Results on non local impulsive implicit Caputo-Hadamard fractional differential equations by K. Venkatachalam, M. Sathish Kumar, P. Jayakumar

“…The results for a new modeling integral boundary value problem using Caputo-Hadamard impulsive implicit fractional differential equations with Banach space are investigated, along with the existence and uniqueness of solutions. …”
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Functions of Bounded κφ-Variation in the Sense of Riesz-Korenblum by Mariela Castillo, Sergio Rivas, María Sanoja, Iván Zea

“…Moreover, we prove that the space generated by this class of functions is a Banach space with a given norm and we prove that the uniformly bounded composition operator satisfies Matkowski's weak condition.…”
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Noncoercive Perturbed Densely Defined Operators and Application to Parabolic Problems by Teffera M. Asfaw

“…Let X be a real locally uniformly convex reflexive separable Banach space with locally uniformly convex dual space X∗. …”
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Strong Convergence of Viscosity Iteration Methods for Nonexpansive Mappings by Jong Soo Jung

“…We propose a new viscosity iterative scheme for finding fixed points of nonexpansive mappings in a reflexive Banach space having a uniformly Gâteaux differentiable norm and satisfying that every weakly compact convex subset of the space has the fixed point property for nonexpansive mappings. …”
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On a Numerical Radius Preserving Onto Isometry on L(X) by Sun Kwang Kim

“…As a main result, when X is a complex Banach space having both uniform smoothness and uniform convexity, we show that an onto isometry T on L(X) is numerical radius preserving if and only if there exists a scalar cT of modulus 1 such that cTT is numerical range preserving. …”
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Fixed points of a certain class of mappings in spaces with uniformly normal structure by Jong Soo Jung, Balwant Singh Thakur, Daya Ram Sahu

“…A fixed point theorem is proved in a Banach space E which has uniformly normal structure for asymptotically regular mapping T satisfying: for each x,y in the domain and for n=1,2,⋯,‖Tnx−Tny‖≤an‖x−y‖+bn(‖x−Tnx‖+‖y−Tny‖)+cn(‖x−Tny‖+‖y−Tny‖), where an,bn,cn are nonnegative constants satisfying certain conditions. …”
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A New Exceptional Family of Elements and Solvability of General Order Complementarity Problems by Na Huang, Changfeng Ma

“…By using the concept of exceptional family, we propose a sufficient condition of a solution to general order complementarity problems (denoted by GOCP) in Banach space, which is weaker than that in Németh, 2010 (Theorem 3.1). …”
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A formula to calculate the spectral radius of a compact linear operator by Fernando Garibay Bonales, Rigoberto Vera Mendoza

“…There is a formula (Gelfand's formula) to find the spectral radius of a linear operator defined on a Banach space. That formula does not apply even in normed spaces which are not complete. …”
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Local solvability of a constrainedgradient system of total variation by C. E. Chidume, H. Zegeye

“…Suppose X is a real q-uniformly smooth Banach space and F,K:X→X with D(K)=F(X)=X are accretive maps. …”
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Asymptotic Behavior of Solution for Functional Evolution Equations with Stepanov Forcing Terms by Zhong-Hua Wu

“…Through the use of the measure theory, evolution family, “Acquistapace–Terreni” condition, and Hölder inequality, the core objective of this work is to seek to analyze whether there is unique μ-pseudo almost periodic solution to a functional evolution equation with Stepanov forcing terms in a Banach space. Certain adequate conditions are derived guaranteeing there is unique μ-pseudo almost periodic solution to the equation by Lipschitz condition and contraction mapping principle. …”
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Strong Convergence Theorems for Common Fixed Points of an Infinite Family of Asymptotically Nonexpansive Mappings by Yuanheng Wang

“…In the framework of a real Banach space with uniformly Gateaux differentiable norm, some new viscosity iterative sequences {xn} are introduced for an infinite family of asymptotically nonexpansive mappings Tii=1∞ in this paper. …”
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A Newton-type method and its application by V. Antony Vijesh, P. V. Subrahmanyam

“…We prove an existence and uniqueness theorem for solving the operator equation F(x)+G(x)=0, where F is a continuous and Gâteaux differentiable operator and the operator G satisfies Lipschitz condition on an open convex subset of a Banach space. As corollaries, a recent theorem of Argyros (2003) and the classical convergence theorem for modified Newton iterates are deduced. …”
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A note on uniformly dominated sets of summing operators by J. M. Delgado, C. Piñeiro

“…Let Y be a Banach space that has no finite cotype and p a real number satisfying 1≤p<∞. …”
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Coercive solvability of the nonlocal boundary value problem for parabolic differential equations by A. Ashyralyev, A. Hanalyev, P. E. Sobolevskii

“…The nonlocal boundary value problem, v′(t)+Av(t)=f(t)(0≤t≤1),v(0)=v(λ)+μ(0<λ≤1), in an arbitrary Banach space E with the strongly positive operator A, is considered. …”
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Estimation of Newly Established Iterative Scheme for Generalized Nonexpansive Mappings by Aftab Hussain, Nawab Hussain, Danish Ali

“…Finally, in a uniformly convex Banach space environment, we present weak as well as strong convergence theorems for Suzuki’s generalized nonexpansive maps. …”
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Orlicz Generalized Difference Sequence Space and the Linked Pre-Quasi Operator Ideal by Awad A. Bakery, OM Kalthum S. K. Mohamed

“…We investigate the sufficient conditions on this sequence space to be premodular Banach special space of sequences, and the constructed pre-quasi operator ideal becomes small, simple, closed, Banach space and has eigenvalues identical with its s-numbers.…”
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On strong laws of large numbers for arrays of rowwise independent random elements by Abolghassem Bozorgnia, Ronald Frank Patterson, Robert Lee Taylor

“…Let {Xnk} be an array of rowwise independent random elements in a separable Banach space of type r, 1≤r≤2. Complete convergence of n1/p∑k=1nXnk to 0, 0<p<r≤2 is obtained when sup1≤k≤nE ‖Xnk‖v=O(nα), α≥0 with v(1p−1r)>α+1. …”
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On some classes of almost periodic functions in abstract spaces by Dariusz Bugajewski, Gaston M. N'Guérékata

“…We deal with C(n)-almost periodic functions taking values in a Banach space. We give several properties of such functions, in particular, we investigate their behavior in view of differentiation as well as integration. …”
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A New Approach to the Approximation of Common Fixed Points of an Infinite Family of Relatively Quasinonexpansive Mappings with Applications by Wei-Qi Deng

“…A strong convergence theorem without the stronger assumptions of the AKTT condition and the ∗AKTT condition imposed on the involved mappings is established in the framework of Banach space. As application, an iterative solution to a system of equilibrium problems is studied. …”
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On calculation of the relative index of a fixed point in the nondegenerate case by A. V. Guminskaya, P. P. Zabreiko

“…Also the case of a nonlinear completely continuous operator A whose domain and image are situated in a closed convex set Q of a Banach space is considered. For this case, we formulate the rules for calculating the index of an arbitrary fixed point and the asymptotic index under the assumption that the corresponding linearizations exist and the operators of derivative do not have eigenvectors with eigenvalue 1 in some wedges.…”
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