Fixed Point Theorems for Some Iteration Processes with Generalized Zamfirescu Mappings in Uniformly Convex Banach Spaces
Keywords:
Generalised Zamfirescu Mappings, Fixed Point, Uniformly Convex Banach Spaces, Iterative Scheme
Abstract
The paper establish fixed point theorems for some iteration processes in uniformly convex Banach spaces with generalized Zamfirescu mappings. Our results improve a multitude of recent results in literature.
References
[1] Zamfirescu T.; Fix Point Theorem in Metric spaces: Arch. Math., Vol. 23, (1972), pp. 292-298.
[2] Berinde V. ; Iterative approximation of fixed points for pseudo-contractive operators: Seminar on Fixed point Theory, Vol.3,(2002), pp.209-216.
[3] Bosede A.O.; On fixed point theorems for Mann and Ishikawa iteration processes in the class of Zamfirescu mappings in Uniformly convex Banach spaces.
[4] Ciric L.B.; Fixed point theory : Construction Mapping Principle, FME Press.Beograd (2003).
[5] Bosede A.O ; Noor Iterations Associated with Zamfirescu mappings in Uniformly convex Banach spaces: Fasciculli Mathematici,Vol. 42, (2009), pp. 29-38.
[6] Mann W.R.; Mean value method in Iteration : Proc. Amer. Math.Soc,Vol. 44, (1953), pp. 506-510.
[7] Ishikawa S.; Fixed point by a new iteration method : Proc. Amer.Math. Soc., Vol. 44(1), (1974), pp. 147-150.
[8] Noor, M. A., New approximation schemes for general variational inequalities J. Math. Anal. Appl., 251 (2000), pp. 217-229
[9] Akeve, H. ; The stability of a Modified Jungck-Mann Hybrid Fixed Point Iteration Procedure, International Journal of Mathematical Sciences and Optimizations: Theory and Applications, Vol. 1, (2016), pp. 95-104.
[10] Berinde V. ; On the convergence of Ishikawa iteration in the class of quasi-contractive operators: Acta Math.Univ.Comenianae.Vol. LXXIII (1), (2004), pp.119-120.
[11] Bosede A.O., Akinbo G.; On the continuous dependence of fixed points for the Picard and Mann iteration processes for a class of
ϕ
ϕ-Contractions:International Journal of Contemporary Mathematical Sciences,(2006).
[12] Bosede A.O.; Some Common fixed point Theorems in Normed Linear Spaces: Acta Univ. Palacki. Olomuc.Fac.rer.nat. Mathematics, Vol.49(1), (2010), pp. 19-26.
[13] Bosede A.O.; Strong Convergence Results for the Jungck-Ishikawa and Jungck Mann Iteration processes : Bulletin of Mathematical Analysis and Application,Vol. 2(3), (2010), pp. 65-73.
[14] Bosede A.O. and Akinbo G.; Some stability theorems associated with A-distance and E-distance in uniform spaces: Acta Universities Apulensis,Vol. 26, (2011), pp. 121-128.
[15] Bosede A.O.; Strong convergence of Noor iteration for a general class of function : Bulletin of Mathematical Analysis and Applications, Volume Issue (2011),pp.140-145.
[16] Bosede A.O. and Rhoades B.E.; Stability of Picard and Mann iterations for a general class of functions : Journal of advanced Mathematical studies,Vol. 3(2), (2010), pp. 1-3.
[17] Goebel K., Kirk W. and T. Shimi ; A fixed point theorem in uniformly convex spaces : Bull. U.M.E, Vol.(4)7, (1976), pp. 67-75.
[18] Imoru C.O. and Olatinwo M.O. ; On the stability of picard and Mann iteration processes : carpathian,J. Math., Vol. (19)(2),(2003), pp. 155-160.
[19] Imoru C.O., Olatinwo M.O., Akinbo G. and Bosede A.O. ; On a version of the Banach's fixed Point theorem, General Mathematics : Vol. 16(1), (2008), pp. 25-32.
