Some Fixed Point Theorems in Banach Spaces with Application to Semilinear Cauchy Problem

Toseef Ahmed Malik; Masood Ahmed Choudhary

doi:https://doi.org/10.14445/22315373/IJMTT-V55P504

International Journal of Mathematics Trends and Technology

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Volume 55 | Number 1 | Year 2018 | Article Id. IJMTT-V55P504 | DOI : https://doi.org/10.14445/22315373/IJMTT-V55P504

Some Fixed Point Theorems in Banach Spaces with Application to Semilinear Cauchy Problem

Toseef Ahmed Malik, Masood Ahmed Choudhary

Abstract

In this paper, we present a fixed point theorem for a new type of contractive mapping in Banach spaces. We also consider a semi-linear Cauchy problem in Banach spaces and prove the existence of its solution by using our fixed point theorem.

Keywords

Fixed points, non-expansive mapping, sequence of iterates, convex, uniformaly convex, compact, normal structure, diameter of a set, strongly continuous semigroup, mild solution, Cauchy problem.

References

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Citation :

Toseef Ahmed Malik, Masood Ahmed Choudhary, "Some Fixed Point Theorems in Banach Spaces with Application to Semilinear Cauchy Problem," International Journal of Mathematics Trends and Technology (IJMTT), vol. 55, no. 1, pp. 24-29, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V55P504