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2016•Asian-European Journal of MathematicsRequires access

Weak and strong convergence theorems and a nonlinear ergodic theorem for N-generalized hybrid mappings

Sattar Alizadeh, Fridoun Moradlou

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Abstract

In this paper, assuming an appropriate condition, we prove that [Formula: see text]-generalized hybrid mappings are demiclosed in Hilbert spaces. Using this fact, we prove a weak convergence theorem of Ishikawa type for these nonlinear mappings. Also, a strong convergence theorem of Halpern–Ishikawa type and a nonlinear ergodic theorem for [Formula: see text]-generalized hybrid mappings have been proven in Hilbert spaces.

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What this paper is about

In this paper, assuming an appropriate condition, we prove that [Formula: see text]-generalized hybrid mappings are demiclosed in Hilbert spaces. Using this fact, we prove a weak convergence theorem of Ishikawa type for these nonlinear mappings. Also, a strong convergence theorem of Halpern–Ishikawa type and a nonlinear ergodic theorem for [Formula: see text]-generalized hybrid mappings have been proven in Hilbert spaces.

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Available abstract

In this paper, assuming an appropriate condition, we prove that [Formula: see text]-generalized hybrid mappings are demiclosed in Hilbert spaces. Using this fact, we prove a weak convergence theorem of Ishikawa type for these nonlinear mappings. Also, a strong convergence theorem of Halpern–Ishikawa type and a nonlinear ergodic theorem for [Formula: see text]-generalized hybrid mappings have been proven in Hilbert spaces.

Key concepts: Ergodic theory, Mathematics, Convergence (economics), Hilbert space, Nonlinear system, Pure mathematics, Type (biology), Discrete mathematics

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