We prove a Filippov type existence theorem for solutions of a higher order differential inclusion in Banach spaces with nonconvex valued right hand side by applying the contraction principle in the space of the derivatives of solutions instead of the space of solutions.

In this research paper, we prove some fixed point theorems for digital images. The papers main goal is to present another generalisation of the well-known Banach contraction principle fundamental concepts images are discussed, as an application theorem image compression and fractal compression. contractive type mappings in metric space introduced, uniqueness points proved.

In this manuscript, the existence, uniqueness, and stability of solutions to terminal value problem Riemann-Liouville fractional equations are established in variable exponent Lebesgue spaces L p ( . ) $$ {L}^{p(.)} We convert using generalized intervals piece-wise constant function. Further, Banach contraction principle is used, Ulam-Hyers-stability examined, finally, we construct an example.

The original approach of Hutchinson to fractals considers the defining equation as a fixed point problem, and then applies Banach Contraction Principle. To do this, Blaschke Completeness Theorem is essential. Avoiding Blaschke’s result, this note presents an alternative way via Kuratowski noncompactness measure. Moreover, our technique extends existence part Hutchinson’s condensing maps instead...

We give some generalizations of the Banach Contraction Principle to mappings on a metric space endowed with a graph. This extends and subsumes many recent results of other authors which were obtained for mappings on a partially ordered metric space. As an application, we present a theorem on the convergence of successive approximations for some linear operators on a Banach space. In particular,...

The subject of this paper is the existence, uniqueness and stability solutions for a new sequential Van der Pol–Duffing (VdPD) jerk fractional differential oscillator with Caputo–Hadamard derivatives. arguments are based upon Banach contraction principle, Krasnoselskii fixed-point theorem Ulam–Hyers stabilities. As applications, one illustrative example included to show applicability our results.

The existence of solutions for a class nonlinear neutral Hadamard-type fractional integro-differential equations with infinite delay is researched in this paper. By constructing an appropriate normed space and utilizing the Banach contraction principle, Krasnoselskii’s fixed point theorem, we obtain some sufficient conditions solutions. Finally, provide example to illustrate validity our main r...

Recently, Altun et al. [1] introduced the notion of p-proximal contractions and discussed about best proximity point results for this class mappings. Then Gabeleh Markin [4] showed that theorem proved by in follows from fixed theory. In short note, we show if contraction constant $$k<\frac{1}{3}$$ then existence celebrated Banach principle.

&lt;abstract&gt;&lt;p&gt;In this paper, we introduce the concept of an S-asymptotically $ \omega $-periodic process in distribution for first time, and by means successive approximation Banach contraction mapping principle, respectively, obtain sufficient conditions existence uniqueness solutions a class stochastic fractional functional differential equations.&lt;/p&gt;&lt;/abstract&gt;

Abstract The renorming technique allows one to apply the Banach Contraction Principle for maps which are not contractions with respect original metric. This method was invented by Bielecki and manifested in an extremely elegant proof of Global Existence Uniqueness Theorem ODEs. present paper provides further extensions applications Bielecki’s problems stemming from functional analysis theory eq...