Krasnosel’skii-type fixed point theorems with applications to Volterra integral equations

By Nawab Hussain, M. Taoudi. Fixed Point Theory and Applications, 2013

57 citations recorded by the source corpus.

In this paper we present some fixed point results for the sum S+T of two mappings where S is a strict contraction and T is not necessarily weakly compact and satisfies a new condition formulated in terms of an axiomatic measure of weak noncompactness. Our fixed point results extend and improve several earlier results in the literature. In particular, our results encompass the analogues of Krasnosel’skii’s and Sadovskii’s fixed point theorems for sequentially weakly continuous mappings and a number of their generalizations. Finally, an application to integral equations is given to illustrate the usability of the obtained results. MSC:37C25, 40D05, 31B10.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/043a9190d9bf27dcd0440e77569a33bfbbeb0914

How researchers see this paper

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In Applied Mathematics

1. Peyman Salimi
2. Vahid Parvaneh
3. Nawab Hussain

In Astronomy and Astrophysics

1. Peyman Salimi
2. Nawab Hussain
3. Vahid Parvaneh

In Geometry and Topology

1. Peyman Salimi
2. Nawab Hussain
3. Vahid Parvaneh
4. Ljubomir Ciric
5. Stojan Radenovic

Citations in the corpus

• Fixed point results for various contractions in parametric and fuzzy b-metric spaces (2015, background): “Results under Geraghty-type conditions Fixed point theorems for monotone operators in ordered metric spaces are widely investigated and have found various applications in differential and integral equations (see [1, 15, 20, 24] and references therein).”