A new implicit iteration process for approximating common fixed points of $\alpha$-demicontraction semigroup

Subject Areas : Fixed point theory

A. E.  Ofem ¹ (Department of Mathematics, University of Uyo, Uyo, Nigeria)
D. I.  Igbokwe ² (Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Nigeria)

Received: 2020-08-03 Accepted : 2021-02-26 Published : 2021-03-01

Keywords: fixed point, Banach space, strong convergence, $alpha$-demicontraction semigroup, implicit iteration process,

Abstract :

It is our purpose in this paper to introduce the concept of $\alpha$-demicontractive semigroup. Also, we construct a new implicit iterative scheme for approximating the common fixed points of $\alpha$-demicontractive semigroup. We prove strong convergence of our new iterative scheme to the common fixed points of $\alpha$-demicontractive semigroup in Banach spaces. Our result is an improvement and generalization of several well known results in the existing literature.

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