Convergence results of iterative algorithms for the sum of two monotone operators in reflexive Banach spaces

2021 ◽  
pp. 1-24
Author(s):  
Yan Tang ◽  
Ratthaprom Promkam ◽  
Prasit Cholamjiak ◽  
Pongsakorn Sunthrayuth
Keyword(s):  
Banach Spaces ◽  
Iterative Algorithms ◽  
Monotone Operators ◽  
Reflexive Banach Spaces ◽  
Convergence Results

scholarly journals Weak and strong convergence results for sum of two monotone operators in reflexive Banach spaces

2020 ◽  
Vol 21 (1) ◽  
pp. 281-304
Author(s):  
Ferdinard U. Ogbuisi ◽  
◽  
Lateef O. Jolaoso ◽  
Yekini Shehu ◽  
◽  
...  
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Monotone Operators ◽  
Reflexive Banach Spaces ◽  
Weak And Strong Convergence ◽  
Convergence Results

scholarly journals Iterative methods for generalized split feasibility problems in Banach spaces

2017 ◽  
Vol 33 (1) ◽  
pp. 09-26
Author(s):  
QAMRUL HASAN ANSARI ◽  
◽  
AISHA REHAN ◽  
◽  
Keyword(s):  
Weak Convergence ◽  
Banach Spaces ◽  
Iterative Methods ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Iterative Algorithms ◽  
Approximate Solutions ◽  
Split Feasibility Problems ◽  
Convergence Results ◽  
Split Feasibility

Inspired by the recent work of Takahashi et al. [W. Takahashi, H.-K. Xu and J.-C. Yao, Iterative methods for generalized split feasibility problems in Hilbert spaces, Set-Valued Var. Anal., 23 (2015), 205–221], in this paper, we study generalized split feasibility problems (GSFPs) in the setting of Banach spaces. We propose iterative algorithms to compute the approximate solutions of such problems. The weak convergence of the sequence generated by the proposed algorithms is studied. As applications, we derive some algorithms and convergence results for some problems from nonlinear analysis, namely, split feasibility problems, equilibrium problems, etc. Our results generalize several known results in the literature including the results of Takahashi et al. [W. Takahashi, H.-K. Xu and J.-C. Yao, Iterative methods for generalized split feasibility problems in Hilbert spaces, SetValued Var. Anal., 23 (2015), 205–221].

An iterative method for solving minimization, variational inequality and fixed point problems in reflexive Banach spaces

2018 ◽  
Vol 9 (3) ◽  
pp. 167-184 ◽  
Author(s):  
Lateef Olakunle Jolaoso ◽  
Ferdinard Udochukwu Ogbuisi ◽  
Oluwatosin Temitope Mewomo
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Infinite Family ◽  
Monotone Operators ◽  
Convergence Result ◽  
Reflexive Banach Spaces ◽  
Strongly Monotone Operators ◽  
System Of Equilibrium Problems

Abstract In this paper, we propose an iterative algorithm for approximating a common fixed point of an infinite family of quasi-Bregman nonexpansive mappings which is also a solution to finite systems of convex minimization problems and variational inequality problems in real reflexive Banach spaces. We obtain a strong convergence result and give applications of our result to finding zeroes of an infinite family of Bregman inverse strongly monotone operators and a finite system of equilibrium problems in real reflexive Banach spaces. Our result extends many recent corresponding results in literature.

scholarly journals Tykhonov triples, well-posedness and convergence results

2021 ◽  
Vol 37 (1) ◽  
pp. 135-143
Author(s):  
YI-BIN XIAO ◽  
MIRCEA SOFONEA
Keyword(s):  
Nonlinear Equation ◽  
Banach Spaces ◽  
Metric Spaces ◽  
Mathematical Object ◽  
Multivalued Function ◽  
Well Posedness ◽  
Unified Theory ◽  
Reflexive Banach Spaces ◽  
Preliminary Results ◽  
Convergence Results

"In this paper we present a unified theory of convergence results in the study of abstract problems. To this end we introduce a new mathematical object, the so-called Tykhonov triple $\cT=(I,\Omega,\cC)$, constructed by using a set of parameters $I$, a multivalued function $\Omega$ and a set of sequences $\cC$. Given a problem $\cP$ and a Tykhonov triple $\cT$, we introduce the notion of well-posedness of problem $\cP$ with respect to $\cT$ and provide several preliminary results, in the framework of metric spaces. Then we show how these abstract results can be used to obtain various convergences in the study of a nonlinear equation in reflexive Banach spaces. "

scholarly journals On Generalized Nonexpansive Maps in Banach Spaces

Computation ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 61 ◽  
Author(s):  
Kifayat Ullah ◽  
Junaid Ahmad ◽  
Manuel de la Sen
Keyword(s):  
Banach Spaces ◽  
General Class ◽  
Iterative Algorithms ◽  
Uniformly Convex ◽  
Demiclosed Principle ◽  
New Class ◽  
Nonexpansive Maps ◽  
Convergence Results ◽  
Uniformly Convex Banach Spaces ◽  
Expansive Maps

We introduce a very general class of generalized non-expansive maps. This new class of maps properly includes the class of Suzuki non-expansive maps, Reich–Suzuki type non-expansive maps, and generalized α -non-expansive maps. We establish some basic properties and demiclosed principle for this class of maps. After this, we establish existence and convergence results for this class of maps in the context of uniformly convex Banach spaces and compare several well known iterative algorithms.

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