New existence theorems of positive solutions for singular boundary value problems.
New extended Weyl type theorems
New fixed point free nonexpansive maps on weakly compact, convex subsets of L¹[0,1]
We show that every subset of L¹[0,1] that contains the nontrivial intersection of an order interval and finitely many hyperplanes fails to have the fixed point property for nonexpansive mappings.
New fixed point theorems of mixed monotone operators and applications to singular boundary value problems on time scales.
New hybrid iterative schemes for an infinite family of nonexpansive mappings in Hilbert spaces.
New iteration methods for asymptotically nonexpansive mappings in uniformly smooth real Banach spaces
New iteration methods for pseudocontractive and accretive operators in arbitrary Banach spaces
New iterative approximation methods for a countable family of nonexpansive mappings in Banach spaces.
New iterative scheme for finite families of equilibrium, variational inequality, and fixed point problems in Banach spaces.
New iterative schemes for asymptotically quasi-nonexpansive mappings.
New perturbed iterations for a generalized class of strongly nonlinear operator inclusion problems in Banach spaces.
New Proof of Naimark's Theorem on the Existence of Nonpositive Invariant Subspaces for Commuting Families of Unitary Operators in Pontryagin Spaces.
New result of existence of periodic solution for a Hopfield neural networks with neutral time-varying delays.
New results for EP matrices in indefinite inner product spaces
In this paper we study -EP matrices, as a generalization of EP-matrices in indefinite inner product spaces, with respect to indefinite matrix product. We give some properties concerning EP and -EP matrices and find connection between them. Also, we present some results for reverse order law for Moore-Penrose inverse in indefinite setting. Finally, we deal with the star partial ordering and improve some results given in the “EP matrices in indefinite inner product spaces” (2012), by relaxing some...
New results on periodic solutions for a kind of Rayleigh equation
The paper deals with the existence of periodic solutions for a kind of non-autonomous time-delay Rayleigh equation. With the continuation theorem of the coincidence degree and a priori estimates, some new results on the existence of periodic solutions for this kind of Rayleigh equation are established.
New results on the positive solutions of nonlinear second-order differential systems.
New solutions of equations on
New spectral criteria for almost periodic solutions of evolution equations
We present a general spectral decomposition technique for bounded solutions to inhomogeneous linear periodic evolution equations of the form ẋ = A(t)x + f(t) (*), with f having precompact range, which is then applied to find new spectral criteria for the existence of almost periodic solutions with specific spectral properties in the resonant case where may intersect the spectrum of the monodromy operator P of (*) (here sp(f) denotes the Carleman spectrum of f). We show that if (*) has a bounded...
New sufficient convergence conditions for the secant method
We provide new sufficient conditions for the convergence of the secant method to a locally unique solution of a nonlinear equation in a Banach space. Our new idea uses “Lipschitz-type” and center-“Lipschitz-type” instead of just “Lipschitz-type” conditions on the divided difference of the operator involved. It turns out that this way our error bounds are more precise than the earlier ones and under our convergence hypotheses we can cover cases where the earlier conditions are violated.
New unifying convergence criteria for Newton-like methods
We present a local and a semilocal analysis for Newton-like methods in a Banach space. Our hypotheses on the operators involved are very general. It turns out that by choosing special cases for the "majorizing" functions we obtain all previous results in the literature, but not vice versa. Since our results give a deeper insight into the structure of the functions involved, we can obtain semilocal convergence under weaker conditions and in the case of local convergence a larger convergence radius....