Integrable solutions of a mixed type operator equation

We introduce iterative methods approximating fixed points for nonlinear operators defined on infinitedimensional spaces. The starting points are the Implicit and Explicit Midpoint Rules, which generate polygonal functions approximating a solution for an ordinary differential equation in finite-dimensional spaces. The purpose is to determine suitable conditions on the mapping and the underlying space, in order to get strong convergence of the generated sequence to a common solution of a fixed point problem and a variational inequality. The authors contributions appear in the papers [34], [60], [61].

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“…Let us recall the definition of ψ-expansive mapping (see papers [31], [32], [33], [54], [80] and references therein). • ψ(r) > 0 ∀r > 0;…”

Section: Definition 24 [18]mentioning

confidence: 99%

On some midpoint-type algorithms.

Marino

Zaccone

2018

Advances in the Theory of Nonlinear Analysis and Its Application

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“…Remark 1.7. The concept of ws-compact mappings arises naturally in the study of both integral and partial differential equations see [11][12][13][14][15][16][17][18][19] . Definition 1.8.…”

Section: Definition 13 Seementioning

confidence: 99%

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

Agarwal

Hussain

Taoudi

2012

Abstract and Applied Analysis

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“…The maps considered will be weakly compact and map weakly compact sets into relatively compact sets. These conditions are useful in applications namely in the study of existence of solution to differential and integral equations and inclusions with lack of compactness (see for example [13,14,21,22] and the references therein). Our fixed point theorems are obtained under Schauder, Leray-Schauder, Sadovskii and Furi-Pera boundary conditions.…”

Section: Introductionmentioning

confidence: 98%

Fixed Point Theorems for General Classes of Maps Acting on Topological Vector Spaces

Agarwal

O’Regan

Taoudi

2011

Asian-European J. Math.

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We present new fixed point theorems for multivalued U k c -admissible maps acting on locally convex topological vector spaces. The considered multivalued maps need not be compact. We merely assume that they are weakly compact and map weakly compact sets into relatively compact sets. Our fixed point results are obtained under Schauder, Leray-Schauder and Furi-Pera type conditions. These results are useful in applications and extend earlier works.

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Integrable solutions of a mixed type operator equation

Cited by 8 publications

References 14 publications

On some midpoint-type algorithms.

On some midpoint-type algorithms.

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

Fixed Point Theorems for General Classes of Maps Acting on Topological Vector Spaces

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