pareto optimal strategy for stochastic weakly coupled large scale systems with state dependent system noise this note is concerned with the decentralized infinite horizon stochastic pareto optimal static output feedback strategy for a class of weakly coupled systems with state dependent noise first pareto optimal control problems are formulated using a static output feedback strategy the necessary conditions are given by the cross coupled stochastic algebraic riccati type equations csares for proving the existence of the static output feedback strategy that minimizes the quadratic cost function after determining the asymptotic structure of the solutions of the csares a new sequential numerical algorithm and newton s method for solving the csares are described the resulting numerical solution is used to develop the pareto optimal strategy finally the efficiency of the proposed algorithm is demonstrated by solving a numerical example for a practical megawatt frequency control problem

a newton kantorovich convergence theorem for the inverse free jarratt method in banach space abstract under the weaken conditions we establish the newton kantorovich convergence theorem of inverse free jarratt method in banach space which is used to solve the nonlinear operator equation finally some examples are provided to show the application of our theorem

convergence for a class of improved sixth order chebyshev halley type methods in this paper we consider the semilocal convergence on a class of improved chebyshev halley type methods for solving f x 0 where f x y is a nonlinear operator x and y are two banach spaces is a non empty open convex subset in x to solve the problems that f x is unbounded in and it can not satisfy the whole lipschitz or h o lder continuity f x n is replaced by f x 0 n for all x where n n 0 x0 is an initial point moreover f x is assumed to be local h o lder continuous so the convergence conditions are relaxed we prove an existence uniqueness theorem for the solution which shows that the r order of these methods is at least 5 q where q 0 1 especially when f x is local lipschitz continuous the r order will become six

on the number of homomorphisms from a finite group to a general linear group abstract we study the number of homomorphisms from a finite group to a general linear group over a finite field in particular we give a generating function of such numbers then the rogers ramanujan identities are applicable

local convergence for multi point parametric chebyshev halley type methods of high convergence order we present a local convergence analysis for general multi point chebyshev halley type methods mmchtm of high convergence order in order to approximate a solution of an equation in a banach space setting mmchtm includes earlier methods given by others as special cases the convergence ball for a class of mmchtm methods is obtained under weaker hypotheses than before numerical examples are also presented in this study

on the error estimates of several newton like methods1partial supported by the national natural science foundation of china and by natural science foundation of zhejiang province 1 in this paper convergence theorems and error estimates for several newton like iteration methods under new kantorovitch ostrowski type conditions using the information of higher derivatives at initial point s are established we get not only the convergence speed estimates of iterative sequence x n but also the estimates of f x n 1 f x n

a method for finding sharp error bounds for newton s method under the kantorovic assumptions this paper gives a method for finding sharpa posteriori error bounds for newton s method under the assumptions of kantorovich s theorem on the basis of this method new error bounds are derived and comparison is made among the known bounds of dennis 2 doring 4 gragg tapia 5 kantorovich 6 7 kornstaedt 9 lancaster 10 miel 11 13 moret 14 ostrowski 17 18 potra 19 and potra ptak 20

a unified derivation of several error bounds for newton s process abstract this paper gives a unified derivation of the upper and lower bounds of the errors in newton s process obtained by dennis 4 tapia 27 gragg tapia 6 and recently by potra ptak 20 and miel 15 with the use of different techniques our argument is based upon the kantorovich theorem and the kantorovich recurrence relations from the proof it is concluded that the recent upper and lower bounds of miel are finer than those of potra ptak but do not improve the basic error bounds which are directly obtained from the kantorovich theorem further it is shown that the error bounds obtained with the use of the recurrence relations are the same as those obtained by the majorant principle finally results on the newton method in partially ordered space are surveyed a method is also described for estimating the componentwise errors for computed solutions

toward a unified theory for third r order iterative methods for operators with unbounded second derivative in this paper we provide a semilocal convergence analysis for a family of newton like methods which contains the best known third order iterative methods for solving a nonlinear equation f x 0 in banach spaces it is assumed that the operator f is twice frechet differentiable and f satisfies a lipschitz type condition but it is unbounded by using majorant sequences we provide sufficient convergence conditions to obtain cubic semilocal convergence results on existence and uniqueness of solutions and error estimates are also given finally a numerical example is provided

