SOME CONVERGENCE PROBLEM OF ITERATIVE SEQUENCESFOR ACCRETIVE AND PSEUDO-CONTRACTIVETYPE MAPPING IN BANACH SPACES

Some necessary and sufficient conditions for convergence of Ishikawa Mann and steepest descent iterative sequence for accretive and pseudo-contractive type mapping in Banach spaces were obtained. The results improve, extend and include some recent results.

AN ITERATIVE PROCESS FOR FINDING APPROXIMATE SOLUTIONS TO NONLINEAR EQUATIONS OF STRONGLY ACCRETIVE OPERATORS

In this paper, we investigate the Ishikawa iteration process in a p-uniformly smooth Banach space X. We prove that the Ishikawa iteration process converges strongly to the unique solution of the equation Tx=f when T is a Lipschitzian and strongly accretive operator frow X to X, or to the unique fixed point of T when T is a Lipschitzian and strictly pseudocontractive mapping from a nonempty closed convex subset K of X into itself. Our results are the extension and improvements of the earlier and recent results in this field.

REGULARIZATION METHODS FOR NONLINEAR ILL-POSED PROBLEMS WITH ACCRETIVE OPERATORS

This article is devoted to the regularization of nonlinear ill-posed problems with accretive operators in Banach spaces. The data involved are assumed to be known approximately. The authors concentrate their discussion on the convergence rates of regular solutions.

ISHIKAWA TYPE ITERATIVE SEQUENCES WITH ERRORS FOR LIPSCHITZIAN φ-STRONGLY ACCRETIVE OPERATOR EQUATIONS IN ARBITRARY BANACH SPACES

In this paper, we investigate the problem of approximating solutions of the equations of Lipschitzian ψ-strongly accretive operators and fixed points of Lipschitzian ψ-hemicontractive operators by lshikawa type iterative sequences with errors. Our results unify, improve and extend the results obtained previously by several authors including Li and Liu (Acta Math. Sinica 41 (4)(1998), 845-850), and Osilike (Nonlinear Anal. TMA, 36(1)(1999), 1-9), and also answer completely the open problems mentioned by Chidume (J. Math. Anal. Appl. 151 (2)(1990), 453-461).

ITERATIVE SOLUTION OF NONLINEAR EQUATIONS WITH STRONGLY ACCRETIVE OPERATORS IN BANACH SPACES

Let X be a real Banach space with a uniformly convex dual X*. Let T: X a X be a Lipschitzian and strongly accretive mapping with a Lipschitzian constant L greater than or equal to 1 and a strongly accretive constant k epsilon (0,1). Let {alpha(n)} and {beta(n)} be two real sequences in [0,1] satisfying: (i) alpha(n) --> 0 as n --> infinity (ii) beta(n) < k(1 - k)/L(1 + L), for all n greater than or equal to 0; (iii) Pi(infinity) alpha(n) = infinity Set Sx = f - Tx + x, For All x epsilon X. Assume that {u(n)}(n=0)(infinity) and {v(n)}(n=0)(infinity) be two sequences in X satisfying parallel to u(n) parallel to = o(alpha(n)) and nu(n) --> 0 as n --> infinity. For arbitrary x(0) epsilon X, the iteration sequence {x(n)} is defined by (IS)(I) {x(n+1) = (1 - alpha(n))x(n) + alpha(n)Sy(n) + u(n), {y(n) = (1 - beta(n)) x(n) + beta(n)Sx(n) + v(n) (n greater than or equal to 0) then {x(n)} converges strongly to the unique solution of the equation Tx = f. related result deals with iterative approximation of fixed points of phi-hemicontractive mappings.

1-set-contractive perturbations of accretive operators in Menger PN-spaces

Based on the topological degree for 1-set-contractive fields established in [11], we discuss the 1-set-contractive perturbation and the existence of zero points for nonlinear equations with accretive mappings in Menger PN-spaces and obtain some new results.

A Note on Iterative Solutions of Nonlinear Accretive Operator Equations

Suppose that X is a real Banach space, H: X→X is a Lipschitz operator, T: X→X is a uniformly continuous operator with bounded range, and H+T is strongly accretive. Then the Ishikawa iteration process converges strongly to the unique solution of the equation Hx+Tx=f . This conclusion extends the corresponding results in recent papers.