[20] Omidire O.J. ; Common Fixed point of some certain generalized contractive conditions in convex Metric space settings, International Journal of Mathematical sciences and Optimization: Theory and Applications, Vol. 10 (3),(2024), pp.1-9.
[21] Osilike M.O.;Stability Results for Fixed Point Iteration Procedure: Applied Mathematics E-Notes,Vol. 6, (2006), pp. 289-293.
[22] Rafiq A.; On the convergence of a three step Iteration Process in the class of quasi-Contractive Operators : Acta Math. Acad. Paedagog Nitreghazienis, Vol.22, (2006), pp. 305-309.
[23] Rhoades B.E.; Fixed Point Iteration Using Infinite Matrices :Trans. Amer.Math. Soc.,Vol. 196, (1974), pp. 161-176.
[24] Rhoades B.E.; Fixed Point Theorems and Stability Results for Fixed point Iteration Methods : J.Math.Anal. Appl., Vol. 56(2), (1976), pp. 741-750.
[25] Weng X.L. ; Fixed point iteration for local strictly pseudo contractive mapping : Proc. Amer.Math. Soc., Vol.103,(1991), pp. 727-731.
[26] Rus I.A., Petrusel A and Petrusel G. ; Fixed Point Iteration Procedures : Indian J.Pure Appl., Vol. 56(2), (1976), pp. 741-750.
[27] Xu H.K. ; Inequalities in Banach spaces with applications : Nonlinear Analysis, Theory and Applications, Vol. 16(20), (1991), pp. 1127-1138.
[28] Xu B. and Noor M.A.; Fixed point iterations for asymptotically nonexpansive mappings in Banach spaces : Journal of Mathematical Analysis and Applications, Vol. 267,(2002), pp.444-453.
[29] Zeider E. ; Nonlinear Functional Analysis and it's application : fixed point theorems, Springer Verlag, New York, Inc., Vol. 43, (1986), pp. 1-909.
[2] Berinde V. ; Iterative approximation of fixed points for pseudo-contractive operators: Seminar on Fixed point Theory, Vol.3,(2002), pp.209-216.
[3] Bosede A.O.; On fixed point theorems for Mann and Ishikawa iteration processes in the class of Zamfirescu mappings in Uniformly convex Banach spaces.
[4] Ciric L.B.; Fixed point theory : Construction Mapping Principle, FME Press.Beograd (2003).
[5] Bosede A.O ; Noor Iterations Associated with Zamfirescu mappings in Uniformly convex Banach spaces: Fasciculli Mathematici,Vol. 42, (2009), pp. 29-38.
[6] Mann W.R.; Mean value method in Iteration : Proc. Amer. Math.Soc,Vol. 44, (1953), pp. 506-510.
[7] Ishikawa S.; Fixed point by a new iteration method : Proc. Amer.Math. Soc., Vol. 44(1), (1974), pp. 147-150.
[8] Noor, M. A., New approximation schemes for general variational inequalities J. Math. Anal. Appl., 251 (2000), pp. 217-229
[9] Akeve, H. ; The stability of a Modified Jungck-Mann Hybrid Fixed Point Iteration Procedure, International Journal of Mathematical Sciences and Optimizations: Theory and Applications, Vol. 1, (2016), pp. 95-104.
[10] Berinde V. ; On the convergence of Ishikawa iteration in the class of quasi-contractive operators: Acta Math.Univ.Comenianae.Vol. LXXIII (1), (2004), pp.119-120.
[11] Bosede A.O., Akinbo G.; On the continuous dependence of fixed points for the Picard and Mann iteration processes for a class of
ϕ
ϕ-Contractions:International Journal of Contemporary Mathematical Sciences,(2006).
