Stability data dependency and errors estimation for a general iteration method

Abstract In this paper, we present a result of stability, data Dependency and errors estimation for D Iteration Method. We also prove that errors in D iterative process is controllable. Especially stability, data dependence, controllability, error accumulation of such iterative methods are being studied.

[1]  E. Karapınar,et al.  Large Contractions on Quasi-Metric Spaces with an Application to Nonlinear Fractional Differential Equations , 2019, Mathematics.

[2]  T. Grosan,et al.  Data Dependence for Ishikawa Iteration When Dealing with Contractive-Like Operators , 2008 .

[3]  K. Ullah,et al.  New three-step iteration process and fixed point approximation in Banach spaces , 2018 .

[4]  Mihai Postolache,et al.  A new iterative scheme for numerical reckoning fixed points of Suzuki's generalized nonexpansive mappings , 2016, Appl. Math. Comput..

[5]  W. R. Mann,et al.  Mean value methods in iteration , 1953 .

[6]  Abdon Atangana.  Convergence and stability analysis of a novel iteration method for fractional biological population equation , 2014, Neural Computing and Applications.

[7]  Erdal Karapinar,et al.  Solutions of the Nonlinear Integral Equation and Fractional Differential Equation Using the Technique of a Fixed Point with a Numerical Experiment in Extended b-Metric Space , 2019, Symmetry.

[8]  Hassen Aydi,et al.  On Interpolative Hardy-Rogers Type Contractions , 2018, Symmetry.

[9]  E. Karapınar,et al.  ω-Interpolative Ćirić-Reich-Rus-Type Contractions , 2019, Mathematics.

[10]  On estimation and control of errors of the Mann iteration process , 2003 .

[11]  Safeer Hussain Khan.  A Picard-Mann hybrid iterative process , 2013 .

[12]  Hassen Aydi,et al.  Interpolative Ćirić-Reich-Rus Type Contractions via the Branciari Distance , 2019, Mathematics.

[13]  K. Ullah,et al.  Numerical reckoning fixed points for Suzuki’s generalized nonexpansive mappings via new iteration process , 2018 .

[14]  Hassen Aydi,et al.  On generalized α-ψ-Geraghty contractions on b-metric spaces , 2018 .

[15]  Abdon Atangana,et al.  On the stability and convergence of the time-fractional variable order telegraph equation , 2015, J. Comput. Phys..

[16]  Alberta Marie Harder,et al.  Fixed point theory and stability results for fixed point iteration procedures , 1987 .

[17]  Shin Min Kang,et al.  Accumulation and control of random errors in the Ishikawa iterative process in arbitrary Banach space , 2011, Comput. Math. Appl..

[18]  A. Atangana,et al.  Stability and convergence of the space fractional variable-order Schrödinger equation , 2013 .

[19]  Alqahtani,et al.  A Solution for Volterra Fractional Integral Equations by Hybrid Contractions , 2019, Mathematics.

[20]  E. Karapınar,et al.  Applying new fixed point theorems on fractional and ordinary differential equations , 2019, Advances in Difference Equations.

[21]  R. Agarwal,et al.  Interpolative Reich–Rus–Ćirić Type Contractions on Partial Metric Spaces , 2018, Mathematics.

[22]  V. Berinde.  Iterative Approximation of Fixed Points , 2007 .