In recent years, extensive research has been conducted by eminent mathematicians and engineers whose results and proposed problems are presented in this new volume. It is addressed to graduate students, research mathematicians, physicists, and engineers. Individual contributions are devoted to topics of approximation theory, functional equations and inequalities, fixed point theory, numerical analysis, theory of wavelets, convex analysis, topology, operator theory, differential operators, fractional integral operators, integro-differential equations, ternary algebras, super and hyper relators, variational analysis, discrete mathematics, cryptography, and a variety of applications in interdisciplinary topics. Several of these domains have a strong connection with both theories and problems of linear and nonlinear optimization. The combination of results from various domains provides the reader with a solid, state-of-the-art interdisciplinary reference to theory and problems. Someof the works provide guidelines for further research and proposals for new directions and open problems with relevant discussions.

Autorentext

Nicholas J. Daras is the Dean and professor of mathematics at the Hellenic Military Academy. He has authored over 70 articles, as well as several books and edited volumes. Professor Daras has received a "Best paper in mathematics Award" by the Academy of Athens. Daras is also the supervisor of several doctoral, master, and diploma theses. Themistocles M. Rassias is professor of mathematics at the National Technical University of Athens. His research interests include nonlinear analysis, global analysis, approximation theory, functional analysis, functional equations, inequalities and their applications. Professor Rassias received his PhD in mathematics from the University of California, Berkeley in 1976; his thesis advisor was Stephen Smale and his academic advisor was Shiing-Shen Chern. In addition to his extensive list of journal publications, Professor Rassias has published as author or volume editor several books published with Springer. Th. M. Rassias has received several awards and is an active editorial board member of an array of journals in mathematical analysis and optimization. His publications have received a large number of citations, with h-index 47.

Inhalt

Rearrangements, L-superadditivity and Jensen type inequalities (Abramovich).- Approximate generalized Jensen mappings in 2-Banach spaces (Almahalebi).- The asymptotic expansion for a class of convergent sequences defined by integrals (Andrica).- Weak Pseudoprimality Associated with the Generalized Lucas Sequences (Rassias).- Shift Invariant Spaces of Periodic Functions: Characterization, Approximation and Applications (Atreas)..- Generalized intensity dependent multiphoton Jaynes-Cummings model (N. Merlemis).- Functional inequalities for multi-additive-quadratic-cubic mappings (Bodaghi).- Generalizations of Truncated M-Fractional Derivative Associated with (p, k)-Mittag-Leffler function With Classical Properties (Agarwal).- On Hyers-Ulam-Rassias stability of a Volterra-Hammerstein functional integral equation (Marian).- Analysis of Electroencephalography (EEG) signals based on the HaarWavelet transformation (P. Papadopoulos).- Perov type contractions (Karapinar).- On a logarithmic equation by primes (S. I. Dimitrov).- Hermite-Hadamard trapezoid and mid-point divergences (Dragomir).- Hermite-Hadamard type integral inequalities for perspective function (Dragomir).- On the maximum value of a multi-variable function (Hassani).- Image reconstruction for positron emission tomography based on Chebyshev polynomials (Kalantonis).- Approximation by Mixed Operators of Max-Product-Choquet Type (G. Gal).- On the Approximation of Extinction Time for the Discrete-Time Birth-Death Circuit Chains in Random Environments (Ganatsiou).- Some hyperstability results in Non Archimedean 2-Banach space for a $\sigma$-Jensen functional equation (Ghali).- A characterization for the validity of the Hermite-Hadamard inequality on a simplex (Guessab).- "On the stability of the triangular equilibrium points in the photogravitational R3BP with an oblate infinitesimal and triaxial primaries for the binary Lalande 21258 system" (E. Perdiou).- Normalized Symmetric Differential Operators in the Open Unit Disk (W. Ibrahim).- New Hermite-Hadamard inequalities concerning twice differentiable generalized $\psi$--convex mappings via conformable fractional integrals (Kashuri).- Some new fractional inequalities using n-polynomials s-type convexity (Kashuri).- Hyperstability of orthogonally 3-Lie homomorphism: an orthogonally fixed point approach (Keshavarz).- Some New Inequalities for Fractional Integral Operators (J. Kuang).- New Generalized Convexity and Their Applications (J. Kuang).- Ternary biderivations and ternary bihomorphisms in $C^*$-ternary algebras (Park).- Hyers-Ulam stability of an additive-quadratic functional equation (Park).- Orthogonal Dirichlet Polynomials (S. Lubinsky).- Generalizations and improvements of approximations of some analytic functions: a survey (MaleSevic).- Some classes of Meir-Keeler contractions (Gavruta).- Interpolation of the Zech's Logarithm - Explicit Forms (Rassias).- Numerical calculations on multi-photon processes in alkali metal vapors (Merlemis).- General preinvex functions and variational-like inequalities (A. Noor).- A variational formulation of network games with random utility functions (Raciti).- Fixed point theory in graph metric spaces (Petrusel).- Approximate Solution of Fredholm Integral and Integro-Differential Equations with Non-Separable Kernels (E. Providas).- Ordinary, Super and Hyper Relators Can Be Used To Treat the Various Generalized Open Sets in a Unified Way (Szaz).- Applications of Apostol-type numbers and polynomials: Approach to techniques of computation algorithms in approximation and interpolation functions (Simsek).- Spectra of signed graphs (Triantafillou).- Perturbed Geometric Contractions in Ordered Metric Spaces (Turinici).- On ${\mathrm{G}}^{(\sigma,{\textit{h}})}$-convexity of the functions and applications to Hermite-Hadamard's inequality (U. Awan).