Fixed Point Theorems in Ordered Banach Spaces and Applications to Nonlinear Integral Equations

By Ravi P. Agarwal, Nawab Hussain, M. Taoudi. 2012

150 citations recorded by the source corpus.

We present some new common fixed point theorems for a pair of nonlinear mappings defined on an ordered Banach space. Our results extend several earlier works. An application is given to show the usefulness and the applicability of the obtained results.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/31ab06d1e8dfee9a15b8323c6834cf5c94ba1b3d

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In Applied Mathematics

In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

Best Proximity Point Results for Modified --Proximal Rational Contractions (2013, unknown): “Existence of best proximity and fixed points in partially ordered metric spaces has been considered recently by many authors (see, [7, 8, 11, 25, 33]).”
Common fixed point results for new Ciric-type rational multivalued F-contraction with an application (2018, background): “Fixed point theorems for operators in ordered metric spaces are widely investigated and have found various applications in differential and integral equations (see [4,18,24,28] and references therein).”
Fixed Points for -Graphic Contractions with Application to Integral Equations (2013, background): “Application to Existence of Solutions of Integral Equations Fixed point theorems for monotone operators in ordered metric spaces are widely investigated and have found various applications in differential and integral equations (see [30, 31] and references therein).”
Fixed point results for various contractions in parametric and fuzzy b-metric spaces (2015, background): “• Let x, y ∈ [2,∞) with x ≤ y, then, 2P(Tx, Ty, t) = 2t(14 + 1 4) 2 = 12 t ≤ t = 1 4 t(1 + 1) 2 ≤ 14 t(x+ y) 2 = 14P(x, y, t) ≤ 14M(x, y, t) = β(P(x, y, t))M(x, y, t) • Let x ∈ [0, 1) and y ∈ [1, 2) (clearly with x ≤ y), then, 2P(Tx, Ty, t) = 2t(18x 2 + 18y) 2 ≤ 2t(18x+ 1 8y) 2 = 1 32 t(x 2 + y2)2 ≤”