Abstract
The aim of this paper is to introduce a modified viscosity iterative method to approximate a solution of the split variational inclusion problem and fixed point problem for a uniformly continuous multivalued total asymptotically strictly pseudocontractive mapping in C A T ( 0 ) spaces. A strong convergence theorem for the above problem is established and several important known results are deduced as corollaries to it. Furthermore, we solve a split Hammerstein integral inclusion problem and fixed point problem as an application to validate our result. It seems that our main result in the split variational inclusion problem is new in the setting of C A T ( 0 ) spaces.
Highlights
The space ( X, d) is said to be a geodesic space if any two points of X are joined by a geodesic segment
He established that a nonexpansive mapping defined on a bounded, closed and convex subset of a complete CAT (0) space has a fixed point
In this paper, motivated by (8), we present a modified viscosity algorithm sequence and prove strong convergence theorem for split variational inclusion problem and fixed point problem of a total asymptotically strictly pseudocontractive mapping in the setting of two different CAT (0) spaces
Summary
C is an isometry: d(c(t), c(s)) = |t − s| for all t, s ∈ [0, l ] In this case, c([0, l ]) is called a geodesic segment joining x and y which when unique is denoted by [ x, y]. The space ( X, d) is said to be a geodesic space if any two points of X are joined by a geodesic segment. A geodesic triangle ∆( x1 , x2 , x3 ) in a geodesic space ( X, d) consists of three points in X (the vertices of ∆) and a geodesic segment between each pair of vertices (the edges of ∆). A metric space X is said to be a CAT (0) space if it is geodesically connected and every geodesic triangle in X is at least as ’thin’ as its comparison triangle in the Euclidean plane. Riemannian manifold with non-positive sectional curvature, Pre-Hilbert spaces [2], Euclidean buildings [3], R-trees [18], and Hilbert ball with a hyperbolic metric [10,16]
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