The convergence of a new iteration process for the solution of nonlinear functional equations in banach space

1968 ◽  
Vol 4 (3) ◽  
pp. 680-685
Author(s):  
D. K. Lika
Keyword(s):  
Banach Space ◽  
Functional Equations ◽  
Iteration Process ◽  
Nonlinear Functional

scholarly journals Approximating Fixed Points of Nonself Contractive Type Mappings in Banach Spaces Endowed with a Graph

2016 ◽  
Vol 24 (2) ◽  
pp. 27-43 ◽  
Author(s):  
Laszlo Balog ◽  
Vasile Berinde ◽  
Mădălina Păcurar
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Points ◽  
Banach Spaces ◽  
Closed Subset ◽  
Functional Equations ◽  
Fixed Point Theorems ◽  
Contraction Principle ◽  
Nonlinear Functional ◽  
Contractive Type

Abstract Let K be a non-empty closed subset of a Banach space X endowed with a graph G. We obtain fixed point theorems for nonself G-contractions of Chatterjea type. Our new results complement and extend recent related results [Berinde, V., Păcurar, M., The contraction principle for nonself mappings on Banach spaces endowed with a graph, J. Nonlinear Convex Anal. 16 (2015), no. 9, 1925-1936; Balog, L., Berinde, V., Fixed point theorems for nonself Kannan type contractions in Banach spaces endowed with a graph, Carpathian J. Math. 32 (2016), no. 3 (in press)] and thus provide more general and flexible tools for studying nonlinear functional equations.

On a Theorem of Beurling and Livingston

1965 ◽  
Vol 17 ◽  
pp. 367-372 ◽  
Author(s):  
Felix E. Browder
Keyword(s):  
Banach Space ◽  
Fourier Series ◽  
Banach Spaces ◽  
General Result ◽  
Functional Equations ◽  
Linear Functional ◽  
Monotone Mappings ◽  
Conjugate Space ◽  
Non Linear ◽  
Duality Mappings

In their paper (1), Beurling and Livingston established a generalization of the Riesz-Fischer theorem for Fourier series in Lp using a theorem on duality mappings of a Banach space B into its conjugate space B*. It is our purpose in the present paper to give another proof of this theorem by deriving it from a more general result concerning monotone mappings related to recent results on non-linear functional equations in Banach spaces obtained by the writer (2, 3, 4, 5) and G. J. Minty (6).

scholarly journals Convergence of the New Iterative Method

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Sachin Bhalekar ◽  
Varsha Daftardar-Gejji
Keyword(s):  
Iterative Method ◽  
Functional Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Efficient Technique ◽  
Nonlinear Functional ◽  
Adomian Decomposition ◽  
New Iterative Method ◽  
Sufficiency Conditions

A new iterative method introduced by Daftardar-Gejji and Jafari (2006) (DJ Method) is an efficient technique to solve nonlinear functional equations. In the present paper, sufficiency conditions for convergence of DJM have been presented. Further equivalence of DJM and Adomian decomposition method is established.

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