündüz, Birol. “A CONVERGENCE THEOREM IN GENERALIZED CONVEX”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 67/2 (August 2018), 147-155.
JAMA	Gündüz B. A CONVERGENCE THEOREM IN GENERALIZED CONVEX. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2018;67:147–155.
MLA	Gündüz, Birol. “A CONVERGENCE THEOREM IN GENERALIZED CONVEX”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 67, no. 2, 2018, pp. 147-55.
Vancouver	Gündüz B. A CONVERGENCE THEOREM IN GENERALIZED CONVEX. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2018;67(2):147-55.