APPROXIMATING FINITE FAMILIES OF RESOLVENTS OF CONVEX FUNCTIONS AND FIXED POINT PROBLEM OF DEMICONTRACTIVE TYPE MAPPINGS

K. K. Makgeru; H. A. Abass; M. Aphane

doi:10.28924/APJM/10-35

APPROXIMATING FINITE FAMILIES OF RESOLVENTS OF CONVEX FUNCTIONS AND FIXED POINT PROBLEM OF DEMICONTRACTIVE TYPE MAPPINGS

K. K. Makgeru, H. A. Abass^*, M. Aphane

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we introduce and study a modified Halpern iterative method for approximating a common solution of finite families of the resolvents of convex functions and fixed point problems of demicontractive-type mappings in Hadamard spaces. Under some mild assumptions, we prove a strong convergence theorem of the sequence generated by the modified Halpern method to an element in the intersection of the set of solutions of the aforementioned problems. We present some consequences and applications of our main result. Our results improves and generalizes many recent results in the literature.

Original language	English
Article number	35
Journal	Asia Pacific Journal of Mathematics
Volume	10
DOIs	https://doi.org/10.28924/APJM/10-35
Publication status	Published - 2023
Externally published	Yes

Keywords

Hadamard spaces
convex minimization problem
demicontractive mapping
fixed point problem

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10.28924/APJM/10-35

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abstract = "In this paper, we introduce and study a modified Halpern iterative method for approximating a common solution of finite families of the resolvents of convex functions and fixed point problems of demicontractive-type mappings in Hadamard spaces. Under some mild assumptions, we prove a strong convergence theorem of the sequence generated by the modified Halpern method to an element in the intersection of the set of solutions of the aforementioned problems. We present some consequences and applications of our main result. Our results improves and generalizes many recent results in the literature.",

keywords = "Hadamard spaces, convex minimization problem, demicontractive mapping, fixed point problem",

author = "Makgeru, {K. K.} and Abass, {H. A.} and M. Aphane",

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AU - Abass, H. A.

AU - Aphane, M.

PY - 2023

Y1 - 2023

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AB - In this paper, we introduce and study a modified Halpern iterative method for approximating a common solution of finite families of the resolvents of convex functions and fixed point problems of demicontractive-type mappings in Hadamard spaces. Under some mild assumptions, we prove a strong convergence theorem of the sequence generated by the modified Halpern method to an element in the intersection of the set of solutions of the aforementioned problems. We present some consequences and applications of our main result. Our results improves and generalizes many recent results in the literature.

KW - Hadamard spaces

KW - convex minimization problem

KW - demicontractive mapping

KW - fixed point problem

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DO - 10.28924/APJM/10-35

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SN - 2357-2205

VL - 10

JO - Asia Pacific Journal of Mathematics

JF - Asia Pacific Journal of Mathematics

M1 - 35

ER -

APPROXIMATING FINITE FAMILIES OF RESOLVENTS OF CONVEX FUNCTIONS AND FIXED POINT PROBLEM OF DEMICONTRACTIVE TYPE MAPPINGS

Abstract

Keywords

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