Lebesgue Decomposition Theorem and Weak Radon-Nikodým Theorem for Generalized Fuzzy Number Measures by Cai-Li Zhou, Fu-Gui Shi

“…The Lebesgue type decomposition theorem and weak Radon-Nikodým theorem for fuzzy valued measures in separable Banach spaces are established.…”
Get full text

Quasi-incomplete regular LB-space by Jan Kucera, Kelly McKennon

“…A regular quasi-incomplete locally convex inductive limit of Banach spaces is constructed.…”
Get full text

Stability of Admissible Functions by Rabha W. Ibrahim

“…By using the concept of the weak subordination, we examine the stability (a class of analytic functions in the unit disk is said to be stable if it is closed under weak subordination) for a class of admissible functions in complex Banach spaces. The stability of analytic functions in the following classes is discussed: Bloch class, little Bloch class, hyperbolic little Bloch class, extend Bloch class (Qp), and Hilbert Hardy class (H2).…”
Get full text

Strong Convergence for Hybrid S-Iteration Scheme by Shin Min Kang, Arif Rafiq, Young Chel Kwun

“…We establish a strong convergence for the hybrid S-iterative scheme associated with nonexpansive and Lipschitz strongly pseudocontractive mappings in real Banach spaces.…”
Get full text

Existence of Mild Solutions to Nonlocal Fractional Cauchy Problems via Compactness by Rodrigo Ponce

“…We obtain characterizations of compactness for resolvent families of operators and as applications we study the existence of mild solutions to nonlocal Cauchy problems for fractional derivatives in Banach spaces. We discuss here simultaneously the Caputo and Riemann-Liouville fractional derivatives in the cases 0<α<1 and 1<α<2.…”
Get full text

Stability of Impulsive Differential Systems by Andrejs Reinfelds, Lelde Sermone

“…The asymptotic phase property and reduction principle for stability of a trivial solution is generalized to the case of the noninvertible impulsive differential equations in Banach spaces whose linear parts split into two parts and satisfy the condition of separation.…”
Get full text

Existence of Nontrivial Solutions for Unilaterally Asymptotically Linear Three-Point Boundary Value Problems by Hongyu Li

“…Using fixed point theorems in ordered Banach spaces with the lattice structure, we consider the existence of nontrivial solutions under the condition that the nonlinear term can change sign and study the existence of sign-changing solutions for some second order three-point boundary value problems. …”
Get full text

Fixed points of multivalued nonexpansive maps by T. Husain, Abdul Latif

“…Fixed point theorems for multivalued contractive-type and nonexpansive-type maps on complete metric spaces and on certain closed bounded convex subsets of Banach spaces have been proved. They extend some known results due to Browder, Husain and Tarafdar, Karlovitz and Kirk.…”
Get full text

p-Uniform Convexity and q-Uniform Smoothness of Absolute Normalized Norms on ℂ2 by Tomonari Suzuki

“…Using these, we present some examples of Banach spaces. One of them is a uniformly convex Banach space which is not p-uniformly convex.…”
Get full text

An Existence Result for Second-Order Impulsive Differential Equations with Nonlocal Conditions by Meili Li, Haiqiang Liu

“…The Leray-Schauder alternative is used to investigate the existence of solutions for second-order impulsive differential equations with nonlocal conditions in Banach spaces. The results improve some recent results.…”
Get full text

Fixed Points for Multivalued Mappings in Uniformly Convex Metric Spaces by A. Kaewcharoen, B. Panyanak

“…This extends a result of Lim (1980) in Banach spaces. All results of Dhompongsa et al. (2005) and Chaoha and Phon-on (2006) are also extended.…”
Get full text

On Regularized Quasi-Semigroups and Evolution Equations by M. Janfada

“…We introduce the notion of regularized quasi-semigroup of bounded linear operators on Banach spaces and its infinitesimal generator, as a generalization of regularized semigroups of operators. …”
Get full text

Existence of Solution to a Second-Order Boundary Value Problem via Noncompactness Measures by Wen-Xue Zhou, Jigen Peng

“…The existence and uniqueness of the solutions to the Dirichlet boundary value problem in the Banach spaces is discussed by using the fixed point theory of condensing mapping, doing precise computation of measure of noncompactness, and calculating the spectral radius of linear operator.…”
Get full text

Perturbations of normally solvable nonlinear operators, I by William O. Ray, Anita M. Walker

“…Let X and Y be Banach spaces and let ℱ and 𝒢 be Gateaux differentiable mappings from X to Y In this note we study when the operator ℱ+𝒢 is surjective for sufficiently small perturbations 𝒢 of a surjective operator ℱ The methods extend previous results in the area of normal solvability for nonlinear operators.…”
Get full text

Approximation structures and applications to evolution equations by Adrian Duma, Cristian Vladimirescu

“…We construct, via appropriate Browder-Petryshyn approximation schemes, approximative solutions for linear evolution equations in Banach spaces.…”
Get full text

Topological structure of solution sets of differential inclusions: the constrained case by Wojciech Kryszewski

“…We survey and announce some current results on the existence, the viability, and the topological structure of the viable solutions of differential equations and inclusion in Banach spaces under set constraints. Some new results concerning semilinear differential inclusions with state variables constrained to the so-called regular and strictly regular sets, together with their applications, are presented and discussed.…”
Get full text

Multiplicity of positive solutions to semilinear elliptic boundary value problems by Kenichiro Umezu

“…Our approach is based on super- and sub-solutions, and relies on the topological degree theory on the positive cones of ordered Banach spaces. A concrete example is also presented.…”
Get full text

Spaces of compact operators which are M-ideals in L(X,Y) by Chong-Man Cho

“…Suppose X and Y are reflexive Banach spaces. If K(X,Y), the space of all compact linear operaters from X to Y is an M-ideal in L(X,Y), the space of all bounded linear operators from X to Y, then the second dual space K(X,Y)** of K(X,Y) is isometrically isomorphic to L(X,Y).…”
Get full text

Positive Solutions for the Initial Value Problem of Fractional Evolution Equations by He Yang, Yue Liang

“…By using the fixed point theorems and the theory of analytic semigroup, we investigate the existence of positive mild solutions to the Cauchy problem of Caputo fractional evolution equations in Banach spaces. Some existence theorems are obtained under the case that the analytic semigroup is compact and noncompact, respectively. …”
Get full text

New Iterative Manner Involving Sunny Nonexpansive Retractions for Pseudocontractive Mappings by Yaqin Zheng, Jinwei Shi

“…In the present paper, we firstly propose a new iterative method involving sunny nonexpansive retractions for pseudocontractions in Banach spaces. Consequently, we show that the suggested algorithm converges strongly to a fixed point of the pseudocontractive mapping which also solves some variational inequality.…”
Get full text