@article{8665723b28554d62b4b67784470828db,

title = "Solving split equality equilibrium and fixed point problems in Banach spaces without prior knowledge of the operator norms",

abstract = "The purpose of this paper is to study the approximation of solution of split equality generalized mixed equilibrium problem and fixed point problem for right Bregman strongly quasi-nonexpansive mappings in q-uniformly convex Banach spaces which are also uniformly smooth. We introduce a simultaneous algorithm and prove strong convergence without prior information of the operator norms involved. This is very important because norms of bounded linear operators are rarely know explicitly. We also give applications of our result to approximation of solution of split equality mixed convex differentiable minimization problem and split equality feasibility fixed point problem in Banach spaces. Our result in this paper improve and extend many results on split equality fixed point problem and common solution of split equality fixed point and equilibrium problems in literature.",

keywords = "Banach spaces, Fixed point problem, Generalized mixed equilibrium problem, Operator norms, Right Bregman quasi-nonexpansive mapping, Split equality problem",

author = "Okeke, {C. C.} and Jolaoso, {L. O.} and Isiogugu, {F. O.} and Mewomo, {O. T.}",

note = "Funding Information: 2010 Mathematics Subject Classification. 47H06, 47H09, 49J53, 65K10. Key words and phrases. split equality problem, generalized mixed equilibrium problem, fixed point problem, right Bregman quasi-nonexpansive mapping, operator norms, Banach spaces. ∗†The first and third author acknowledge with thanks the bursary and financial support from Department of Science and Technology and National Research Foundation, Republic of South Africa Center of Excellence in Mathematical and Statistical Sciences (DST-NRF COE-MaSS) Doctoral Bursary and Postdoctoral fellowship . Funding Information: ??The first and third author acknowledge with thanks the bursary and financial support from Department of Science and Technology and National Research Foundation, Republic of South Africa Center of Excellence in Mathematical and Statistical Sciences (DST-NRF COE-MaSS) Doctoral Bursary and Postdoctoral fellowship . Publisher Copyright: {\textcopyright} 2019 Yokohama Publications. All rights reserved.",

year = "2019",

language = "English",

volume = "20",

pages = "661--683",

journal = "Journal of Nonlinear and Convex Analysis",

issn = "1345-4773",

publisher = "Yokohama Publishers",

number = "4",

}