ITERATIVE PROCESS TO -HEMICONTRACTIVE OPERATOR AND-STRONGLY ACCRETIVE OPERATOR EQUATIONS

Let E be an arbitrary real Banach space and K be a nonempty closed convex subsets of E. Let T:K→K be a uniformly continuous _hemicontractive operator with bounded range and a n,b n,c n,a ′ n,b ′ n,c ′ n be sequences in [0,1] satisfying:ⅰ) a n+b n+c n=a ′ n+b ′ n+c ′ n=1. n≥0; ⅱ) lim b n= lim b ′ n= lim c ′ n= 0; ⅲ)∑∞n=0b n=∞; ⅳ) c n=o(b n). For any given x 0,u 0,v 0∈K, define the Ishikawa type iterative sequence x n as follows: x n+1 =a nx n+b nTy n+c nu n, y n=a ′ nx n+b ′ nTx n+c ′ nv n (n≥0), where u n and v n are bounded sequences in K. Then x n converges strongly to the unique fixed point of T. Related result deals with the convergence of Ishikawa type iterative sequence to the solution of _strongly accretive operator equations.

ON THE EXISTENCE OF SOLUTIONS FOR EQUATIONS WITH ACCRETIVE MAPPINGS IN PROBABILISTIC NORMED SPACES

The purpose of this paper is to introduce the concept of accretive mapping in probabilistic normed space (PN space, in short) and to study the existence problem of solutions for equations with accretive mappings in PN space and some existence theorems are shown.

EXISTENCE AND APPROXIMATION OF SOLUTIONS TO VARIATIONAL INCLUSIONS WITH ACCRETIVE MAPPINGS IN BANACH SPACES

The purpose of this paper is to study the existence and approximation problem of solutions for a class of variational inclusions with accretive mappings in Banach spaces. The results extend and improve some recent results.

Iterative Approximation with Errors for Generalized Set-Valued Strongly Accretive Mapping in Banach Spaces

A new concept of generalized set-valued strongly accretive mappings in Banach spaces was given and some strong convergence theorems of Ishikawa and Mann iterative process with errors approximation methods by Huang et al. was proved. The results presented in this paper improve and extend the earlier results obtained by Huang et al.

Convergence Theorems of Mann and Ishikawa Iterative Processes with Errors for Multivalued Φ-strongly Accretive Mapping

Let X be a real Banach space and A : X→ 2x a bounded uniformly continuous Φ-strongly accretive multivalued mapping. For any f ∈ X, Mann and Ishikawa iterative processes with errors converge strongly to the unique solution of Ax (?) f. The conclusion in this paper weakens the stronger conditions about errors in Chidume and Moore's theorem (J. Math. Anal. Appl, 245(2000), 142-160).

<i>H</i>(.,.)<i>- φ - η -</i>Accretive Operators and Generalized Variational-Like Inclusions

In this paper, we generalize H(.,.) accretive operator introduced by Zou and Huang [1] and we call it H(.,.)- φ - η - accretive operator. We define the resolvent operator associated with H(.,.)- φ - η - accretive operator and prove its Lipschitz continuity. By using these concepts an iterative algorithm is suggested to solve a generalized variational-like inclusion problem. Some examples are given to justify the definition of H(.,.)- φ - η - accretive operator.

Iterative Construction of Solutions to Nonlinear Equations of Strongly Accretive Operators in Banach Spaces *

In this paper, we investigate the Ishikawa iteration process in a p -uniformly smooth Banach space X . Motivated by Deng and Tan and Xu , we prove that the Ishikawa iteration process converges strongly to the unique solution of the equation Tx=f when T is a Lipschitzian and strongly accretive operator from X to X , or to the unique fixed point of T when T is a Lipschitzian and strictly pseudo contractive mapping from a bounded closed convex subset C of X into itself. Our results improve and extend Theorem 4.1 and 4.2 of Tan and Xu by removing the restrion lim n→∞β n=0 or lim n→∞α n= lim n→∞β n=0 in their theorems. These also extend Theorems 1 and 2 of Deng to the p -uniformly smooth Banach space setting.

