A strong convergence theorem for $H(cdot , cdot)-phi-eta$-accretive mapping using proximal point algorithms

Poonam Mishra 1 * and Shailesh Dhar Diwan 2

doi:10.26637/MJM0702/0010

A strong convergence theorem for $H(cdot , cdot)-phi-eta$-accretive mapping using proximal point algorithms

Authors :

Poonam Mishra ^{1 *} and Shailesh Dhar Diwan ²

Author Address :

^1,2 Department of Applied Mathematics, Amity University Chhattisgarh, Raipur-492001, India.

*Corresponding author.

Abstract :

In this paper, we study an explicit iterative algorithm with resolvent technique using a more general $H(cdot,cdot)-phi-eta-$accretive operator in uniformly convex Banach space. Using suitable conditions,we show that the corresponding iterative sequence converges strongly to a common point of two sets.It also becomes solution to the related variational inequality. The main result generalizes many such results..

Keywords :

$H(cdot,cdot)-phi-eta-$Accretive operator,variational inequality, fixed point, weakly continuous duality mapping, contractive mapping, uniformly convex, resolvent, nonexpansive mapping.

DOI :

10.26637/MJM0702/0010

Article Info :

Received : January 19, 2019; Accepted : March 18, 2019.