In this paper, we establish the Caccioppoli estimates for the nonlinear differential equation − D ‾ (| D v | p − 2 D v) = λ | v | p − 2 v , 1 < p < ∞ , where D is the Dirac operator. Moreover, we obtain general weighted versions of the Caccioppoli-type inequalities for the Dirac operators. [ABSTRACT FROM AUTHOR]
Sagheer, D., Batul, S., Daim, A., Saghir, A., Aydi, H., Mansour, S., and Kallel, W.
Subjects
NONLINEAR operators, METRIC spaces, FIXED point theory
Abstract
The present research is aimed to analyze the existence of strict fixed points (SFPs) and fixed points of multivalued generalized contractions on the platform of controlled metric spaces (CMSs). Wardowski-type multivalued nonlinear operators have been introduced employing auxiliary functions, modifying a new contractive requirement form. Well-posedness of obtained fixed point results is also established. Moreover, data dependence result for fixed points is provided. Some supporting examples are also available for better perception. Many existing results in the literature are particular cases of the results established. [ABSTRACT FROM AUTHOR]
The article focuses on the introduction of neutrosophic continuity and neutrosophic boundedness, which is a fair extension of intuitionistic fuzzy continuity and intuitionistic fuzzy boundedness, respectively. The article further advances to illustrate the Fréchet derivative of nonlinear operators between neutrosophic normed spaces (NNS). Examples have been provided in compliance with the theory with the aid of some standard sequence spaces. [ABSTRACT FROM AUTHOR]