Approximation of Fixed Point and Solution for -Hemicontraction and -Strongly Quasi-Accretive Operator without Lipschitz Assumption

Let X be a real uniformly smooth Banach space and let T:D(T)(?)X→Xbe (?)-hemicontractive and locally bounded at its fixed point q∈F(T).Under somesuitable assumptions on the iteration parameters {αn}and{βn},we have proved thatthe Mann and Ishikawa iteration processes for T converge strongly to the unique fixedpoint q of T.Several related results deal with iterative solutions of nonlinear equationsinvolving (?)-strongly quasi-accretive operators.Our results extend and generalize thosecorresponding ones by Xu and Roach,Zhou and Jia and others.

On the Characteristics of the Convergence of Ishikawa Type Iterative Sequences for Strong Pseudocontractions and Strongly Accretive Operators

In this paper, the results characterize the convergence of Ishikawa type iterative sequences (with errors) for constructing the solutions of strongly accretive operator equations, the solutions of rn-accretive operator equations, and the fixed points of strong pseudocontractions. These results extend and improve Theorems 1-3 of Chidume and Osilike (Nonlinear Anal. TMA, 1999, 36(7): 863-872).

Remarks on the Mapping Theorems Involving Compact Perturbations of M-Accretive Operators in Banach Spaces

In the present paper, by virtue of new approch techniques, we obtain several mapping theorems involving compact perturbations of m—accretive operators.These results improve and extend the corresponding those obtained by Kartsatos,Zhu, and Kartsatos and Mabry.

Three-step Iterations with Errors for Nonlinear Strongly Accretive Operator Equations

In this paper, we suggest and analyse a three-step iterative scheme with errors for solving nonlinear strongly accretive operator equation Tx = f without the Lipshitz condition. The results presented in this paper improve and extend current results in the more general setting.

A Possible X-ray Quasi-periodic Oscillation in the Narrow-line Seyfert 1 Galaxy Mrk 142

A possible quasi-periodic oscillation(QPO) at frequency 7.045 × 10^(-5) Hz is found in the narrow-line Seyfert 1galaxy Mrk 142 in the data of XMM-Newton collected on 2020 April 11.We find that the QPO signal is statistically significantly larger than the 5σ level and highly coherent with quality factor Q > 5 at the 0.3–10 keV band by using the method of the Lomb–Scargle Periodogram,the Weighted Wavelet Z-transform and the REDFIT.We analyze the data in 0.3–0.6 keV,0.6–1 keV,1–3 keV and 3–10 keV energy bands,and find obvious QPO signals at 0.3–0.6 keV and 1–3 keV bands.We then analyze the time-average spectra and time variability at the QPO frequency of 7.045 × 10^(-5) Hz,and use a model to fit them.We find that the QPO signal mainly comes from the X-ray hot corona.

Timing and Spectral Analysis of the Black Hole X-Ray Binary MAXI J1803-298 with Insight-HXMT Data

We present a comprehensive analysis of the 2021 outburst of MAXI J1803–298 utilizing observations of the Insight-Hard X-ray Modulation Telescope(Insight-HXMT)spanning from the low hard state to the high soft state.Within the Insight-HXMT data set,compared to the previous work,we identify a more prolonged presence of typeC quasi-periodic oscillations(QPOs)with centroid frequencies ranging from~0.16 to 6.3 Hz,which present correlations with the hardness ratio and the photon index of the Comptonized component.For QPO frequencies less than~2 Hz,the QPO phase lags are hard(photons of 10–19 keV arrive later than those of 1–4 keV),while at higher frequencies,the lags become soft at and above~4 Hz.Furthermore,the spectra in all Insight-HXMT observations consist of a multi-color blackbody component and a Comptonized component,as commonly observed in classical black hole X-ray binaries.We analyze state transitions and the evolution of accretion geometry in this work.The fitted inner disk radius increases abnormally during the low hard state,hypothesized to result from the corona condensing onto the inner disk.Additionally,two significant drops in flux are observed during the soft intermediate state,maybe implying changes in the corona/jet and the disk,respectively.