What question did this study set out to answer?

To develop a cone b-metric fixed point framework for nonlinear and operator-valued Reich contractions that avoids limitations caused by the partial ordering of cone-valued distances.

August 20, 2026Fixed Point Theory and Algorithms for Sciences and EngineeringOpen Access

Nonlinear operator-valued Reich contractions via cone b-metric spaces

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TSThokchom Chhatrajit Singh

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Overview

Theoretical analysis establishes a nonlinear comparison principle for cone b-metric spaces, demonstrating fixed-point existence and uniqueness in Caputo fractional differential systems.

Key Points

To develop a cone b-metric fixed point framework for nonlinear and operator-valued Reich contractions that avoids limitations caused by the partial ordering of cone-valued distances.
Formulated a nonlinear comparison principle using an order-preserving mapping on cones satisfying an s-Picard summability condition, separating cone-order arguments from scalar reductions.
Applied nonlinear scalarization to recover maximum-type contractions and established conditions for positive operator-valued Reich contractions using spectral radius bounds.
Evaluated the framework on the positive cone of C[0,1] and applied it to analyze solutions of a Caputo fractional Volterra-type initial value problem.
Proved fixed point existence, uniqueness, constructive Picard convergence, Ulam–Hyers stability, and error estimates for operator-valued Reich contractions when the resolvent spectral radius satisfies r(R) < 1/s.
Demonstrated uniqueness of solutions to a Caputo fractional Volterra initial value problem without imposing customary smallness constraints on Lipschitz bounds, fractional horizons, or interval lengths.

Cite This Study

Thokchom Chhatrajit Singh (2026) studied this question.

synapsesocial.com/papers/6a86b5da8a91293e6a1cd64a https://doi.org/10.1186/s13663-026-00851-7

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August 20, 2026Fixed Point Theory and Algorithms for Sciences and EngineeringOpen Access

Nonlinear operator-valued Reich contractions via cone b-metric spaces

View Full Paper

Ask AI

Bookmark

Authors

TSThokchom Chhatrajit Singh

Discussion

Member takes

Overview

Theoretical analysis establishes a nonlinear comparison principle for cone b-metric spaces, demonstrating fixed-point existence and uniqueness in Caputo fractional differential systems.

Key Points

To develop a cone b-metric fixed point framework for nonlinear and operator-valued Reich contractions that avoids limitations caused by the partial ordering of cone-valued distances.
Formulated a nonlinear comparison principle using an order-preserving mapping on cones satisfying an s-Picard summability condition, separating cone-order arguments from scalar reductions.
Applied nonlinear scalarization to recover maximum-type contractions and established conditions for positive operator-valued Reich contractions using spectral radius bounds.
Evaluated the framework on the positive cone of C[0,1] and applied it to analyze solutions of a Caputo fractional Volterra-type initial value problem.
Proved fixed point existence, uniqueness, constructive Picard convergence, Ulam–Hyers stability, and error estimates for operator-valued Reich contractions when the resolvent spectral radius satisfies r(R) < 1/s.
Demonstrated uniqueness of solutions to a Caputo fractional Volterra initial value problem without imposing customary smallness constraints on Lipschitz bounds, fractional horizons, or interval lengths.

Cite This Study

Thokchom Chhatrajit Singh (2026) studied this question.

synapsesocial.com/papers/6a86b5da8a91293e6a1cd64a https://doi.org/10.1186/s13663-026-00851-7

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