[12] Bosede A.O.; Some Common fixed point Theorems in Normed Linear Spaces: Acta Univ. Palacki. Olomuc.Fac.rer.nat. Mathematics, Vol.49(1), (2010), pp. 19-26.
[13] Bosede A.O.; Strong Convergence Results for the Jungck-Ishikawa and Jungck Mann Iteration processes : Bulletin of Mathematical Analysis and Application,Vol. 2(3), (2010), pp. 65-73.
[14] Bosede A.O. and Akinbo G.; Some stability theorems associated with A-distance and E-distance in uniform spaces: Acta Universities Apulensis,Vol. 26, (2011), pp. 121-128.
[15] Bosede A.O.; Strong convergence of Noor iteration for a general class of function : Bulletin of Mathematical Analysis and Applications, Volume Issue (2011),pp.140-145.
[16] Bosede A.O. and Rhoades B.E.; Stability of Picard and Mann iterations for a general class of functions : Journal of advanced Mathematical studies,Vol. 3(2), (2010), pp. 1-3.
[17] Goebel K., Kirk W. and T. Shimi ; A fixed point theorem in uniformly convex spaces : Bull. U.M.E, Vol.(4)7, (1976), pp. 67-75.
[18] Imoru C.O. and Olatinwo M.O. ; On the stability of picard and Mann iteration processes : carpathian,J. Math., Vol. (19)(2),(2003), pp. 155-160.
[19] Imoru C.O., Olatinwo M.O., Akinbo G. and Bosede A.O. ; On a version of the Banach's fixed Point theorem, General Mathematics : Vol. 16(1), (2008), pp. 25-32.
[20] Omidire O.J. ; Common Fixed point of some certain generalized contractive conditions in convex Metric space settings, International Journal of Mathematical sciences and Optimization: Theory and Applications, Vol. 10 (3),(2024), pp.1-9.
[21] Osilike M.O.;Stability Results for Fixed Point Iteration Procedure: Applied Mathematics E-Notes,Vol. 6, (2006), pp. 289-293.
[22] Rafiq A.; On the convergence of a three step Iteration Process in the class of quasi-Contractive Operators : Acta Math. Acad. Paedagog Nitreghazienis, Vol.22, (2006), pp. 305-309.
[23] Rhoades B.E.; Fixed Point Iteration Using Infinite Matrices :Trans. Amer.Math. Soc.,Vol. 196, (1974), pp. 161-176.
[24] Rhoades B.E.; Fixed Point Theorems and Stability Results for Fixed point Iteration Methods : J.Math.Anal. Appl., Vol. 56(2), (1976), pp. 741-750.
[25] Weng X.L. ; Fixed point iteration for local strictly pseudo contractive mapping : Proc. Amer.Math. Soc., Vol.103,(1991), pp. 727-731.
[26] Rus I.A., Petrusel A and Petrusel G. ; Fixed Point Iteration Procedures : Indian J.Pure Appl., Vol. 56(2), (1976), pp. 741-750.
[27] Xu H.K. ; Inequalities in Banach spaces with applications : Nonlinear Analysis, Theory and Applications, Vol. 16(20), (1991), pp. 1127-1138.
[28] Xu B. and Noor M.A.; Fixed point iterations for asymptotically nonexpansive mappings in Banach spaces : Journal of Mathematical Analysis and Applications, Vol. 267,(2002), pp.444-453.
[29] Zeider E. ; Nonlinear Functional Analysis and it's application : fixed point theorems, Springer Verlag, New York, Inc., Vol. 43, (1986), pp. 1-909.
Published
2025-06-10
How to Cite
Bosede, A. O., Raji, S. A., Wusu, S. A., Ayodele, S. O., Adewale, O. K., & Loyinmi, A. C. (2025). Fixed Point Theorems for Some Iteration Processes with Generalized Zamfirescu Mappings in Uniformly Convex Banach Spaces. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 11(2), 103 - 110. Retrieved from https://ijmso.unilag.edu.ng/article/view/2897
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