Abstract
We propose a modified version of the classical Cesáro means method endowed with the hybrid shrinking projection method to solve the split equilibrium and fixed point problems (SEFPP) in Hilbert spaces. One of the main reasons to equip the classical Cesáro means method with the shrinking projection method is to establish strong convergence results which are often required in infinite-dimensional functional spaces. As a consequence, the convergence analysis is carried out under mild conditions on the underlying shrinking Cesáro means method. We emphasize that the results accounted in this manuscript can be considered as an improvement and generalization of various existing exciting results in this field of study.
Highlights
Throughout the introduction, we first fix some necessary notions and concepts which will be required in the sequel
For a sequence {xn}∞ n=1 in H, the strong convergence characteristics of {xn}∞ n=1 is denoted as xn → x
In 1975, Baillon [2] established the nonlinear version of a classical ergodic theorem involving a nonexpansive self-mapping T defined over a closed bounded convex subset C of a Hilbert space H
Summary
Throughout the introduction, we first fix some necessary notions and concepts which will be required in the sequel. The inner product and the induced norm associated with a real Hilbert space H are denoted by ·, · and · := √ ·, · , respectively. For a sequence {xn}∞ n=1 in H, the strong convergence characteristics Weak convergence characteristics) of {xn}∞ n=1 is denoted as xn → x For a self-mapping T over a nonempty subset C of H, the set of all fixed points of the mapping T is denoted by F(T). Where {un} and {vn} are nonnegative sequences satisfying λn, μn −→ 0 and ξ : [0, ∞) → [0, ∞) satisfying ξ (0) = 0 and ξ (x) < ξ (y) for x < y
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