an application of the kantorovich theoremto nonlinear finite element analysis finite element solutions of strongly nonlinear elliptic boundary value problems are considered in this paper using the kantorovich theorem we show that if the frechet derivative of the nonlinear operator defined by the boundary value problem is an isomorphism at an exact solution then there exists a locally unique finite element solution near the exact solution moreover several a priori error estimates are obtained

numerical computation of sign indefinite linear quadratic differential games for weakly coupled large scale systems in this paper n player linear quadratic differential games that are sign indefinite for infinite horizon weakly coupled large scale systems are discussed after establishing the asymptotic structure and local uniqueness of the solution for cross coupled sign indefinite algebraic riccati equations csare a new algorithm for solving csare is provided it is shown that the proposed algorithm attains linear convergence moreover in order to reduce the computational workspace the recursive algorithm is combined finally a high order approximation strategy based on the proposed iterative solutions is described as a result it was recently proved that the numerical strategy achieves a high order approximation of the equilibrium value as another important feature when the small parameters are unknown a parameter independent strategy is developed

on a family of halley like methods to find simple roots of nonlinear equations there are many methods for solving a nonlinear algebraic equation here we introduce a family of halley like methods and show that euler chebyshev and bsc are just members of the family we discuss the conjugacy maps and the effect of the extraneous roots on the basins of attraction

a modified chebyshev s iterative method with at least sixth order of convergence this paper is devoted to the construction and analysis of a high order variant of the classical chebyshev method the method has order of convergence at least six for simple roots the extension to system of equations and its semilocal convergence for nonlinear equations are presented finally an application to well known algebraic riccati equation is considered

hom a g abstract in this paper we prove that for any finite group g and any finite abelian group a the number of homomorphism from a to g is divisible by the greatest common divisor of a and g this result is a generalization of an old theorem of frobenius on the number of solutions of the equation x n 1 on a finite group

recurrence relations for semilocal convergence of a newton like method in banach spaces abstract the aim of this paper is to establish the semilocal convergence of a multipoint third order newton like method for solving f x 0 in banach spaces by using recurrence relations the convergence of this method is studied under the assumption that the second frechet derivative of f satisfies holder continuity condition this continuity condition is milder than the usual lipschitz continuity condition a new family of recurrence relations are defined based on the two new constants which depend on the operator f these recurrence relations give a priori error bounds for the method two numerical examples are worked out to demonstrate the applicability of the method in cases where the lipschitz continuity condition over second derivative of f fails but holder continuity condition holds

a note on halley s method we introduce the degree of logarithmic convexity which provides a measure of the convexity of a function at each point making use of this concept we obtain a new theorem of global convergence for halley s method

hom a g iv abstract in this paper we prove that for any finite groups a and g the number of homomorphisms from a to g is divisible by the greatest common divisor of a a a a and g where a is the commutator subgroup of a and a a is the frattini subgroup of a a

enlarging the convergence ball of the method of parabola for finding zero of derivatives we present a new technique for enlarging the convergence ball of the method of parabola in order to approximate a zero of derivatives this approach also leads to more precise error estimates on the distances involved than in earlier studies such as hua 1974 ren and wu 2009 and wand 1975 these advantages are obtained under the same computational cost on the lipschitz constants involved as in the earlier studies numerical examples are also given to show the advantages over the earlier work

the application of an inverse free jarratt type approximation to nonlinear integral equations of hammerstein type abstract we consider an inverse free jarratt type approximation whose order of convergence is four for solving nonlinear equations the convergence of this method is analysed under two different types of conditions we use a new technique based on constructing a system of real sequences finally this method is applied to the study of hammerstein s integral equations

two conditions concerning newton s method in this note we compare two conditions concerning newton s method and find out that even under some weaker condition one has the convergence of the newton s method and a better error bound than the relative strong condition

near optimal control of linear multiparameter singularly perturbed systems in this note the linear quadratic optimal control for multipa rameter singularly perturbed systems is studied the attention is focused on the design of a new near optimal controller the resulting controller achieves approximation of the optimal cost the proposed algorithm has been numerically tested on a real physical example and pro duced useful results

semilocal convergence by using recurrence relations for a fifth order method in banach spaces in this paper a semilocal convergence result in banach spaces of an efficient fifth order method is analyzed recurrence relations are used in order to prove this convergence and some a priori error bounds are found this scheme is finally used to estimate the solution of an integral equation and so the theoretical results are numerically checked we use this example to show the better efficiency of the current method compared with other existing ones including newton s scheme

