TY  - JOUR
T1  - Some new results on convergence, stability and data dependence in n-normed spaces
AU  - Doğan, Kadri
AU  - Gürsoy, Faik
AU  - Karakaya, Vatan
AU  - Khan, Safeer Hussain
PY  - 2020
DA  - June
Y2  - 2019
DO  - 10.31801/cfsuasmas.560471
JF  - Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics
JO  - Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.
PB  - Ankara University
WT  - DergiPark
SN  - 1303-5991
SP  - 112
EP  - 122
VL  - 69
IS  - 1
LA  - en
AB  - We introduce a new contractive condition and a new iterativemethod in n0normed space setting. We employ both of these tostudy convergence, stability, and data dependence. The results presentedhere extend and improve some recent results announced in the existingliterature.
KW  - Iterative methods
KW  - convergence
KW  - stability
KW  - data dependence
KW  - quasi--contractive operators
CR  - Misiak, A., n-inner product spaces, Math. Nachr., vol. 140, (1989), 299--319.
CR  - Gähler, S., Linear 2-normietre räume, Math. Nachr., vol. 28, (1965), 1--43.
CR  - Dutta, H., Some iterated convergence and fixed point theorems in real linear n-normed spaces, Miskolc Mathematical Notes, vol. 15, no. 2, (2014), 423-437.
CR  - Gunawan, H. and Mashadi, M., On n-normed spaces,  Int. J. Math. Math. Sci., vol. 2, (2001), 631--639.
CR  - Chugh, R. and Sushma, L., On Generalized n-inner product spaces, Novi Sad J. Math., vol. 41, no. 2, (2011),  73-80.
CR  - Owojori, O. O. and Imoru, C. O., New iteration methods for pseudocontractive and accretive operators in arbitrary banach spaces,  Kragujevac J. Math., vol. 25, (2003),  97--110.
CR  - Thianwan, S., Common fixed points of new iterations for two asymptotically nonexpansive nonself mappings in a banach space, J. Comput. Appl. Math., vol. 224, (2009),  688--695.
CR  - Raphael, P. and Pulickakunnel, S.,  Fixed point theorems in normed linear spaces using a generalized Z-type condition, Kragujevac J. Math., vol. 36, no. 2, (2012), 207--214.
CR  - Khan, S.H., Approximating Fixed Points by a Two-Step Iterative Algorithm,World Academy of Science, Engineering and Technology International Journal of Mathematical, Computational, Physical and Quantum Engineering, vol. 8, no. 6, (2014),  939-941.
CR  - Bosede, A.O. and Rhoades, B.E.,  Stability of Picard and Mann iteration for a general class of functions,  J. Adv. Math. Studies, vol. 3, no. 2, (2010), 23-25.
CR  - Weng, X., Fixed point iteration for local strictly pseudocontractive mapping, Proc. Amer. Math. Soc., vol. 113, (1991), 727--731.
CR  - Soltuz, S. M. and Grosan, T.,  Data dependence for Ishikawa iteration when dealing with contractive like operators, Fixed Point Theory Appl., vol. 2008, (2008), 7 pages.
CR  - Urabe, M., Convergence of numerical iteration in solution of equations,  Journal of Science of the Hiroshima University A, vol.19, (1956),  479--489.
CR  - Ostrowski, A. M.,  The round-off stability of iterations, Z. Angew. Math. Mech., vol. 47, (1967), 77-81.
CR  - Harder, A. M. and Hicks, T. L., Stability results for xed point iteration procedures, Math. Jap., vol. 33, no. 5, (1988), 693-706.
CR  - Bosede, A. O.,Stability of Noor Iteration for a General Class of Functions in Banach Spaces, Acta Univ. Palacki. Olomuc., Fac. Rer. Nat., Mathematica,  vol. 51, no. 2, (2012), 19--25.
CR  - Khan, A. R., Kumar, V. and Hussain, N.  Analytical and numerical treatment of Jungck-type iterative schemes,  Appl. Math. Comput., vol. 231, (2014), 521-535.
CR  - Imoru, C. O. and Olatinwo, M. O., On the stability of Picard and Mann iteration processes,  Carp. J. Math., vol. 19, no. 2, (2003), 155-160.
CR  - Gürsoy, F., Karakaya, V. and Rhoades, B. E., Some convergence and stability results for the Kirk multistep and Kirk-SP fixed point iterative algorithms, Abstr. Appl. Anal., vol. 2014, (2014), 12 pages.
CR  - Osilike, M. O., Stability of the Mann and Ishikawa iteration procedures for-strong pseudocontractions and nonlinearequations of the-strongly accretive type,  J. Math. Anal. Appl., vol. 227, no. 2, (1998), 319-334.
CR  - Verinde, V. B., Summable almost stability of fixed point iteration procedures,  Carpathian J. Math., vol. 19, (2003), 81-88.
CR  - Ishikawa, S.,  Fixed points by a new iteration method,  Proc. Amer. Math. Soc., vol. 44, (1974),  147--150.
CR  - Mann, W. R.,  Mean value in iteration,  Proc. Amer. Math. Soc., vol. 4, (1953), 506--510.
CR  - Agarwal, R. P., O' Regan, D. and Sahu, D. R.,  Iterative construction of fixed points of nearly asymptotically nonexpansive mappings, J. Nonlinear Convex Anal., vol. 8, 2007,  61-79.
CR  - Gürsoy, F., Karakaya, V. and Rhoades, B.E.,  Data dependence results of new multi-step and S-iterative schemes for contractive-like operators, Fixed Point Theory Appl., vol. 76, (2013), 12 pages.
UR  - https://doi.org/10.31801/cfsuasmas.560471
L1  - https://dergipark.org.tr/en/download/article-file/824347
ER  -