Iterative approximation of common fixed points of generalized nonexpansive maps in convex metric spaces

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Original research article

Author(s):

Venkata Ravindranadh Babu Gutti^a, Satyanarayana Gedala^b

^aDepartment of Mathematics, Andhra University, Visakhapatnam – 530 003, India
^bPresent address: Department of Mathematics, Andhra University, Visakhapatnam – 530 003, India.
Permanent address: Department of Mathematics, Dr. Lankapalli Bullayya College, Visakhapatnam – 530 013, India

Advances in the Theory of Nonlinear Analysis and its Applications 4(2), 112-120.

Received: November 20, 2019

Accepted: April 24, 2020

Published: April 26, 2020

Abstract

We define SP-iteration procedure associated with three self maps T1; T2; T3 defined on a nonempty convex subset of a convex metric space X and prove -convergence of this iteration procedure to a common fixed point of T1; T2; T3 under the hypotheses that each Ti is either an -nonexpansive map or a Suzuki nonexpansive map in the setting of uniformly convex metric spaces. Also, we prove the strong convergence of this iteration procedure to a common fixed point of T1; T2; T3 under certain additional hypotheses namely either semicompact or condition (D).

Keywords: SP-iteration procedure; α-nonexpansive map; Suzuki nonexpansive map; common fixed point; Δ-convergence; strong convergence; uniformly convex metric space.

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APA Style

Satyanarayana, G., & Babu, G. V. R. Iterative approximation of common fixed points of generalized nonexpansive maps in convex metric spaces. Advances in the Theory of Nonlinear Analysis and its Application, 4(2), 112-120.