Applied Functional Analysis and Its Applications

• Other Authors: Yao, Jen-Chih (Editor), Shahram Rezapour, Shahram (Editor)
• Format: Electronic Book Chapter
• Language: English
• Published: Basel, Switzerland MDPI - Multidisciplinary Digital Publishing Institute 2020
• Subjects: Research & information: general; Mathematics & science; vector variational-like inequalities; vector optimization problems; limiting (p,r)-α-(η,θ)-invexity; Lipschitz continuity; Fan-KKM theorem; set-valued optimization problems; higher-order weak adjacent epiderivatives; higher-order mond-weir type dual; benson proper efficiency; fractional calculus; ψ-fractional integrals; fractional differential equations; contraction; hybrid contractions; volterra fractional integral equations; fixed point; inertial-like subgradient-like extragradient method with line-search process; pseudomonotone variational inequality problem; asymptotically nonexpansive mapping; strictly pseudocontractive mapping; sequentially weak continuity; method with line-search process; pseudomonotone variational inequality; strictly pseudocontractive mappings; common fixed point; hyperspace; informal open sets; informal norms; null set; open balls; modified implicit iterative methods with perturbed mapping; pseudocontractive mapping; strongly pseudocontractive mapping; nonexpansive mapping; weakly continuous duality mapping; set optimization; set relations; nonlinear scalarizing functional; algebraic interior; vector closure; conjugate gradient method; steepest descent method; hybrid projection; shrinking projection; inertial Mann; strongly convergence; strict pseudo-contraction; variational inequality problem; inclusion problem; signal processing
• Online Access: DOAB: download the publication; DOAB: description of the publication

Applied functional analysis has an extensive history. In the last century, this field has often been used in physical sciences, such as wave and heat phenomena. In recent decades, with the development of nonlinear functional analysis, this field has been used to model a variety of engineering, medical, and computer sciences. Two of the most significant issues in this area are modeling and optimization. Thus, we consider some recently published works on fixed point, variational inequalities, and optimization problems. These works could lead readers to obtain new novelties and familiarize them with some applications of this area.