historical developments in convergence analysis for newton s and newton like methods historical developments in convergence theory as well as error estimates for newton s method and newton like methods for nonlinear equations are described mainly for differentiable equations in banach spaces

chebyshev method and convexity from convexity we obtain new convergence theorems for the chebyshev method applied to a nonlinear scalar equation f x 0 moreover kantorovich type conditions for the convergence of the chebyshev method in the complex plane are given finally a new type of assumptions are considered to prove the convergence of this method in banach spaces

recurrence relations for a newton like method in banach spaces the convergence of iterative methods for solving nonlinear operator equations in banach spaces is established from the convergence of majorizing sequences an alternative approach is developed to establish this convergence by using recurrence relations for example the recurrence relations are used in establishing the convergence of newton s method l b rall computational solution of nonlinear operator equations robert e krieger new york 1979 and the third order methods such as halley s chebyshev s and super halley s v candela a marquina recurrence relations for rational cubic methods i the halley method computing 44 1990 169 184 v candela a marquina recurrence relations for rational cubic methods ii the halley method computing 45 1990 355 367 j a ezquerro m a hernandez recurrence relations for chebyshev type methods appl math optim 41 2000 227 236 j m gutierrez m a hernandez third order iterative methods for operators with bounded second derivative j comput appl math 82 1997 171 183 j m gutierrez m a hernandez recurrence relations for the super halley method comput math appl 7 36 1998 1 8 m a hernandez chebyshev s approximation algorithms and applications comput math appl 41 2001 433 445 10 in this paper an attempt is made to use recurrence relations to establish the convergence of a third order newton like method used for solving a nonlinear operator equation f x 0 where f email protected x y be a nonlinear operator on an open convex subset w of a banach space x with values in a banach space y here first we derive the recurrence relations based on two constants which depend on the operator f then based on this recurrence relations a priori error bounds are obtained for the said iterative method finally some numerical examples are worked out for demonstrating our approach

ball convergence comparison between three iterative methods in banach space under hypothese only on the first derivative we present a convergence ball comparison between three iterative methods for approximating a locally unique solution of a nonlinear equation in a banach space setting the convergence ball and error estimates are given for these methods under hypotheses only on the first frechet derivative in contrast to earlier studies such as adomian 1994 1 babajee et al 2008 13 cordero and torregrosa 2007 17 cordero et al 18 darvishi and barati 2007 19 using hypotheses reaching up to the fourth frechet derivative although only the first derivative appears in these methods this way we expand the applicability of these methods numerical examples are also presented in this study

efficient numerical procedures for solving closed loop stackelberg strategies with small singular perturbation parameter in this paper the computation of the linear closed loop stackelberg strategies with small singular perturbation parameter that characterizes singularly perturbed systems sps are studied the attention is focused on a new numerical algorithm for solving a set of cross coupled algebraic lyapunov and riccati equations calre it is proven that the new algorithm guarantees the local quadratic convergence a numerical example is solved to show a reduction of the average cpu time compared with the existing algorithm

on the newton kantorovich hypothesis for solving equations the famous newton kantorovich hypothesis has been used for a long time as a sufficient condition for the convergence of newton s method to a solution of an equation in connection with the lipschitz continuity of the frechet derivative of the operator involved here using lipschitz and center lipschitz conditions we show that the newton kantorovich hypothesis can be weakened the error bounds obtained under our semilocal convergence result are more precise than the corresponding ones given by the dominating newton kantorovich theorem

convergence of the variants of the chebyshev halley iteration family under the holder condition of the first derivative the present paper is concerned with the convergence problem of the variants of the chebyshev halley iteration family with parameters for solving nonlinear operator equations in banach spaces under the assumption that the first derivative of the operator satisfies the holder condition of order p a convergence criterion of order 1 p for the iteration family is established an application to a nonlinear hammerstein integral equation of the second kind is provided

third order iterative methods for operators with bounded second derivative abstract we analyse the classical third order methods chebyshev halley super halley to solve a nonlnnear equation f x 0 where f is an operator defined between two banach spaces until now the convergence of these methods is established assuming that the second derivative f satisfies a lipschitz condition in this paper we prove by using recurrence relations the convergence of these and other third order methods just assuming f is bounded we show examples where our conditions are fulfilled and the classical ones fail

