Existence Theorems for Solvability of a Functional Equation Arising in Dynamic Programming by Deepmala

“…The paper deals with the existence, uniqueness, and iterative approximations of solutions for the functional equations arising in dynamic programming of multistage decision making processes in Banach spaces BC(S) and B(S) and complete metric space BB(S), respectively. …”
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Impulsive Problems for Fractional Differential Equations with Functional Boundary Value Conditions at Resonance by Bingzhi Sun, Shuqin Zhang, Weihua Jiang

“…Our results are based on the degree theory due to Mawhin, which requires appropriate Banach spaces and suitable projection schemes.…”
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Linear Sequences and Weighted Ergodic Theorems by Tanja Eisner

“…These weights are deterministic and come from orbits of certain bounded linear operators on Banach spaces. This extends the known results for nilsequences and return time sequences of the form for a measure preserving system and , avoiding in the latter case the problem of finding the full measure set of appropriate points .…”
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Fuzzy approximation of an additive functional equation by G. Zamani Eskandani, Ali Reza Zamani, H. Vaezi

“…In this paper, we investigate the generalized Hyers– Ulam– Rassias stability of the functional equation ∑i=1mf(mxi+∑j=1, j≠imxj)+f(∑i=1mxi)=2f(∑i=1mmxi) in fuzzy Banach spaces and some applications of our results in the stability of above mapping from a normed space to a Banach space will be exhibited.…”
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Admissibility for Nonuniform (μ,ν) Contraction and Dichotomy by Yongxin Jiang, Fang-fang Liao

“…A collection of admissible Banach spaces for any given nonuniform (μ,ν) contraction and dichotomy is provided.…”
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Certain Sequence Spaces over the Non-Newtonian Complex Field by Sebiha Tekin, Feyzi Başar

“…It is known from functional analysis that in classical calculus, the sets , , , and of all bounded, convergent, null and -absolutely summable sequences are Banach spaces with their natural norms and they are complete according to the metric reduced from their norm, where . …”
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Random Fixed Point Theorems of Random Comparable Operators and an Application by Jiandong Yin, Zhongdong Liu

“…We introduce the new concept of random comparable operators as a generalization of random monotone operators and prove several random fixed point theorems for such a class of operators in partially ordered Banach spaces. Part of the presented results generalize and extend some known results of random monotone operators. …”
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Convergence Behavior for Newton-Steffensen’s Method under -Condition of Second Derivative by Yonghui Ling, Xiubin Xu, Shaohua Yu

“…The present paper is concerned with the semilocal as well as the local convergence problems of Newton-Steffensen’s method to solve nonlinear operator equations in Banach spaces. Under the assumption that the second derivative of the operator satisfies -condition, the convergence criterion and convergence ball for Newton-Steffensen’s method are established.…”
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On Some Vector-Valued Inequalities of Gronwall Type by Dah-Chin Luor

“…In this paper we established some vector-valued inequalities of Gronwall type in ordered Banach spaces. Our results can be applied to investigate systems of real-valued Gronwall-type inequalities. …”
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The Existence Results of Solutions for System of Fractional Differential Equations with Integral Boundary Conditions by Dongxia Zan, Run Xu

“…By using a fixed point theorem in the Banach spaces, we get the existence of solutions for the fractional differential system. …”
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Implicit Approximation Scheme for the Solution of K-Positive Definite Operator Equation by Naseer Shahzad, Arif Rafiq, Habtu Zegeye

“…We construct an implicit sequence suitable for the approximation of solutions of K-positive definite operator equations in real Banach spaces. Furthermore, implicit error estimate is obtained and the convergence is shown to be faster in comparsion to the explicit error estimate obtained by Osilike and Udomene (2001).…”
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Strong Convergence Theorems for a Countable Family of Total Quasi-ϕ-Asymptotically Nonexpansive Nonself Mappings by Liang-cai Zhao, Shih-sen Chang

“…The purpose of this paper is to introduce a class of total quasi-ϕ-asymptotically nonexpansive-nonself mappings and to study the strong convergence under a limit condition only in the framework of Banach spaces. As an application, we utilize our results to study the approximation problem of solution to a system of equilibrium problems. …”
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On Nonlinear Neutral Fractional Integrodifferential Inclusions with Infinite Delay by Fang Li, Ti-Jun Xiao, Hong-Kun Xu

“…Of concern is a class of nonlinear neutral fractional integrodifferential inclusions with infinite delay in Banach spaces. A theorem about the existence of mild solutions to the fractional integrodifferential inclusions is obtained based on Martelli’s fixed point theorem. …”
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Existence and Iterative Algorithm of Solutions for a System of Generalized Nonlinear Mixed Variational-Like Inequalities by Yan-Mei Du

“…We introduce and study a system of generalized nonlinear mixed variational-like inequality problems (SGNMVLIPs) in Banach spaces. The auxiliary principle technique is applied to study the existence and iterative algorithm of solutions for the SGNMVLIP. …”
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Stability Theory for Nullity and Deficiency of Linear Relations by Silas Luliro Kito, Gerald Wanjala

“…Let A and B be two closed linear relations acting between two Banach spaces X and Y, and let λ be a complex number. …”
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Convergence of a New Modified Ishikawa Type Iteration for Common Fixed Points of Total Asymptotically Strict Pseudocontractive Semigroups by Yuanheng Wang, Chunjie Wang

“…Under the reduction of some conditions, both strong convergence and weak convergence of the iteration algorithm are proved in Banach spaces with new methods of proofs, respectively. …”
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Some extremal properties of section spaces of Banach bundles and their duals by D. A. Robbins

“…What happens if the Banach spaces in which the functions on X take their values vary over X? …”
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Best Possible Sufficient Conditions for Strong Law of Large Numbers for Multi-Indexed Orthogonal Random Elements by Kuo-Liang Su

“…It will be shown and induced that the d-dimensional indices in the Banach spaces version conditions ∑n(E‖Xn‖p/|nα|p)<∞ are sufficient to yield limmin1≤j≤d(nj)→∞(1/|nα|)∑k≤n∏j=1d(1−(kj−1)/nj)Xk=0 a.s. for arrays of James-type orthogonal random elements. …”
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Existence of Solution via Integral Inequality of Volterra-Fredholm Neutral Functional Integrodifferential Equations with Infinite Delay by Kishor D. Kucche, Machindra B. Dhakne

“…In this work we study existence results for mixed Volterra-Fredholm neutral functional integrodifferential equations with infinite delay in Banach spaces. To obtain a priori bounds of solutions required in Krasnoselski-Schaefer type fixed point theorem, we have used an integral inequality established by B. …”
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Quadruple Best Proximity Points with Applications to Functional and Integral Equations by Hasanen A. Hammad, Rashwan A. Rashwan, A. Nafea, Fahd Jarad

“…The validity of the theoretical results is also discussed in uniformly convex Banach spaces. Furthermore, some examples are given to strengthen our study. …”
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