TY - JOUR

T1 - OPERATOR NORM INDEPENDENT SOLUTION OF SPLIT EQUALITY EQUILIBRIUM PROBLEM AND FIXED POINT PROBLEM FOR CERTAIN MULTIVALUED MAPS

AU - Jolaoso, Lateef Olakunle

AU - Ogbuisi, Ferdinard Udochukwu

AU - Mewomo, Oluwatosin Temitope

N1 - Funding Information:
Acknowledgement: The authors thank the reviewer for valuable and useful suggestions and comments which led to the great improvement of the paper. The second 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. Opinions expressed and conclusions arrived are those of the authors and are not necessarily to be attributed to the CoE-MaSS.
Publisher Copyright:
© 2020 Watam Press.

PY - 2020

Y1 - 2020

N2 - In this paper, we introduce a new multivalued k-strictly pseudononpsreading mapping T with type-one condition and prove that the set of fixed points of T is closed and convex. We also proved that I − T is demiclosed at zero without the condition that the set of fixed point of T is strict. Using this new mapping, we study the strong convergence of a new iterative algorithm for approximating a common element of the set of solutions of a system of split equality generalized mixed equilibrium problems and fixed point problem of k-strictly pseudononspreading multivalued type-one mappings without a prior knowledge of the operator norm in real Hilbert space. Furthermore, we give a numerical example of our main theorem in real Hilbert spaces. Our result improves and complements some recent corresponding results in the literature.

AB - In this paper, we introduce a new multivalued k-strictly pseudononpsreading mapping T with type-one condition and prove that the set of fixed points of T is closed and convex. We also proved that I − T is demiclosed at zero without the condition that the set of fixed point of T is strict. Using this new mapping, we study the strong convergence of a new iterative algorithm for approximating a common element of the set of solutions of a system of split equality generalized mixed equilibrium problems and fixed point problem of k-strictly pseudononspreading multivalued type-one mappings without a prior knowledge of the operator norm in real Hilbert space. Furthermore, we give a numerical example of our main theorem in real Hilbert spaces. Our result improves and complements some recent corresponding results in the literature.

KW - Finite family

KW - fixed point problems

KW - generalized equilibrium

KW - k-strictly pseudononspreading

KW - multivalued mappings

KW - split equality

UR - http://www.scopus.com/inward/record.url?scp=85131047165&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85131047165

SN - 1492-8760

VL - 27

SP - 195

EP - 221

JO - Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms

JF - Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms

IS - 4

ER -