A Filippov-Type Existence Theorem for Some Nonlinear q-Difference Inclusions

2016 ◽  
pp. 71-77
Author(s):  
Aurelian Cernea
Keyword(s):  
Existence Theorem ◽  
Difference Inclusions ◽  
Filippov Type

scholarly journals Some New Extensions of Multivalued Contractions in a b-metric Space and Its Applications

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 12
Author(s):  
Reny George ◽  
Hemanth Kumar Pathak
Keyword(s):  
Fixed Point ◽  
Existence Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
The Other ◽  
Inclusion Problem ◽  
Integral Inclusion ◽  
New Variant ◽  
Multivalued Contractions ◽  
Filippov Type

The Hβ-Hausdorff–Pompeiu b-metric for β∈[0,1] is introduced as a new variant of the Hausdorff–Pompeiu b-metric H. Various types of multi-valued Hβ-contractions are introduced and fixed point theorems are proved for such contractions in a b-metric space. The multi-valued Nadler contraction, Czervik contraction, q-quasi contraction, Hardy Rogers contraction, weak quasi contraction and Ciric contraction existing in literature are all one or the other type of multi-valued Hβ-contraction but the converse is not necessarily true. Proper examples are given in support of our claim. As applications of our results, we have proved the existence of a unique multi-valued fractal of an iterated multifunction system defined on a b-metric space and an existence theorem of Filippov type for an integral inclusion problem by introducing a generalized norm on the space of selections of the multifunction.

scholarly journals An Existence Theorem for Fractionalq-Difference Inclusions with Nonlocal Substrip Type Boundary Conditions

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Ahmed Alsaedi ◽  
Sotiris K. Ntouyas ◽  
Bashir Ahmad
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Existence Theorem ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Nonlinear Alternative ◽  
Difference Inclusions ◽  
Contractive Maps ◽  
Type Boundary

By employing a nonlinear alternative for contractive maps, we investigate the existence of solutions for a boundary value problem of fractionalq-difference inclusions with nonlocal substrip type boundary conditions. The main result is illustrated with the aid of an example.

Existence results of mild solutions for impulsive fractional integro-differential evolution equations with infinite delay

2014 ◽  
Vol 17 (4) ◽  
Author(s):  
Shengli Xie
Keyword(s):  
Differential Equations ◽  
Differential Evolution ◽  
Existence Theorem ◽  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Infinite Delay ◽  
Mild Solutions ◽  
Existence Results ◽  
Order Case

AbstractIn this paper we prove the existence and uniqueness of mild solutions for impulsive fractional integro-differential evolution equations with infinite delay in Banach spaces. We generalize the existence theorem for integer order differential equations to the fractional order case. The results obtained here improve and generalize many known results.

Triharmonic Riemannian submersions from 3-dimensional space forms

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Tomoya Miura ◽  
Shun Maeta
Keyword(s):  
Existence Theorem ◽  
Space Form ◽  
Dimensional Space ◽  
Riemannian Submersion ◽  
Partial Answer ◽  
Riemannian Submersions ◽  
Space Forms ◽  
3 Dimensional

Abstract We show that any triharmonic Riemannian submersion from a 3-dimensional space form into a surface is harmonic. This is an affirmative partial answer to the submersion version of the generalized Chen conjecture. Moreover, a non-existence theorem for f -biharmonic Riemannian submersions is also presented.

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