on partial smoothness tilt stability and the mathcal vu decomposition under the assumption of prox regularity and the presence of a tilt stable local minimum we are able to show that a mathcal vu like decomposition gives rise to the existence of a smooth manifold on which the function in question coincides locally with a smooth function

indices of convexity and concavity application to halley method we define an index to measure the convexity of a convex function f at each point we use this index to establish conditions on the convergence of the halley method in the complex plane and in banach spaces

convergence of the family of the deformed euler halley iterations under the holder condition of the second derivative the convergence problem of the family of the deformed euler halley iterations with parameters for solving nonlinear operator equations in banach spaces is studied under the assumption that the second derivative of the operator satisfies the holder condition a convergence criterion of the order 2 p of the iteration family is established an application to a nonlinear hammerstein integral equation of the second kind is provided

a note on the kantorovich theorem for newton iteration abstract in this paper a new theorem for the newton method convergence is obtained its condition is different from that of the kantorovich theorem and therefore it has theoretical and practical value

error bounds for newton s iterates derived from the kantorovich theorem in this paper it is shown that the upper and lower bounds of the errors in the newton iterates recently obtained by potra ptak 11 and miel 7 with the use of nondiscrete induction and majorizing sequence respectively follow immediately from the kantorovich theorem and the kantorovich recurrence relations it is also shown that the upper and lower bounds of miel are finer than those of potra ptak

geometric constructions of iterative functions to solve nonlinear equations in this paper we present the geometrical interpretation of several iterative methods to solve a nonlinear scalar equation in addition we also review the extension to general banach spaces and some computational aspects of these methods

on the r order of convergence of newton s method under mild differentiability conditions a new technique is used instead of the classical majorant principle to analyze the r order of convergence of the newton process when more general conditions than the kantorovich ones are considered

on zeta functions of modular representations of a discrete group abstract it is proved that the generating function defined by the numbers of isomorphism classes of absolutely irreducible representations of a finitely generated group g into gl d f q n for n 1 is a rational function it is also proved that the generating function defined by weighted sums over isomorphism classes of representations of g into gl d f q n for n 1 is meromorphic over both the complex numbers and the p adic complex numbers

a discretization scheme for some conservative problems we approximate a locally unique solution of an equation in banach spaces using a newton like method of r order three then we apply this method to obtain an existence uniqueness result for a basic conservative problem given by a nonlinear boundary value problem next by means of a discretization method we approximate the solution of the conservative problem

third order family of methods in banach spaces recently parida and gupta p k parida d k gupta recurrence relations for a newton like method in banach spaces j comput appl math 206 2007 873 877 used rall s recurrence relation approach from 1961 to approximate roots of nonlinear equations by developing several methods the latest of which is free of second derivative and it is of third order in this paper we use an idea of kou and li j s kou y t li modified chebyshev s method free from second derivative for non linear equations appl math comput 187 2007 1027 1032 and modify the approach of parida and gupta obtaining yet another third order method to approximate a solution of a nonlinear equation in a banach space we give several applications to our method

on a characterization of some newton like methods of r order at least three in this paper we extend to banach spaces the result given by gander in amer math monthly 92 1985 131 to obtain a characterization of newton like iterative process with r order of convergence at least three to do this we consider the construction and the study of the semilocal convergence of a multiparametric family of iterative processes in banach spaces for solving the nonlinear equation f x 0

recurrence relations for the super halley method in this paper we give sufficient conditions in order to assure the convergence of the super halley method in banach spaces we use a system of recurrence relations analogous to those given in the classical newton kantorovich theorem or those given for chebyshev and halley methods by different authors 1998 elsevier science ltd all rights reserved

a third order method for fixed points in banach spaces this paper deals with a third order stirling like method used for finding fixed points of nonlinear operator equations in banach spaces the semilocal convergence of the method is established by using recurrence relations under the assumption that the first frechet derivative of the involved operator satisfies the holder continuity condition a theorem is given to establish the error bounds and the existence and uniqueness regions for fixed points the r order of the method is also shown to be equal to at least 2p 1 for p 0 1 the efficacy of our approach is shown by solving three nonlinear elementary scalar functions and two nonlinear integral equations by using both stirling like method and newton like method it is observed that our convergence analysis is more effective and give better results

