Norm estimates are developed between the Bochner integral of a vector-valued function in Banach s... more Norm estimates are developed between the Bochner integral of a vector-valued function in Banach spaces having the Radon-Nikodym property and the convex combination of function values taken on a division of the interval [ , b] .
In this paper, we introduce a new class of Bregman generalized $\\alpha$-nonexpansive mappings in... more In this paper, we introduce a new class of Bregman generalized $\\alpha$-nonexpansive mappings in terms of Bregman distances, and investigate the Ishikawa and Noor iterations for these mappings. We establish weak and strong convergence theorems of Ishikawa and Noor iterative schemes for Bregman generalized $\\alpha$-nonexpansive mappings in Banach spaces. Furthermore, we propose an example of our generated mapping and some numerical examples which support our main theorem. Our results are new and improve the recent ones in the literature.
In this paper, we study the following operator equation: p∈Ax+Cx in a Banach space X, where A:D(A... more In this paper, we study the following operator equation: p∈Ax+Cx in a Banach space X, where A:D(A)⊆X→2X is an accretive mapping, C:D(C)⊆X→X is a nonlinear mapping and p∈X. Various existence results of solutions of nonlinear operator equations in Banach spaces are obtained under a countably condensing type condition.
Norm estimates are developed between the Bochner integral of a vector-valued function in Banach s... more Norm estimates are developed between the Bochner integral of a vector-valued function in Banach spaces having the Radon-Nikodym property and the convex combination of function values taken on a division of the interval [ , b] .
In this paper, we introduce a new class of Bregman generalized $\\alpha$-nonexpansive mappings in... more In this paper, we introduce a new class of Bregman generalized $\\alpha$-nonexpansive mappings in terms of Bregman distances, and investigate the Ishikawa and Noor iterations for these mappings. We establish weak and strong convergence theorems of Ishikawa and Noor iterative schemes for Bregman generalized $\\alpha$-nonexpansive mappings in Banach spaces. Furthermore, we propose an example of our generated mapping and some numerical examples which support our main theorem. Our results are new and improve the recent ones in the literature.
In this paper, we study the following operator equation: p∈Ax+Cx in a Banach space X, where A:D(A... more In this paper, we study the following operator equation: p∈Ax+Cx in a Banach space X, where A:D(A)⊆X→2X is an accretive mapping, C:D(C)⊆X→X is a nonlinear mapping and p∈X. Various existence results of solutions of nonlinear operator equations in Banach spaces are obtained under a countably condensing type condition.
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