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An iterative approximation of common solutions of split generalized vector mixed equilibrium problem and some certain optimization problems

100%

Mewomo O. T. , Oyewole O. K.

tom Vol. 54, nr 1

335--358

In this paper, we study the problem of finding a common solution of split generalized vector mixed equlibrium problem (SGVMEP), fixed point problem (FPP) and variational inequality problem (VIP). We propose an inertial-type iterative algorithm, which uses a projection onto a feasible set and a linesearch, which can be easily calculated. We prove a strong convergence of the sequence generated by the proposed algorithm to a common solution of SGVMEP, fixed point of a quasi- ϕ -nonexpansive mapping and VIP for a general class of monotone mapping in 2-uniformly convex and uniformly smooth Banach space E1 and a smooth, strictly convex and reflexive Banach space E2 . Some numerical examples are presented to illustrate the performance of our method. Our result improves some existing results in the literature.

Convergence theorems for generalized hemicontractive mapping in p-uniformly convex metric space

80%

Ugwunnadi G. C. , Izuchukwu C. , Mewomo O. T.

2020

tom Vol. 26, nr 2

221--229

In this paper, we introduce and study an Ishikawa-type iteration process for the class of generalized hemicontractive mappings in p-uniformly convex metric spaces, and prove both Delta-convergence and strong convergence theorems for approximating a fixed point of generalized hemicontractive mapping in complete p-uniformly convex metric spaces. We give a surprising example of this class of mapping that is not a hemicontractive mapping. Our results complement, extend and generalize numerous other recent results in CAT(0) spaces.

Convergence theorem for a finite family of asymptotically demicontractive multi-valued mappings in CAT(0) spaces

80%

Ugwunnadi G. C. , Mewomo O. T. , Izuchukwu C.

2020

tom Vol. 26, nr 1

117--130

In this paper, we introduce the class of asymptotically demicontractive multivalued mappings and establish a strong convergence theorem of the modified Mann iteration to a common fixed point of a finite family of asymptotically demicontractive multivalued mappings in a complete CAT(0) space. We also give a numerical example of our iterative method to show its applicability.