a numerical analysis of the nash strategy for weakly coupled large scale systems this note discusses the feedback nash equilibrium of linear quadratic n player nash games for infinite horizon large scale interconnected systems the asymptotic structure along with the uniqueness and positive semidefiniteness of the solutions of the cross coupled algebraic riccati equations cares is newly established via the newton kantorovich theorem the main contribution of this study is the proposal of a new algorithm for solving the cares in order to improve the convergence rate of the algorithm newton s method is combined with a new decoupling algorithm it is shown that the proposed algorithm attains quadratic convergence moreover it is shown for the first time that solutions to the cares can be obtained by solving the independent algebraic lyapunov equation ale by using the reduced order calculation

second derivatives of a convex function and of its legendre fenchel transformate in 1977 crouzeix established a simple relationship between the second order differentials of a convex function f mathbb r n to mathbb r cup infty and its legendre fenchel transformate f mathbb r n to mathbb r cup infty in the first part of this paper the importance of crouzeix s formula is enhanced by illustrating how it can be applied to a large number of classical and modern mathematical problems in the second part the result of crouzeix is extended to the case in which the functions f and f are not necessarily smooth this generalization is based on the works of hiriart urruty and seeger concerning the so called second order subdifferential of a convex function

on the convergence of a higher order family of methods and its dynamics in this paper we present the study of the local convergence of a higher order family of methods moreover the dynamical behavior of this family of iterative methods applied to quadratic polynomials is studied some anomalies are found in this family by means of studying the associated rational function parameter spaces are shown and the study of the stability of all the fixed points is presented

semilocal convergence of a continuation method with holder continuous second derivative in banach spaces in this paper the semilocal convergence of a continuation method combining the chebyshev method and the convex acceleration of newton s method used for solving nonlinear equations in banach spaces is established by using recurrence relations under the assumption that the second frechet derivative satisfies the holder continuity condition this condition is mild and works for problems in which the second frechet derivative fails to satisfy lipschitz continuity condition a new family of recurrence relations are defined based on two constants which depend on the operator the existence and uniqueness regions along with a closed form of the error bounds in terms of a real parameter a 0 1 for the solution x is given two numerical examples are worked out to demonstrate the efficacy of our approach on comparing the existence and uniqueness regions for the solution obtained by our analysis with those obtained by using majorizing sequences under holder continuity condition on f it is found that our analysis gives improved results further we have observed that for particular values of the a our analysis reduces to those for the chebyshev method a 0 and the convex acceleration of newton s method a 1 respectively with improved results

calculus rules on a new set valued second order derivative for convex functions etant donnee une fonction convexe f qui a ete construite a partir d autres fonctions f i dont les differentielles secondes sont aisees a determiner on cherche a exprimer les differentielles secondes de f en fonction des 2 f i

asymptotic expansions and a new numerical algorithm of the algebraic riccati equation for multiparameter singularly perturbed systems abstract in this paper we study a continuous time multiparameter algebraic riccati equation mare with an indefinite sign quadratic term the existence of a unique and bounded solution of the mare is newly established we show that the kleinman algorithm can be used to solve the sign indefinite mare the proof of the convergence and the existence of the unique solution of the kleinman algorithm is done by using the newton kantorovich theorem furthermore we present new algorithms for solving the generalized multiparameter algebraic lyapunov equation gmale by means of the fixed point algorithm

conjugation and second order properties of convex functions abstract we single out some second order properties of convex functions that are well behaved with respect to the conjugacy operator as an application we prove that if a convex lower semicontinuous function f r n r has a second order taylor expansion at the origin f x 1 2 ax x o x 2 as x 0 and the matrix a is symmetric and positive definite then the conjugate function f has a second order taylor expansion at the origin too given by f y 1 2 a 1 y y o y 2 as y 0

semilocal convergence of a family of third order methods in banach spaces under holder continuous second derivative abstract in this paper the semilocal convergence of a family of multipoint third order methods used for solving f x 0 in banach spaces is established it is done by using recurrence relations under the assumption that the second frechet derivative of f satisfies holder continuity condition based on two parameters depending upon f a new family of recurrence relations is defined using these recurrence relations an existence uniqueness theorem is established to prove that the r order convergence of the method is 2 p a priori error bounds for the method are also derived two numerical examples are worked out to demonstrate the efficacy of our approach

chebyshev s approximation algorithms and applications abstract we introduce a new family of multipoint methods to approximate a solution of a nonlinear operator equation in banach spaces an existence uniqueness theorem and error estimates are provided for these iterations using a technique based on a new system of recurrence relations to finish we apply the results obtained to some nonlinear integral equations of the fredholm type

