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2016•Nonlinear functional analysis and applicationsRequires access

WEAK CONVERGENCE THEOREMS FOR TOTAL ASYMPTOTICALLY NONEXPANSIVE NON-SELF MAPPINGS IN UNIFORMLY CONVEX BANACH SPACES

G. S. Saluja, Jong Kyu Kim

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Abstract

In this paper, we establish some weak convergence results of modified S -iteration process to converge to common fixed points for two total asymptotically nonexpansive non-self mappings in the framework of uniformly convex Banach spaces under the following conditions (i) the Banach space E satisfying Opial condition and (ii) the dual E^ ∗ of E has the Kadec-Klee property. Our results extend and improve the previous works from the current existing literature.

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What this paper is about

In this paper, we establish some weak convergence results of modified S -iteration process to converge to common fixed points for two total asymptotically nonexpansive non-self mappings in the framework of uniformly convex Banach spaces under the following conditions (i) the Banach space E satisfying Opial condition and (ii) the dual E^ ∗ of E has the Kadec-Klee property. Our results extend and improve the previous works from the current existing literature.

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Available abstract

In this paper, we establish some weak convergence results of modified S -iteration process to converge to common fixed points for two total asymptotically nonexpansive non-self mappings in the framework of uniformly convex Banach spaces under the following conditions (i) the Banach space E satisfying Opial condition and (ii) the dual E^ ∗ of E has the Kadec-Klee property. Our results extend and improve the previous works from the current existing literature.

Key concepts: Banach space, Mathematics, Regular polygon, Convergence (economics), Fixed point, Pure mathematics, Dual (grammatical number), Uniformly convex space

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WEAK CONVERGENCE THEOREMS FOR TOTAL ASYMPTOTICALLY NONEXPANSIVE NON-SELF MAPPINGS IN UNIFORMLY CONVEX BANACH SPACES — Research Paper | ScholarLens