on the local convergence and the dynamics of chebyshev halley methods with six and eight order of convergence we study the local convergence of chebyshev halley methods with six and eight order of convergence to approximate a locally unique solution of a nonlinear equation in sharma 2015 see theorem 1 p 121 the convergence of the method was shown under hypotheses reaching up to the third derivative the convergence in this study is shown under hypotheses on the first derivative hence the applicability of the method is expanded the dynamics of these methods are also studied finally numerical examples examining dynamical planes are also provided in this study to solve equations in cases where earlier studies cannot apply

semilocal convergence analysis on the modifications for chebyshev halley methods under generalized condition in this paper we consider the semilocal convergence for modifications of chebyshev halley methods in banach space compared with the results on super halley method studied in reference gutierrez and hernandez 1998 these modified methods need less computation of inversion the r order is improved and the lipschitz continuity of second derivative is also relaxed we prove a theorem to show existence uniqueness of solution the r order for these modified methods is analyzed under generalized condition

on halley type iterations with free second derivative in this paper we relax the convergence conditions required in ezquerro and hernandez int j pure appl math 6 1 2003 103 for a multipoint third order iteration of halley type where the conditions provided are the known ones for methods of order three

numerical solution of stochastic nash games with state dependent noise for weakly coupled large scale systems abstract this paper discusses the infinite horizon stochastic nash games with state dependent noise after establishing the asymptotic structure along with the positive semidefiniteness for the solutions of the cross coupled stochastic algebraic riccati equations csares a new algorithm that combines newton s method with two fixed point algorithms for solving the csares is derived as a result it is shown that the proposed algorithm attains quadratic convergence and the reduced order computations for sufficiently small parameter e as another important feature the high order approximate strategy that is based on the iterative solutions is proposed using such strategy the degradation of the cost functional is investigated finally in order to demonstrate the efficiency of the proposed algorithms computational examples are provided

unified convergence domains of newton like methods for solving operator equations we present a unified semilocal convergence analysis in order to approximate a locally unique zero of an operator equation in a banach space setting using our new idea of restricted convergence domains we generate smaller lipschitz constants than in earlier studies leading to the following advantages weaker sufficient convergence criteria tighter error estimates on the distances involved and an at least as precise information on the location of the zero hence the applicability of these methods is extended these advantages are obtained under the same cost on the parameters involved numerical examples where the old sufficient convergence criteria cannot apply to solve equations but the new criteria can apply are also provided in this study

newton kantorovich theorem for a family of modified halley s method under holder continuity conditions in banach space abstract in this study under p holder continuity conditions a family of new modified halley s method with 2 p order is proposed in banach space which is used to solve the nonlinear operator equations the newton kantorovich convergence theorem for the family of new modified halley s method is established under holder continuity conditions the error estimate also is gotten finally two examples are provided to show the application of our theorem

a convergence theorem for newton like methods in banach spaces on the basis of the results obtained in a series of papers 25 28 a convergence theorem for newton s method in banach spaces is given which improves the theorems of kantorovich 4 lancaster 8 and ostrowski 10 the error bounds obtained improve the recent results of potra 17

numerical computation for h output feedback control for strongly coupled large scale systems abstract in this paper h output feedback control for strongly coupled large scale systems are discussed when the positive coupling parameter e which connect the other subsystems is large a successive algorithm for solving the algebraic riccati equations are is developed for the first time since the proposed algorithm is derived using newton s method it is noteworthy that the quadratic convergence and uniqueness of the obtained solution are both guaranteed for strongly coupled parameter e moreover in order to reduce the computation in the resulting newton s method the gradient based iterative gi algorithm is combined as a result it is shown that the reduced order computation is attained finally in order to demonstrate the efficiency of the proposed algorithms computational examples are provided

a stirling like method with holder continuous first derivative in banach spaces in this paper the convergence of a stirling like method used for finding a solution for a nonlinear operator in a banach space is examined under the relaxed assumption that the first frechet derivative of the involved operator satisfies the holder continuity condition many results exist already in the literature to cover the stronger case when the second frechet derivative of the involved operator satisfies the lipschitz holder continuity condition our convergence analysis is done by using recurrence relations the error bounds and the existence and uniqueness regions for the solution are obtained finally two numerical examples are worked out to show that our convergence analysis leads to better error bounds and existence and uniqueness regions for the fixed points